Physical mechanisms generating spontaneous symmetry breaking and a hierarchy of scales

TL;DR

This paper explores the physical mechanisms behind spontaneous symmetry breaking in a scalar field theory, revealing a hierarchy of scales and implications for gravity and cosmology.

Contribution

It introduces a physical perspective on phase transitions in lambda Phi^4 theory, highlighting the role of long-range interactions and the hierarchy of scales in symmetry breaking.

Findings

Spontaneous symmetry breaking involves a Bose-Einstein condensate of phions.

The phase transition occurs before the phion mass becomes negative.

A hierarchy of length scales naturally emerges in the theory.

Abstract

We discuss the phase transition in 3+1 dimensional lambda Phi^4 theory from a very physical perspective. The particles of the symmetric phase (`phions') interact via a hard-core repulsion and an induced, long-range -1/r^3 attraction. If the phion mass is sufficiently small, the lowest-energy state is not the `empty' state with no phions, but is a state with a non-zero density of phions Bose-Einstein condensed in the zero-momentum mode. The condensate corresponds to the spontaneous-symmetry-breaking vacuum with <Phi> neq 0 and its excitations ("phonons" in atomic-physics language) correspond to Higgs particles. The phase transition happens when the phion's physical mass m is still positive; it does not wait until m^2 passes through zero and becomes negative. However, at and near the phase transition, m is much, much less than the Higgs mass M_h. This interesting physics coexists with `triviality;' all scattering amplitudes vanish in the continuum limit, but the vacuum condensate becomes infinitely dense. The ratio m/M_h, which goes to zero in the continuum limit, can be viewed as a measure of non-locality in the regularized theory. An intricate hierarchy of length scales naturally arises. We speculate about the possible implications of these ideas for gravity and inflation.