Wigner functional of fermionic fields

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 the Wigner function has been extended to quantum fields, scalar and electromagnetic....

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Bibliographic Details
Published in:Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2013-03, Vol.87 (6), Article 065026
Main Author: Mrowczynski, Stanislaw
Format: Article
Language:English
Subjects:
Algebra
Conjugates
Cosmology
Equations of motion
Gravitation
Quantum mechanics
Radiation transport
Scalars
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Summary: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 the 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 form, is derived.
ISSN:1550-7998
1550-2368
DOI:10.1103/PhysRevD.87.065026