Wigner functional of fermionic fields

Abstract

The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been extended to quantum fields, scalar and electromagnetic. Then, one deals with the Wigner functional which gives a distribution of field and its conjugate momentum. We introduce here the Wigner functional of fermionic fields of the values in a Grassmann algebra. Properties of the functional are discussed and its equation of motion, which is of the Liouville's form, is derived.

9 pages, no figures

References in corpus (4)

• Density Operators for Fermions
• Wigner Functional Approach to Quantum Field Dynamics
• Schrodinger representation for the polarized Gowdy model
• Infrared degrees of freedom of Yang-Mills theory in the Schroedinger representation

Cited by in corpus (7)

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• Constructing phase space distributions with internal symmetries
• Semiclassical approach to Dynamics of Interacting Fermions
• Grassmann phase-space methods for fermions: uncovering classical probability structure
• Wigner distributions in Rindler spacetime and nonvacuum Minkowski states
• Wigner functional theory for quantum optics
• Fermion quadrature bases for Wigner functionals