Type II defects revisited

TL;DR

This paper investigates the constraints imposed by energy and momentum conservation on type II purely transmitting defects in scalar relativistic field theories, revealing that only known integrable models satisfy these conditions.

Contribution

It demonstrates that the conservation constraints uniquely select known integrable scalar field theories with type II defects, clarifying the defect's role in integrability.

Findings

Constraints are of an unfamiliar type involving Poisson brackets.

Only known integrable models satisfy the conservation constraints.

The results clarify the nature of type II defects in scalar field theories.

Abstract

Energy and momentum conservation in the context of a type II, purely transmitting, defect, within a single scalar relativistic two-dimensional field theory, places a severe constraint not only on the nature of the defect but also on the potentials for the scalar fields to either side of it. The constraint is of an unfamiliar type since it requires the Poisson Bracket of the defect contributions to energy and momentum with respect to the defect discontinuity and its conjugate to be balanced by the potential difference across the defect. It is shown that the only solutions to the constraint correspond to the known integrable field theories.