Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories

TL;DR

This paper integrates the generalized uncertainty principle into Lifshitz-scaled field theories, including bosonic, fermionic, and non-abelian gauge theories, and explores their gauge invariance and quantization.

Contribution

It introduces a novel approach to incorporate the generalized uncertainty principle into Lifshitz field theories, including non-local gauge actions and stochastic quantization methods.

Findings

Gauge invariance preserved despite non-local actions

Successful construction of bosonic and fermionic Lifshitz theories with GUP

Demonstrated stochastic quantization of Lifshitz fermionic theory

Abstract

In this paper, we will incorporation the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bososnic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into an non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.