Time Parametrizations in Long-Range Interacting Bose-Einstein Condensates

TL;DR

This paper investigates time parametrizations in long-range interacting Bose-Einstein condensates, revealing a counterexample to time-reparametrization invariance in a specific quantum system, with implications for understanding gauge invariance.

Contribution

It provides a theoretical counterexample to time-reparametrization invariance in quantum systems with long-range interactions, focusing on Bose-Einstein condensates.

Findings

Counterexample to time-reparametrization invariance found

Proper-time translational invariance remains valid

Implications for gauge invariance in quantum systems

Abstract

Time-reparametrization invariance in general relativistic space-time does not allow us to single out a time in quantum mechanics in a mechanical way of measurement. Motivated by this problem, we examine this gauge invariance in the ground state of the quasi-stationary coarse-grained state of a long-range interacting closed system of identical or identified, macroscopic, and spatiotemporally inhomogeneous Bose-Einstein condensates in the thermodynamic and Newtonian limits. As a result, we find that it is a theoretical counterexample of this gauge invariance, except for proper-time translational invariance, at a coarse-grained level.