Gauge Invariance, Cauchy Problem, Indeterminism, and Symmetry Breaking

Abstract

The concepts in the title refer to properties of physical theories (which are given, in this paper, a model-theoretic formulation and appropriate idealizations) and this paper investigates their nature and relations. The first three concepts, especially gauge invariance and indeterminism, have been widely discussed in connection to spacetime theories and the hole argument. Since the gauge invariance principle is at the crux of the issue, this paper aims at clarifying the nature of gauge invariance (either in general or as general covariance). I first explore the following chain of relations: gauge invariance => the conservation laws => the Cauchy problem => indeterminism. Then I discuss gauge invariance in light of our understanding of the above relations and the possibility of spontaneous symmetry breaking.