5D thermal field theory, Einstein field equations and spontaneous symmetry breaking

Abstract

It has been shown previously, that the spatial thermal variation of a thermal medium can be recast as a variation in the Euclidean metric. It is now extended to temporal variations in temperature, for a non-relativistic thermal bath, which remains in local thermal equilibrium. This is achieved by examining the thermal field theory in a five-dimensional (5D) space–time–temperature. The bulk thermodynamic quantity, namely the energy density, is calculated for a neutral scalar field with a time-dependent Hamiltonian. Furthermore, the concept of recasting thermal variations as a variation in the metric is extended to thermal systems in a gravitational field. The Einstein field equations, in the 5D space–time–temperature, is determined. It is shown that, if the scalar Lagrangian is non-minimally coupled with gravity, the resulting Ricci scalar can lead to spontaneous symmetry breaking, leading to the Higgs mechanism. In essence, the asymmetry in the distribution of temperature in space–time can translate to spontaneous symmetry breaking of particle fields, in a very strong gravitational field.