# Generalized SU(2) covariant Wigner functions and some of their applications

@article{Klimov2017GeneralizedSC, title={Generalized SU(2) covariant Wigner functions and some of their applications}, author={Andrei B. Klimov and Jos{\'e} Luis Romero and Hubert de Guise}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2017}, volume={50} }

We survey some applications of SU(2) covariant maps to the phase space quantum mechanics of systems with fixed or variable spin. A generalization to SU(3) symmetry is also briefly discussed in framework of the axiomatic Stratonovich–Weyl formulation.

## 35 Citations

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

- Mathematics
- 2020

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…

### Correspondence rules for Wigner functions over SU(3)/U(2)

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2019

A form of the so-called correspondence rules, which provide a differential form of of the product and when is an generator for the Wigner map are presented.

### Twisted Fourier analysis and pseudo-probability distributions

- Mathematics
- 2020

We use a noncommutative generalization of Fourier analysis to define a broad class of pseudo-probability representations, which includes the known bosonic and discrete Wigner functions. We…

### On the discrete Wigner function for SU(N)

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and…

### On the Moduli Space of Wigner Quasiprobability Distributions for N-Dimensional Quantum Systems

- Mathematics, PhysicsJournal of Mathematical Sciences
- 2019

A mapping between operators on the Hilbert space of an N-dimensional quantum system and Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner…

### SU(3) Clebsch–Gordan coefficients and some of their symmetries

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

We discuss the construction and symmetries of Clebsch–Gordan coefficients arising from basis states constructed as triple tensor products of two-dimensional harmonic oscillator states. Because of the…

### Quasiprobability currents on the sphere

- PhysicsPhysical Review A
- 2020

We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents…

### On Families of Wigner Functions for N-Level Quantum Systems

- PhysicsSymmetry
- 2021

It is shown that among all possible Stratonovich–Weyl kernels for a N=(2j+1)-level system, one can always identify the representative that realizes the so-called SU(2)-symmetric spin-j symbol correspondence.

### On symbol correspondences for quark systems

- Mathematics
- 2022

. We present the characterization of symbol correspondences for me- chanical systems that are symmetric under SU (3), which we refer to as quark systems . The quantum systems are the unitary…

### Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane

- MathematicsEntropy
- 2018

It is shown that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

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