The semiclassical energy density of kinks and solitons

TL;DR

This paper calculates semiclassical energy corrections for kinks and solitons in 1+1 dimensional scalar field theories, revealing a subtlety in defining conserved stress tensors using advanced renormalization techniques.

Contribution

It introduces a covariant renormalization approach to compute semiclassical energy densities and clarifies issues in defining conserved stress tensors in 1+1 dimensions.

Findings

Reproduces known semiclassical energy corrections

Highlights a subtlety in stress tensor definition

Uses local and covariant renormalization techniques

Abstract

We compute semiclassical corrections to the energy density of kinks in $\phi^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions, using local and covariant renormalization techniques from quantum field theory in curved spacetimes. For the semiclassical correction to the energy, we recover the known results. Our analysis highlights a subtlety in the definition of a conserved stress tensor for scalar field theories in $1+1$ dimension.