Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models

Details Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models

1997-04-09

arxiv.org/abs/quant-ph/9704018v1

Physics

Quantum Physics

8 pages, LATEX

Scientific paper

10.1016/S0034-4877(97)85920-4

Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure functions in commutation relations, are related to pseudogroup structures $\exp V, V\in g_{pd}$ and describe dynamic symmetry of models under study. Physical applications of algebras $g_{pd}$ in quantum optics and in composite field theories are briefly discussed.

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