Bose-Einstein condensation and gauge symmetry breaking

TL;DR

This paper clarifies the fundamental link between Bose-Einstein condensation and spontaneous gauge symmetry breaking, emphasizing that the latter is both necessary and sufficient for the former, and discusses correct theoretical approaches.

Contribution

It establishes that spontaneous gauge symmetry breaking is essential for Bose-Einstein condensation and highlights the importance of proper statistical ensembles for consistent theoretical descriptions.

Findings

Gauge symmetry breaking is necessary and sufficient for Bose-Einstein condensation.

Incorrect calculations without symmetry breaking lead to paradoxes.

Proper ensembles ensure a self-consistent, paradox-free theory.

Abstract

The fundamental problem is analized, the relation between Bose-Einstein condensation and spontaneous gauge symmetry breaking. This relation is largerly misunderstood in physics community. Numerous articles and books contain the statement that, though gauge symmetry breaking helps for describing Bose-Einstein condensation, but the latter, in principle, does not require any symmetry breaking. This, however, is not correct. The analysis is based on the known mathematical theorems. But in order not to overcomplicate the presentation and to make it accessible to all readers, technical details are often omitted here. The emphasis is made on the following basic general facts: Spontaneous breaking of gauge symmetry is the necessary and sufficient condition for Bose-Einstein condensation. Condensate fluctuations, in thermodynamic limit, are negligible. Their catastrophic behavior can arise only as a result of incorrect calculations, when a Bose-condensed system is described without gauge symmetry breaking. It is crucially important to employ the representative statistical ensembles equipped with all conditions that are necessary for a unique and mathematically correct description of the given statistical system. Only then one is able to develop a self-consistent theory, free of paradoxes.