Tomographic probability representation for quantum fermion fields

TL;DR

This paper introduces a tomographic probability framework for fermion fields, mapping fermionic states and operators onto probability distributions and symbols, enabling a probabilistic analysis of fermionic quantum states.

Contribution

It develops a novel tomographic representation for fermion fields, including the mapping of states and operators onto probability distributions and the formulation of star-products.

Findings

Fermionic states are represented by probability distributions of spin projections.

Operators are described by fermionic tomographic symbols.

Star-product kernel for fermionic operators is derived.

Abstract

Tomographic probability representation is introduced for fermion fields. The states of the fermions are mapped onto 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 star-product of the fermionic symbols. The kernel of the star-product is obtained. The antisymmetry of the fermion states is formulated as the specific symmetry property of the tomographic joint probability distribution associated with the states.