Tomographic probability representation for quantum fermion fields

• Published in: Journal of Russian laser research Vol. 30; no. 6; pp. 591 - 598
• Main Authors: Andreev, Vladimir A., Man’ko, Margarita A., Man’ko, Vladimir I., Cong Thanh, Nguyen, Hung Son, Nguyen, Zakharov, Stanislav D.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-11-2009
• Subjects: Fermions; Kernels; Lasers; Microwaves; Operators; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Projection; Representations; RF and Optical Engineering; Symbols; Symmetry; quantum tomography; star-product; scalar field; quantization
• ISSN: 1071-2836; 1573-8760
• DOI: 10.1007/s10946-009-9113-y

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto the probability distribution of discrete random variables (spin projections). The operators acting on the fermion states are described by fermionic tomographic symbols. The product of the operators acting on the fermion states is mapped onto the star-product of the fermionic symbols. The kernel of the star-product is obtained. The antisymmetry of the fermion states is formulated as a specific symmetry property of the tomographic joint probability distribution associated with the states.