Classical approximations of relativistic quantum physics

TL;DR

This paper explores a classical-quantum correspondence that offers nonrelativistic classical interpretations for relativistic quantum physics, enabling approximations of particle dynamics within quantum field theory without relying on the canonical formalism.

Contribution

It introduces a classical approximation method for relativistic quantum physics based on Schrödinger and Ehrenfest's correspondence, bypassing the need for Hermitian operator associations.

Findings

Classical-quantum correspondence applies without Hermitian operator assumptions.

Newtonian mechanics approximates nonrelativistic particle dynamics in quantum field theory.

Provides a new interpretative framework for relativistic quantum physics.

Abstract

A correspondence of classical to quantum physics studied by Schr\"{o}\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a $1/r$ potential provides approximations for the dynamics of nonrelativistic classical particle states within unconstrained quantum field theory (UQFT).