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Correspondence Rules for SU(1,1) Quasidistribution Functions and Quantum Dynamics in the Hyperbolic Phase Space
Miguel Baltazar1, Iván F Valtierra1, Andrei B Klimov1
1Departamento de Física, Universidad de Guadalajara, Guadalajara 44420, Mexico.
Entropy (Basel, Switzerland)
|November 11, 2022
Summary
We derived the differential form for SU(1,1) group generators acting on s-parametrized symbols. This enables evolution equations for phase-space functions and analysis of semiclassical limits in quantum systems.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Group theory
Background:
- The SU(1,1) group is crucial in quantum mechanics, particularly for systems with specific symmetries.
- Understanding the action of group generators on phase-space functions is key to analyzing quantum dynamics.
Purpose of the Study:
- To derive the explicit differential form for the action of SU(1,1) group generators on s-parametrized symbols.
- To obtain evolution equations for phase-space functions on the hyperboloid.
- To analyze the semiclassical limits of these quantum systems.
Main Methods:
- Derivation of differential forms for group generator actions.
- Formulation of evolution equations for phase-space functions.
- Analysis of quantum and semiclassical dynamics.
Main Results:
- Explicit differential form for SU(1,1) generators acting on s-parametrized symbols.
- Derivation of evolution equations for phase-space functions on the upper sheet of the two-sheet hyperboloid.
- Analysis of semiclassical limits.
Conclusions:
- The derived formalism provides a method to study quantum systems with SU(1,1) symmetry.
- The approach is applicable to both compact and non-compact Hamiltonians.
- The study offers insights into the quantum and semiclassical dynamics of these systems.
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