Making a wavefunctional representation of physical states congruent with the false vacuum hypothesis of Sidney Coleman

TL;DR

This paper develops a Gaussian wave functional for false vacuum decay in a driven sine-Gordon system, linking quantum decay, soliton separation, and the false vacuum hypothesis through a modified least action approach.

Contribution

It introduces a novel wave functional construction aligned with the false vacuum hypothesis using a modified least action integral in the sine-Gordon model.

Findings

Gaussian wave functional for false vacuum decay constructed

Soliton-anti soliton separation relates to the least action integral

Quadratic field contribution dominates the decay process

Abstract

We examine quantum decay of the false vacuum in the driven sine-Gordon system and show how both together permit construction of a Gaussian wave functional. This is due to changing a least action integral to be similar with respect to the WKB approximation. In addition we find that the soliton - anti soliton (S-S') separation distance obtained from the Bogomol'nyi inequality permits after rescaling a dominant quadratic field contribution to the least action integrand. This is from an initial scalar potential characterized by a tilted double well potential construction.