Casimir Invariants of Lie Algebras with Applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F12%3A00196523" target="_blank" >RIV/68407700:21340/12:00196523 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Casimir Invariants of Lie Algebras with Applications

Popis výsledku v původním jazyce

Casimir invariants and generalized Casimir invariants play an important role in the theory of Lie algebras, in particular in the theory of their representations. They are also crucial for many applications of Lie algebras in modern physics. We introducethe notion of Casimir invariant as an element of the center of the universal enveloping algebra of the given Lie algebra and indicate its relevance for the theory of representations of Lie algebras, in particular for identification of irreducible representations. Next, we discuss some of its applications in quantum physics: in the theory of angular momentum; irreducible representations of the Poincare algebra, i.e. mathematical description of particles in quantum field theory; and Lie{algebraic computation of the hydrogen spectrum. It turns out that Casimir invariants also can be naturally identified with polynomial invariants of the coadjoint representation of the given Lie algebra. We call the nonpolynomial invariants of the coadjoint

Název v anglickém jazyce

Casimir Invariants of Lie Algebras with Applications

Popis výsledku anglicky

Casimir invariants and generalized Casimir invariants play an important role in the theory of Lie algebras, in particular in the theory of their representations. They are also crucial for many applications of Lie algebras in modern physics. We introducethe notion of Casimir invariant as an element of the center of the universal enveloping algebra of the given Lie algebra and indicate its relevance for the theory of representations of Lie algebras, in particular for identification of irreducible representations. Next, we discuss some of its applications in quantum physics: in the theory of angular momentum; irreducible representations of the Poincare algebra, i.e. mathematical description of particles in quantum field theory; and Lie{algebraic computation of the hydrogen spectrum. It turns out that Casimir invariants also can be naturally identified with polynomial invariants of the coadjoint representation of the given Lie algebra. We call the nonpolynomial invariants of the coadjoint

Druh

O - Ostatní výsledky

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů