Twisting loops and global momentum non-conservation in Relative Locality

TL;DR

This paper reveals that in Relative Locality, certain loops can preserve local momentum but violate global momentum conservation, leading to particles changing properties after decay and recombination.

Contribution

It identifies a new type of loop in Relative Locality where global momentum is not conserved despite local conservation, expanding understanding of the theory's implications.

Findings

Locally conserved momenta in loops do not imply global momentum conservation.

Particles can decay and recombine with altered momentum and mass.

The theory admits non-conservation of global momentum in specific loop configurations.

Abstract

Recent work in Relative Locality has shown that the theory allows for a solution of an on-shell causal loop. We show that the theory contains a different type of a loop in which locally momenta are conserved, but there is no global momentum conservation. Thus a freely propagating particle can decay into two particles, which later recombine to give a particle with momentum and mass different than the original one.