Polynomial Lie Algebras and Associated Pseudogroup Structures in Composite Quantum Models

Abstract

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.

8 pages, LATEX

References in corpus (2)

• An Algebraic Approach to Solving Evolution Problems in Some Nonlinear Quantum Models
• Polynomial Lie Algebras $s{l}_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings and Approximations

Cited by in corpus (4)

• The integrable multiboson systems and orthogonal polynomials
• Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations
• Classical and quantum Kummer shape algebras
• Symmetry as a source of hidden coherent structures in quantum physics: general outlook and examples