Translation in momentum space and minimal length

TL;DR

This paper explores how the Snyder algebra modifies translation in momentum space, revealing a connection to Lorentz transformations and relativistic velocity addition, thus deepening understanding of minimal length effects in quantum gravity.

Contribution

It demonstrates that Snyder algebra alters momentum space translations to resemble relativistic velocity addition, establishing a link between minimal length theories and Lorentz symmetry.

Findings

Translation in momentum space is modified to resemble relativistic velocity addition.

Snyder algebra is closely connected to the Lorentz group.

Results confirm the compatibility of minimal length frameworks with Lorentz symmetry.

Abstract

We show that in presence of the Snyder algebra the notion of translation in momentum space is modified to a formula similar to the relativistic addition of velocities. These results confirm the strict connection between Snyder algebra and the Lorentz group.