Tunneling Hamiltonian representation of false vacuum decay I. Comparison with the Bogomil'nyi inequality

TL;DR

This paper extends the tunneling Hamiltonian approach to quantum field theory, analyzing false vacuum decay in the driven Sine-Gordon system and comparing it with the Bogomil'nyi inequality, demonstrating consistency and novel wave functional representations.

Contribution

It introduces a generalized tunneling Hamiltonian formalism for quantum fields and compares it with the Bogomil'nyi inequality in false vacuum decay analysis.

Findings

The formalism aligns with the false vacuum decay process.

Wave functionals constructed via the Bogomil'nyi inequality match decay dynamics.

The approach provides a new perspective on soliton-anti soliton nucleation.

Abstract

The tunneling Hamiltonian has proven to be a useful method in many body physics to treat particle tunneling between different states represented as wave functions. Here we present a generalization of the tunneling Hamiltonian to quantum field theory, in which tunneling between states represented as wave functionals of a scalar quantum field is considered. We examine quantum decay of the false vacuum in the driven Sine-Gordon system, and show it is consistent with the tunneling formalism derived here and matches up with the soliton - anti soliton separation obtained from the Bogomil'nyi inequality. This inequality permits construction of a gaussian wave functional representation of soliton - anti soliton nucleated states and is consistent with respect to the false vacuum hypothesis