Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry

TL;DR

This paper explores how non-commutative Snyder space modifies Heisenberg uncertainty relations, leading to diverse physical predictions and connecting to loop quantum cosmology bounce scenarios.

Contribution

It demonstrates the impact of Snyder non-commutative geometry on uncertainty relations and links these modifications to cosmological bounce models.

Findings

Multiple physical predictions arise from Snyder space.

Generalized uncertainty relations are derived.

Connection to loop quantum cosmology bounce is established.

Abstract

We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering the one-dimensional case in the minisuperspace arena, the bouncing Universe dynamics of loop quantum cosmology can be recovered.