Coherent and squeezed condensates in massless $\lambda \varphi^4$ theory

TL;DR

This paper extends the Bogoliubov model to massless $ ext{ extbackslash lambda} ext{ extbackslash phi}^4$ theory, showing that a coherent vacuum leads to spontaneous symmetry breaking with lower energy than previous methods, while squeezed vacua do not.

Contribution

It demonstrates that spontaneous symmetry breaking in massless $ ext{ extbackslash lambda} ext{ extbackslash phi}^4$ theory occurs via a coherent vacuum, providing a lower energy state than the Coleman-Weinberg approach.

Findings

Coherent condensates lead to spontaneous symmetry breaking with lower vacuum energy.

Squeezed condensates do not produce spontaneous symmetry breaking in this theory.

The vacuum energy density is lower than that obtained by Coleman and Weinberg.

Abstract

Generalizing the Bogoliubov model of a weakly non-ideal Bose gas to massless $\lambda\varphi^4$ theory we show that spontaneous breaking of symmetry occurs due to condensation in a coherent vacuum % which is energetically favoured compared to the perturbative one. and leads to a vacuum energy density which is lower than that obtained by Coleman and Weinberg using the one-loop effective potential method. We discuss the alternative of a squeezed condensate and find that for the massless $\lambda \varphi^4$ theory spontaneous symmetry breaking to a squeezed vacuum does not occur.