Casimir Invariants of Lie Algebras with Applications

Result code in IS VaVaI
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Casimir Invariants of Lie Algebras with Applications
Original language description
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
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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