A quantum energy inequality in the Sine--Gordon model

TL;DR

This paper proves a quantum energy inequality for the stress tensor in the massless Sine-Gordon model, establishing a state-independent lower bound on energy density along a worldline.

Contribution

It extends techniques from free theories to the interacting Sine-Gordon model, demonstrating convergence of the stress tensor series and a universal energy bound.

Findings

Proven convergence of the renormalised stress tensor series.

Established a state-independent lower bound on energy density.

Extended free theory techniques to an interacting quantum field theory.

Abstract

We consider the stress tensor in the massless Sine--Gordon model in the finite regime $\beta^2 < 4 \pi$ of the theory. We prove convergence of the renormalised perturbative series for the interacting stress tensor defined using the Bogoliubov formula in an arbitrary Hadamard state, even for the case that the smearing is only along a one-dimensional time-like worldline and not in space-time. We then show that the interacting energy density, as seen by an observer following this worldline, satisfies an absolute lower bound, that is a bound independent of the quantum state. Our proof employs and generalises existing techniques developed for free theories by Flanagan, Fewster and Smith.