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Tomographic probability representation for quantum fermion fields |
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| Authors: | Vladimir A. Andreev Margarita A. Man’ko Vladimir I. Man’ko Nguyen Cong Thanh Nguyen Hung Son Stanislav D. Zakharov |
| Affiliation: | (1) Institute of Theoretical Physics, Masaryk University, 61137 Brno, Czech Republic;(2) Institute for Quantum Information Science, University of Calgary, Calgary, ABT2N 1N4, Canada;(3) Australian Centre of Excellence for Quantum Computer Technology, Macquarie University, Sydney, NSW 2109, Australia;(4) MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA |
| Abstract: | 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. |
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