Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric

TL;DR

This paper introduces three modified relativistic particle models with momentum-dependent metrics and noncommutative space-times, demonstrating their connections to Lifshitz field theories, Snyder space-time, and anisotropic field theories.

Contribution

It presents novel particle models linking momentum-dependent metrics and noncommutative geometries, unifying various field theories within a quantum framework.

Findings

Quantum versions include Lifshitz field theories.

Models yield Snyder noncommutative space-time.

Anisotropic field theories emerge as limits of noncommutative theories.

Abstract

In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as Lifshitz field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum dependent metrics. In this last case, we show that anisotropic field theories can be seen as a limit of noncommutative field theory.