Fermion quadrature bases for Wigner functionals

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.

29 pages, no figures, version that was accepted for publication

References in corpus (13)

• Quantum information with continuous variables
• Gaussian Quantum Information
• Continuous variable quantum information: Gaussian states and beyond
• Phase-space formulation of quantum mechanics and quantum state reconstruction for physical systems with Lie-group symmetries
• Quantum Mechanics in Phase Space
• Density Operators for Fermions
• Gaussian phase-space representations for fermions
• Coherent representation of fields and deformation quantization
• Combining spatio-temporal and particle-number degrees of freedom
• Wigner functional of fermionic fields
• Phase space methods for Majorana fermions
• Grassmann Phase Space Methods for Fermions. II. Field Theory
• Grassmann phase-space methods for fermions: uncovering classical probability structure