Fermion quadrature bases for Wigner functionals

TL;DR

This paper develops a Grassmann functional phase space framework for fermionic Wigner functionals, introducing new fermionic quadrature bases analogous to bosonic ones, and demonstrates their application to a two-level fermion system.

Contribution

It introduces a novel fermionic quadrature basis using spin transformations, enabling the definition of Wigner functionals similar to bosonic systems.

Findings

Orthogonal fermionic bases constructed with spin transformations

Wigner functionals defined in a fermionic phase space

Application demonstrated on a two-level fermion system

Abstract

A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use operators that are defined with relative spin transformations between the ladder operators. The eigenstates of these operators are shown to provide orthogonal bases, provided that the dual space is defined with the incorporation of a spin transformation. These bases then serve as quadrature bases in terms of which Wigner functionals are defined in a way equivalent to the bosonic case. As an application, we consider a two-level fermion system.