Spontaneous Symmetry Breaking and Reflectionless Scattering Data

TL;DR

This paper investigates which symmetry-breaking potentials in a 1+1 dimensional scalar field theory produce quantum fluctuations with reflectionless scattering data, linking specific scattering data to well-known models like Phi^4 and sine-Gordon.

Contribution

It formulates the problem of restoring potentials from scattering data and identifies which reflectionless data correspond to symmetry-breaking potentials, providing explicit examples.

Findings

Reflectionless scattering data can correspond to symmetry-breaking potentials.

Restored potentials are similar to Phi^4 or sine-Gordon models.

Not all reflectionless data are compatible with symmetry breaking.

Abstract

We consider the question which potentials in the action of a (1+1) dimensional scalar field theory allowing for spontaneous symmetry breaking have quantum fluctuations corresponding to reflectionless scattering data. The general problem of restoration from known scattering data is formulated and a number of explicit examples is given. Only certain sets of reflectionless scattering data correspond to symmetry breaking and all restored potentials are similar either to the Phi**4-model or to the sine-Gordon model.