Domain Walls: Momentum Conservation in Absence of Asymptotic States

TL;DR

This paper investigates how momentum conservation can be understood in the context of domain walls in linearized gravity, where traditional asymptotic states are not well-defined due to the gravitational potential's growth with distance.

Contribution

It introduces the concept of gravitationally dressed momenta in relativistic scenarios, accounting for momentum flux and losses, thus extending conservation laws to non-asymptotic regimes.

Findings

Relativistic domain wall scattering involves momentum flux through lateral surfaces.

Gravitationally dressed momenta are conserved up to branon wave excitation losses.

Potential energy approach applies in non-relativistic cases, while dressed momenta are used relativistically.

Abstract

Gravitational potentials of the domain walls in the linearized gravity are growing with distance, so the particle scattering by the wall can not be described in terms of free asymptotic states. In the non-relativistic case this problem is solved using the concept of the potential energy. We show that in the relativistic case one is able to introduce gravitationally dressed momenta the sum of which is conserved up to the momentum flux through the lateral surface of the world tube describing losses due to excitation of the branon waves.