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Representationer av SO(3) i C[x,y,z]
KTH, School of Engineering Sciences (SCI).
2019 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Representations of SO(3) in C[x,y,z] (English)
Abstract [sv]

Denna rapport kommer att redogöra en konkret undersökning av representationer av den speciella ortogonala gruppen, SO(3), en grupp med viktiga tillämpningar inom fysik. Mer specifikt kommer vi att studera en naturlig representation av SO(3) i rummet av polynom i tre variabler med komplexa koefficienter, C[x, y, z]. Vi kommer att se att alla irreducibla representationer av SO(3) dyker upp ur detta specialfall, samt presentera några följdsatser angående klotytefunktioner. Förberedande teori angående abstrakt algebra, linjär algebra, topologi och måtteori kommer även att redovisas.

Abstract [en]

This paper will present a concrete study of representations of the special orthogonal group, SO(3), a group of great importance in physics. Specifically, we will study a natural representation of SO(3) in the space of polynomials in three variables with complex coefficients, C[x, y, z]. We will find that this special case provides all irreducible representations of SO(3), and also present some corollaries about spherical harmonics. Some preparatory theory regarding abstract algebra, linear algebra, topology and measure theory will also be presented.

 

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:117
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-254713OAI: oai:DiVA.org:kth-254713DiVA, id: diva2:1334832
Supervisors
Examiners
Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-03Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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