Classical Fermionic Dynamics

TL;DR

This paper develops a rigorous classical mechanics framework for fermionic systems, exploring their mathematical structure, transformations, and quantization methods, linking classical and quantum descriptions.

Contribution

It introduces a mathematically rigorous formulation of classical fermionic mechanics, including canonical transformations, observable algebra, and deformation quantization.

Findings

Defined the algebra of fermionic observables

Derived a formula for the fermionic Poisson bracket

Outlined the deformation quantization process for fermionic systems

Abstract

The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical transformations and the algebra of observables are defined and studied. A formula is given for the analog of the Poisson bracket. The quantization of the theory proceeds according to deformation quantization.