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  • 1.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Hallnäs, Martin
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models2014In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 104, no 7, p. 811-835Article in journal (Refereed)
    Abstract [en]

    We consider the relativistic generalization of the quantum A (N-1) Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh-Feigin-Veselov-Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

  • 2.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hynek, Mariusz
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Variational orthogonalizationManuscript (preprint) (Other academic)
    Abstract [en]

    We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.

  • 3.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Deformed Calogero-Sutherland model and fractional Quantum Hall effectManuscript (preprint) (Other academic)
    Abstract [en]

    The deformed Calogero-Sutherland (CS) model is a quantum integrable systemwith arbitrary numbers of two types of particles and reducing to the standard CSmodel in special cases. We show that a known collective field description of theCS model, which is based on conformal field theory (CFT), is actually a collectivefield description of the deformed CS model. This provides a natural application ofthe deformed CS model in Wen’s effective field theory of the fractional quantumHall effect (FQHE), with the two kinds of particles corresponding to electrons andquasi-hole excitations. In particular, we use known mathematical results aboutsuper Jack polynomials to obtain simple explicit formulas for the orthonormal CFTbasis proposed by van Elburg and Schoutens in the context of the FQHE.

  • 4.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Deformed Calogero-Sutherland model and fractional quantum Hall effect2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 1, article id 011902Article in journal (Refereed)
    Abstract [en]

    The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.

  • 5.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Series solutions of the non-stationary Heun equationManuscript (preprint) (Other academic)
    Abstract [en]

    We consider the non-stationary Heun equation, also known as quantum PainlevéVI, which has appeared in dierent works on quantum integrable models and conformaleld theory. We use a generalized kernel function identity to transform the problemto solve this equation into a dierential-dierence equation which, as we show, canbe solved by ecient recursive algorithms. We thus obtain series representations ofsolutions which provide elliptic generalizations of the Jacobi polynomials. These seriesreproduces, in a limiting case, a perturbative solution of the Heun equation due toTakemura, but our method is dierent in that we expand in non-conventional basisfunctions that allow us to obtain explicit formulas to all orders;

  • 6.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics.
    Series Solutions of the Non-Stationary Heun Equation2018In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 14, article id 011Article in journal (Refereed)
    Abstract [en]

    We consider the non-stationary Heun equation, also known as quantum Painleve VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term.

  • 7. Calogero, F.
    et al.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Goldfishing by gauge theory2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 8Article in journal (Refereed)
    Abstract [en]

    A new solvable many-body problem of goldfish type is identified and used to revisit the connection between two different approaches to solvable dynamical systems. An isochronous variant of this model is identified and investigated. Alternative versions of these models are presented. The behavior of the alternative isochronous model near its equilibrium configurations is investigated, and a remarkable Diophantine result, as well as related Diophantine conjectures, are thereby obtained.

  • 8.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Exact Solution of a 2D Interacting Fermion Model2012In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 314, no 1, p. 1-56Article in journal (Refereed)
    Abstract [en]

    We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.

  • 9.
    De Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Fermions in two dimensions, bosonization, and exactly solvable models2012In: International Journal of Modern Physics B, ISSN 0217-9792, Vol. 26, no 22, p. 1244005-Article, review/survey (Refereed)
    Abstract [en]

    We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square lattice. We review recent work on a specific relation between a variant of Mattis' model and such a lattice fermion system, as well as the exact solution of this model. The background for this work includes well-established results for one-dimensional systems and the high-T c problem. We also mention exactly solvable extensions of Mattis' model.

  • 10.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge invariance, correlated fermions, and Meissner effect in 2+1 dimensionsArticle in journal (Other academic)
    Abstract [en]

    We present a 2+1 dimensional quantum gauge theory model with correlated fermions that is exactly solvable by bosonization. This model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. We show that the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model. Moreover, the exact excitation spectrum of the model has two gapped and one gapless mode. We also compute the magnetic field induced by an external current and show that there is a Meissner effect. We find that the transverse photons have significant effects on the low-energy properties of the model even if the fermion-photon coupling is small.

  • 11.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge Invariance, Correlated Fermions, and Photon Mass in 2+1 Dimensions2014In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 154, no 3, p. 877-894Article in journal (Refereed)
    Abstract [en]

    We present a 2+1 dimensional quantum gauge theory with correlated fermions that is exactly solvable by bosonization. This model describes a system of Luttinger liquids propagating on two sets of equidistant lines forming a grid embedded in two dimensional continuum space; this system has two dimensional character due to density-density interactions and due to a coupling to dynamical photons propagating in the continuous embedding space. We argue that this model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. Our results include the following: after non-trivial renormalizations of the coupling parameters, the model remains well-defined in the quantum field theory limit as the grid of lines becomes a continuum; the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model; the exact excitation spectrum of the model has two gapped and one gapless mode.

  • 12.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Partial continuum limit of the 2D Hubbard modelArticle in journal (Other academic)
  • 13.
    de Woul, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Partially Gapped Fermions in 2D2010In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 139, no 6, p. 1033-1065Article in journal (Refereed)
    Abstract [en]

    We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.

  • 14. Farrokh, Atai
    et al.
    Hallnas, Martin
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators2019In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 51, no 2, p. 353-370Article in journal (Refereed)
    Abstract [en]

    We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).

  • 15. Frank, Rupert L.
    et al.
    Hainzl, Christian
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    The BCS critical temperature in a weak homogeneous magnetic field2019In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403Article in journal (Refereed)
    Abstract [en]

    We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

  • 16. Grosse, H.
    et al.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Chiral Schwinger models without gauge anomalies2000In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 587, no 03-jan, p. 568-584Article in journal (Refereed)
    Abstract [en]

    We find a large class of quantum gauge models with massless fermions where the coupling to the gauge fields is not chirally symmetric and which nevertheless do not suffer from gauge anomalies. To be specific we study two dimensional Abelian models in the Hamiltonian framework which can be constructed and solved by standard techniques. The general model describes Np photon fields and NF flavors of Dirac fermions with 2N(F)N(P) different coupling constants, i.e., the chiral component of each fermion can he coupled to the gauge fields differently We construct these models and find conditions so that no gauge anomaly appears. If these conditions hold it is possible to construct and solve the model explicitly, so that gauge- and Lorentz invariance are manifest.

  • 17. Grosse, Harald
    et al.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Paufler, Cornelius
    KTH, Superseded Departments, Physics.
    Exact solution of a 1D quantum many-body system with momentum-dependent interactions2004In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, no 16, p. 4579-4592Article in journal (Refereed)
    Abstract [en]

    We discuss a ID quantum many-body model of distinguishable particles with local, momentum-dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We show that the generalized model with distinguishable particles remains exactly solvable by the (coordinate) Bethe ansatz. Our solution provides a generalization of the above mentioned boson-fermion duality to particles with arbitrary exchange statistics characterized by any irreducible representation of the permutation group.

  • 18. Hallnaes, Martin
    et al.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A product formula for the eigenfunctions of a quartic oscillator2015In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 426, no 2, p. 1012-1025Article in journal (Refereed)
    Abstract [en]

    We consider the Schrodinger operator on the real line with an even quartic potential. Our main result is a product formula of the type psi(k)(x)psi(k)(y) = integral(R) psi(k)(z)K(x,y, z)dz for its eigenfunctions psi(k). The kernel function K is given explicitly in terms of the Airy function Ai(x), and it is positive for appropriate parameter values. As an application, we obtain a particular asymptotic expansion of the eigenfunctions psi(k).

  • 19. Hallnäs, Martin
    et al.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A Unified Construction of Generalized Classical Polynomials Associated with Operators of Calogero-Sutherland Type2010In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940, Vol. 31, no 3, p. 309-342Article in journal (Refereed)
    Abstract [en]

    In this paper we consider a large class of many-variable polynomials which contains generalizations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero-Sutherland type operators and their deformations recently found and studied by Chalykh, Feigin, Sergeev, and Veselov. We present a unified and explicit construction of all these polynomials.

  • 20.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 5Article in journal (Refereed)
    Abstract [en]

    We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system C-N. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.

  • 21.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Explicit formulae for the eigenfunctions of the N-body Calogero model2006In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, no 14, p. 3511-3533Article in journal (Refereed)
    Abstract [en]

    We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulae for its eigenfunctions, arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems.

  • 22.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Quantum Calogero-Sutherland type models and generalised classical polynomials2007Manuscript (preprint) (Other academic)
    Abstract [en]

    In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero-Sutherland type operators and their deformations recently found and studied by Chalykh, Feigin, Sergeev, and Veselov. We present a unified and explicit construction of all these polynomials.

  • 23.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 22, p. 4957-4974Article in journal (Refereed)
    Abstract [en]

    As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

  • 24.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    (3+1)-Dimensional Schwinger Terms and Non-commutative Geometry1994In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 338, p. 241-248Article in journal (Refereed)
  • 25.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A 2D Luttinger Model2010In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 141, no 1, p. 17-52Article in journal (Refereed)
    Abstract [en]

    A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is shown that the effective model thus obtained can be treated by exact bosonization methods. It is also discussed how this effective model can be used to obtain physical information about the corresponding lattice fermion system.

  • 26.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    A method to derive explicit formulas for an elliptic generalization of the Jack polynomials2006In: Jack, Hall-Littlewood and Macdonald Polynomials / [ed] Kuznetsov, VB; Sahi, S, PROVIDENCE, RI: AMER MATHEMATICAL SOC , 2006, Vol. 417, p. 257-270Conference paper (Refereed)
    Abstract [en]

    We review a method providing explicit formulas for the Jack polynomials. Our method is based on the relation of the Jack polynomials to the eigenfunctions of a well-known exactly solvable quantum many-body system of Calogero-Sutherland type. We also sketch a generalization of our method allowing to find the exact solution of the elliptic generalization of the Calogero-Sutherland model. We present the resulting explicit formulas for certain symmetric functions generalizing the Jack polynomials to the elliptic case.

  • 27.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    A superversion of quasifree second quantization. I. Charged particles1992In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 3, no 3, p. 1032-1046Article in journal (Refereed)
  • 28.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    A Two-Dimensional Analogue of the Luttinger Model2010In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 92, no 2, p. 109-124Article in journal (Refereed)
    Abstract [en]

    We present a fermion model that is, as we suggest, a natural 2D analogue of the Luttinger model. We derive this model as a partial continuum limit of a 2D spinless lattice fermion system with local interactions and away from half filling. In this derivation, we use certain approximations that we motivate by physical arguments. We also present mathematical results that allow an exact treatment of parts of the degrees of freedom of this model by bosonization, and we propose to treat the remaining degrees of freedom by mean field theory.

  • 29.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Algorithms to solve the (quantum) Sutherland model2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 9, p. 4148-4157Article in journal (Refereed)
    Abstract [en]

    We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of 1/sin(2)-type. The first algorithm is due to Sutherland and well-known; the second one is a limiting case of a novel algorithm to solve the elliptic generalization of the Sutherland model. These two algorithms are different in several details. We show that they are equivalent, i.e., they yield the same solution and are equally simple.

  • 30.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    An explicit solution of the (quantum) elliptic Calogero-Sutherland model2005In: SPT 2004: SYMMETRY AND PERTURBATION THEORY / [ed] Gaera, G; Prinari, B; RauchWojciechowshi, S, 2005, p. 159-174Conference paper (Refereed)
    Abstract [en]

    We present explicit formulas for the eigenvalues and eigenfunctions of the elliptic Calogero-Sutherland (eCS) model as formal power series to all orders in the nome of the elliptic functions, for arbitrary values of the (positive) coupling constant and particle number. Our solution gives explicit formulas for an elliptic deformation of the Jack polynomials.

  • 31.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Anyons and the elliptic Calogero-Sutherland model2000In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 54, no 4, p. 279-289Article in journal (Refereed)
    Abstract [en]

    We obtain a second quantization of the elliptic Calogero-Sutherland (eCS) model by constructing a quantum field theory model of anyons on a circle and at a finite temperature. This yields a remarkable identity involving anyon correlation functions and providing an algorithm for solving of the eCS model. The eigenfunctions obtained define an elliptic generalization of the Jack polynomials.

  • 32.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Bc2(T) of anisotropic systems: some explicit results1990In: Physica B: Physics of Condensed Matter, Vol. 65, p. 1061-1062Article in journal (Refereed)
  • 33.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Cocycles for Boson and Fermion Bogoliubov Transformations1994In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 35, p. 96-112Article in journal (Refereed)
  • 34.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Conformal field theory and the solution of the (quantum) elliptic Calogero-Sutherland system2005In: Noncommutative Geometry and Representation Theory in Mathematical Physics / [ed] Fuchs, J; Mickelsson, J; Rozenblioum, G; Stolin, A; Westerberg, A, Providence, Rhode Island: American Mathematical Society (AMS), 2005, p. 223-240Conference paper (Refereed)
    Abstract [en]

    We review the construction of a conformal field theory model which describes anyons on a circle and at finite temperature, including previously unpublished results. This anyon model is closely related to the quantum elliptic Calogero-Sutherland (eCS) system. We describe this relation and how it has led to an explicit construction of the eigenvalues and eigenfunctions of the eCS system.

  • 35.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Consistent axial-like gauge fixing on hypertori1994In: Modern Physics Letters A, ISSN 0217-7323, E-ISSN 1793-6632, Vol. 9, p. 2913-2926Article in journal (Refereed)
  • 36.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Descent equations of Yang-Mills anomalies in noncommutative geometry1997In: Journal of Geometry and Physics, ISSN 0393-0440, E-ISSN 1879-1662, p. 259-279Article in journal (Refereed)
  • 37.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Elementary Derivation of the Chiral Anomaly1996In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 6, p. 45-54Article in journal (Refereed)
  • 38.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Exactly solvable models for 2D interacting fermions2004In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, no 2, p. 407-423Article in journal (Refereed)
    Abstract [en]

    I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl(infinity) circle plus gl(infinity). There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.

  • 39.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Explicit Solution of the (Quantum) Elliptic Calogero-Sutherland Model2014In: Annales de l'Institute Henri Poincare. Physique theorique, ISSN 1424-0637, E-ISSN 1424-0661, Vol. 15, no 4, p. 755-791Article in journal (Refereed)
    Abstract [en]

    The elliptic Calogero-Sutherland model is a quantum many body system of identical particles moving on a circle and interacting via two body potentials proportional to the Weierstrass -function. It also provides a natural many-variable generalization of the Lam, equation. Explicit formulas for the eigenfunctions and eigenvalues of this model as infinite series are obtained, to all orders and for arbitrary particle numbers and coupling parameters. These eigenfunctions are an elliptic deformation of the Jack polynomials. The absolute convergence of these series is proved in special cases, including the two-particle (=Lam,) case for non-integer coupling parameters and sufficiently small elliptic deformation.

  • 40.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Fermion Current Algebras and Schwinger Terms in 3+1 Dimensions1994In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 162, p. 1-32Article in journal (Refereed)
  • 41.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Fermi-surface harmonics in the theory of the upper critical field1992In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, Vol. 46, no 14, p. 9104-Article in journal (Refereed)
  • 42.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories1999In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 563, p. 506-532Article in journal (Refereed)
  • 43.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Gauge Theories on a Cylinder1992In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 296, p. 117-120Article in journal (Refereed)
  • 44.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Gauge theory approach towards an explicit solution of the (classical) elliptic Calogero-Moser system2005In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, E-ISSN 1776-0852, Vol. 12, p. 423-439Article in journal (Refereed)
    Abstract [en]

    We discuss the relation of the trigonometric Calogero-Moser (CM) system to Yang-Mills gauge theories and its generalization to the elliptic case. This yields a linearization of the time evolution of the elliptic CM system and suggests two promising strategies for finding a fully explicit solution of this model. We also present a large class of integrable spin-particle systems generalizing the elliptic CM system.

  • 45.
    Langmann, Edwin
    KTH, Superseded Departments, Physics.
    Generalized Yang-Mills actions from Dirac operator determinants2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 11, p. 5238-5256Article in journal (Refereed)
    Abstract [en]

    We consider the quantum effective action of Dirac fermions on four-dimensional flat Euclidean space coupled to external vector- and axial Yang-Mills fields, i.e., the logarithm of the (regularized) determinant of a Dirac operator on flat R-4 twisted by generalized Yang-Mills fields. According to physics folklore, the logarithmic divergent part of this effective action in the pure vector case is proportional to the Yang-Mills action. We present a simple explicit computation proving this fact and extending it to the chiral case. We use an efficient computation method for quantum effective actions which is based on calculation rules for pseudo-differential operators and which yields an expansion of the logarithm of Dirac operators in local and quasi-gauge invariant polynomials of decreasing scaling dimension.

  • 46.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Gribov ambiguity and non-trivial vacuum structure of gauge theories on a cylinder1993In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 303, p. 303-307Article in journal (Refereed)
  • 47.
    Langmann, Edwin
    KTH, Superseded Departments, Physics. KTH, School of Engineering Sciences (SCI).
    Interacting fermions on non-commutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions2003In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 654, no 3, p. 404-426Article in journal (Refereed)
    Abstract [en]

    I present a novel class of exactly solvable quantum field theories. They describe non-relativistic fermions on even-dimensional flat space, coupled to a constant external magnetic field and a four point interaction defined with the Groenewold-Moyal star product. Using Hamiltonian quantization and a suitable regularization, I show that these models have a dynamical symmetry corresponding to gl(infinity) circle plus gl(infinity) at the special points Btheta = I and Btheta = -I, where B and theta are the matrices defining the magnetic field and the star product, respectively. I construct all eigenvalues and eigenstates, of the many-body Hamiltonian at these special points. I argue that this solution cannot be obtained by any mean-field theory, i.e., the models describe correlated fermions. I also mention other possible interpretations of these models in solid state physics.

  • 48.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Loop groups, anyons and the Calogero-Sutherland model1999In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 201, p. 1-34Article in journal (Refereed)
  • 49.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Physics, Mathematical Physics. KTH, School of Engineering Sciences (SCI), Physics, Condensed Matter Theory.
    Mean field approach to antiferromagnetic domains in the doped Hubbard model1997In: Physical Review B Condensed Matter, ISSN 0163-1829, E-ISSN 1095-3795, p. 9439-9451Article in journal (Refereed)
  • 50.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Non-commutative geometry and exactly solvable systems2008In: INTERNATIONAL CONFERENCE ON NONCOMMUTATIVE GEOMETRY AND PHYSICS  / [ed] Wallet, J.C., 2008, Vol. 103Conference paper (Refereed)
    Abstract [en]

    I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system is a prototype model which provides a generalization of mean field theory taking into account non-trivial correlations which are peculiar to boson systems in two space dimensions and relevant in condensed matter physics. The prologue and epilogue contain a few remarks to relate my main story to recent developments in non-commutative quantum field theory and an addendum to our previous work together with Szabo and Zarembo on this latter subject.

12 1 - 50 of 89
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