Gravitational form factors of a kink in $1+1$ dimensional $\phi^4$ model

TL;DR

This paper computes the one-loop quantum corrections to the energy-momentum distribution around a kink in a 1+1 dimensional $^4$ model, ensuring finiteness and conservation laws.

Contribution

It introduces a method to calculate finite, conserved gravitational form factors of kinks using collective coordinates and vacuum subtraction.

Findings

Analytic, finite result for energy-momentum distribution

Reproduction of known total energy of the kink

Identification of a spatially-uniform correction term

Abstract

We calculate the one-loop correction to the distribution of energy-momentum tensor around a kink in $1+1$ dimensional $\phi^4$ model. We employ the collective coordinate method to eliminate the zero mode that gives rise to infrared divergence. The ultraviolet divergences are removed by vacuum subtraction and mass renormalization. We obtain an analytic result that is finite and satisfies the momentum conservation. The total energy of the kink obtained from the spatial integral of energy density reproduces the known result. Our result obtained on a finite space has a spatially-uniform term that is inversely proportional to the spatial length.