Scattering Relativity in Quantum Mechanics

TL;DR

This paper extends quantum field theory to include translations, deriving semiclassical equations of motion for charged particles in electromagnetic and gravitational fields, revealing new phase and momentum behaviors.

Contribution

It introduces a generalized translation framework in quantum mechanics that leads to semiclassical equations incorporating electromagnetic and gravitational effects.

Findings

Derived semiclassical equations of motion for charged particles.

Identified phase and momentum changes under translations.

Unified description of electromagnetism and gravitation in quantum context.

Abstract

By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the particle field translated along one displacement, particle states are translated along a possibly different displacement. Arbitrary phase results. And particle momentum, a spin (1/2,1/2) quantity, is allowed to change when field and states are translated. It is shown that a path of extreme phase obeys a semiclassical equation for force with derived terms that can describe electromagnetism and gravitation.