Minimal-length quantum field theory: a first-principle approach

TL;DR

This paper introduces a first-principle method to incorporate a minimal length into quantum field theory, inspired by quantum-mechanical models, providing a foundational approach for future research.

Contribution

It proposes a novel two-step procedure to define quantum field theory with a minimal length, bridging quantum mechanics and quantum field theory from first principles.

Findings

A classical field theory model of quantum mechanics with minimal length

Quantization of the classical model to form a quantum field theory

Foundation for exploring minimal length effects in quantum field theory

Abstract

Phenomenological models of quantum gravity often consider the existence of some form of minimal length. This feature is commonly described in the context of quantum mechanics and using the corresponding formalism and techniques. Although few attempts at a quantum field-theoretical description of a minimal length has been proposed, they are rather the exception and there is no general agreement on the correct one. Here, using the quantum-mechanical model as a guidance, we propose a first-principle definition of a quantum field theory including a minimal length. Specifically, we propose a two-step procedure, by first describing the quantum-mechanical models as a classical field theory and subsequently quantizing it. We are thus able to provide a foundation for further exploration of the implications of a minimal length in quantum field theory.