Local phase invariance of the free-particle Schrodinger equation in momentum space

TL;DR

This paper explores the local phase invariance of the free-particle Schrödinger equation in momentum space, revealing gauge structures related to helicity and spin, and predicts potential effects on energy level quantization.

Contribution

It introduces a gauge-theoretic framework in momentum space for free particles, linking phase invariance to helicity and spin, and derives an effective Schrödinger equation with potential screening effects.

Findings

Gauge structure in momentum space linked to helicity and spin

Derived effective Schrödinger equation for helicity-carrying particles

Predicted screening effect influencing energy level splittings

Abstract

The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure over the momentum space of the particle is interpreted in terms of helicity and spin carried by the particle. As a by-product an effective one-particle Schr\"odinger equation of motion for the helicity-carrying particle in external potential field is derived. An effect of screening of the external potential is predicted, that can affect quantization and splittings of energy levels of the particle.