Quantum Uncertainty in Doubly Special Relativity

TL;DR

This paper explores how quantum uncertainty relations are modified in Doubly Special Relativity, analyzing the effects of an invariant length scale on quantum commutators and classical behavior emergence.

Contribution

It identifies modifications to quantum commutators within DSR and discusses two scenarios where classical behavior emerges at high energies or large masses.

Findings

Quantum commutators are altered in DSR due to the invariant length scale.

Classical behavior is approached when energy nears the inverse of the invariant length.

Large mass compared to the inverse length scale also leads to classical limits.

Abstract

The modification of the quantum mechanical commutators in a relativistic theory with an invariant length scale (DSR) is identified. Two examples are discussed where a classical behavior is approached in one case when the energy approaches the inverse of the invariant length which appears as a cutoff in the energy and in the second case when the mass is much larger than the inverse of the invariant length.