$SU(1,1)$ covariant $s$-parametrized maps

Abstract

We propose a practical recipe to compute the $s$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the $Q$ and $P$ symbols through the action of an operator invariant under the group. The particular case of the self-dual (Wigner) phase-space functions, defined on the upper sheet of the two-sheet hyperboloid (or, equivalently, inside the Poincaré disc) are analyzed.

arXiv comment18 pages, 3 figures. Comments welcome!

References in corpus (11)

• Phase space representation of quantum dynamics
• Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
• Wigner Functions for Arbitrary Quantum Systems
• Phase sensitivity at the Heisenberg limit in an SU(1,1) interferometer via parity detection
• Quantization of the canonically conjugate pair angle and orbital angular momentum
• SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
• Orbital angular momentum in phase space
• Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in Terms of the Group SO(1,2)
• Wigner functions for curved spaces I: On hyperboloids
• Wigner Functions for the Pair Angle and Orbital Angular Momentum
• Wigner function for SU(1,1)

Cited by in corpus (2)

• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Sub-Planck phase-space structure and sensitivity for SU(1,1) compass states