Curved momentum space equivalent to the linear and quadratic Generalized Uncertainty Principle

TL;DR

This paper explores the relationship between generalized uncertainty principles and quantum dynamics on curved momentum space, focusing on linear and quadratic GUPs and their associated curvature tensors.

Contribution

It advances the understanding of how linear and quadratic GUPs correspond to curved momentum space and their non-commutative properties.

Findings

Curvature tensor in dual theory is proportional to coordinate non-commutativity.

Deepens the theoretical link between GUPs and curved momentum space.

Analyzes linear and quadratic GUPs in this framework.

Abstract

In this work, we deepen the correspondence between Generalized Uncertainty Principles (GUPs) and quantum dynamics on curved momentum space. In particular, we investigate the linear and quadratic GUP. Similarly to earlier work, the resulting curvature tensor in the dual theory is proportional to the coordinate non-commutativity of the original formulation.