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Gauge Symmetry, Spontaneous Breaking of Gauge Symmetry: Philosophical Approach

This paper deals with the Berry phase, and the ontology of the electromagnetic vector potential. When the state of the system is gauge symmetric, the vector potential may be interpreted as a convenient tool of a mathematical formulation, with no ontological meaning. I argue that this interpretation is in difficulty because the vector potential depends linearly on the supercurrent in the superfluid state, which is a spontaneously broken gauge symmetry state, where particle number is not conserved. I suggest that when gauge symmetry is spontaneously broken, the vector potential becomes an emergent material object of nature. The revised version includes sections on scientific realism, and emergence, and new references on Noether's theorem, among others.