Relativistic Planck-scale polymer

TL;DR

This paper demonstrates that in a one-dimensional polymer quantum model, relativistic symmetries are deformed rather than broken, suggesting a connection to noncommutative spacetime structures and informing Loop Quantum Gravity.

Contribution

It shows that relativistic symmetries in polymer quantum mechanics are deformed, not broken, and links these deformations to noncommutative spacetime descriptions.

Findings

Relativistic symmetries are deformed in the polymer model.

Deformations relate to noncommutative spacetime frameworks.

Supports the idea of a quantum-Minkowski limit in Loop Quantum Gravity.

Abstract

Polymer quantum mechanics has been studied as a simplified picture that reflects some of the key properties of Loop Quantum Gravity; however, while the fate of relativistic symmetries in Loop Quantum Gravity is still not established, it is usually assumed that the discrete polymer structure should lead to a breakdown of relativistic symmetries. We here focus for simplicity on a one-spatial-dimension polymer model and show that relativistic symmetries are deformed, rather than being broken. The specific type of deformed relativistic symmetries which we uncover appears to be closely related to analogous descriptions of relativistic symmetries in some noncommutative spacetimes. This also contributes to an ongoing effort attempting to establish whether the "quantum-Minkowski limit" of Loop Quantum Gravity is a noncommutative spacetime.