Inertial Repulsion from Quantum Geometry

TL;DR

This paper derives a novel inertial, repulsive interaction for Dirac particles in rotating frames, originating from geometric gauge symmetry and Berry phase effects, resulting in a Coulomb-like potential.

Contribution

It introduces a new geometric gauge theory framework to explain inertial repulsion effects in quantum particles within rotating frames.

Findings

Reveals a long-range repulsive interaction akin to Coulomb force.

Shows the inertial repulsion manifests as a $1/|r|^2$ potential.

Connects Berry phase geometry with inertial effects in quantum systems.

Abstract

We derive a repulsive, charge-dipole-like interaction for a Dirac particle in a rotating frame, arising from a geometric $U(1)$ gauge symmetry associated with the Berry phase. The Lagrangian of this system includes a non-inertial correction due to centrifugal field coupling. By imposing gauge symmetry and treating it as a full gauge theory, the Lagrangian is extended to include Berry connection and curvature terms. Upon integrating out the geometric gauge field, the effective action is obtained. This leads to the emergence of a repulsive, long-range effective interaction in the Lagrangian. Explicitly, in the non-inertial frame of the observer, the geometric gauge invariance effectively leads to a repulsive Coulomb-interaction in momentum space. In real space, the inertial repulsion manifests in a $1/\vert r\vert^{2}$ potential, which is symmetric about the origin of rotation and mirrors charge-dipole interaction.