The Moyal-Lie Theory of Phase Space Quantum Mechanics

Abstract

A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an efficient tool in the quantum phase space transformation theory.

15 pages, no figures, to appear in J. Phys. A (2001)

Cited by in corpus (10)

• Noncommutativity, generalized uncertainty principle and FRW cosmology
• Non-commutative multi-dimensional cosmology
• Quantum symmetries and the Weyl-Wigner product of group representations
• Observables and Dynamics, Quantum to Classical, from a Relativity Symmetry and Noncommutative Geometric Perspective
• Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
• Stabilization of internal space in noncommutative multidimensional cosmology
• Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism
• $\hslash$-independent Universality of the Quantum-Classical Canonical Transformations
• Classical limit of the Kepler problem and the contraction of phase space
• Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps