Assumption of nonvanishingness of vacuum expectation of the scalar field for spontaneous symmetry breaking is superfluous

TL;DR

This paper argues that the common assumption of a nonzero vacuum expectation value for scalar fields in spontaneous symmetry breaking is unnecessary, as the phenomenon can be explained by particle number considerations.

Contribution

It demonstrates that spontaneous symmetry breaking does not require a nonvanishing vacuum expectation value, challenging a standard assumption in quantum field theory.

Findings

Spontaneous symmetry breaking can occur without a nonzero vacuum expectation value.

The vacuum corresponds to a nonzero particle number, not necessarily a nonzero field expectation.

The assumption of nonvanishing vacuum expectation is superfluous for explaining symmetry breaking.

Abstract

For spontaneous breaking of global or gauge symmetry, it is superfluous to assume that the vacuum expectation value of the scalar field manifesting the symmetry is nonvanishing. The vacuum with spontaneous symmetry breaking simply corresponds to nonzero number of particles of one or more components of the real scalar field.