Orientability of loop processes in relative locality

TL;DR

This paper classifies loop processes in relative locality based on orientability, revealing how nonorientable loops break key symmetries and causality, while orientable loops preserve them, with implications linked to general relativity.

Contribution

Introduces a classification of loops in relative locality by orientability, connecting loop properties to symmetry breaking and physical implications.

Findings

Nonorientable loops have effective curvature and break translation symmetry.

Orientable loops are flat and preserve causality and momentum conservation.

Classical loops in relative locality may relate to effects from general relativity.

Abstract

Inspired by recent results of unusual properties of loop processes in relative locality, we introduce a way to classify loops in the case of kappa-Poincare momentum space. We show that the notion of orientability is deeply connected to a few essential properties of loop processes. Nonorientable loops have "effective curvature", which explicitly breaks translation symmetry, and can lead to a breaking of causality and global momentum conservation. Orientable loops, on the other hand, are "flat." Causality and global momentum conservation are all well preserved in this kind of loops. We comment that the nontrivial classical loops in relative locality might be understood as dual effects from general relativity, and some physical implications are discussed.