Non-Grassmann "Classicization" of Fermion Dynamics

TL;DR

This paper introduces a symmetric Poisson bracket in classical phase space that mirrors fermionic anticommutation, leading to Schrödinger-type equations and excluding certain older fermion theories.

Contribution

It presents a novel symmetric Poisson bracket framework that reproduces fermionic algebraic identities in classical phase space, connecting classical and quantum fermion dynamics.

Findings

Symmetric Poisson bracket satisfies fermionic algebraic identities.

Generalized Hamilton's equations are of Schrödinger type.

Excludes four-Fermion beta decay theory.

Abstract

A carefully motivated symmetric variant of the Poisson bracket in ordinary (not Grassmann) phase space variables is shown to satisfy identities which are in algebraic correspondence with the anticommutation postulates for quantized Fermion systems. "Symplecticity" in terms of this symmetric Poisson bracket implies generalized Hamilton's equations that can only be of Schroedinger type (e.g., the Dirac equation but not the Klein-Gordon or Maxwell equations). This restriction also excludes the old "four-Fermion" theory of beta decay.