Deformation quantization for systems with second-class constraints in deformed fermionic phase space

TL;DR

This paper develops a deformation quantization approach for fermionic systems with second-class constraints, deriving energy levels, Wigner functions, and entanglement entropy in the deformed phase space.

Contribution

It introduces a star product based on the Dirac bracket for quantizing constrained fermionic systems, extending deformation quantization methods.

Findings

Derived energy levels for the constrained oscillator system

Computed Wigner functions in the deformed fermionic phase space

Analyzed entanglement entropy induced by phase space deformation

Abstract

In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hbar$ is proportional to the Dirac bracket. In this way an oscillator system in a deformed fermionic phase space is analyzed and the corresponding energy level and Wigner functions are evaluated according to scheme of deformation quantization. We also study the entanglement entropy induced by the deformation of the fermionic phase space.