A Field Theory Model With a New Lorentz-Invariant Energy Scale

TL;DR

This paper introduces a Lorentz-invariant field theory framework with a new energy scale, potentially modeling quantum gravity effects, by incorporating curved momentum space via an extra dimension, while maintaining calculational simplicity and unitarity.

Contribution

It proposes a novel Lorentz-invariant field theory with a curved momentum space using an extra dimension, compatible with standard quantum field theory features.

Findings

Deformed scalar field theory is shown to be unitary.

Deformed QED reproduces standard scattering amplitudes at leading order.

Framework allows modeling quantum gravity phenomenology at the Planck scale.

Abstract

A framework is proposed that allows to write down field theories with a new energy scale while explicitly preserving Lorentz invariance and without spoiling the features of standard quantum field theory which allow quick calculations of scattering amplitudes. If the invariant energy is set to the Planck scale, these deformed field theories could serve to model quantum gravity phenomenology. The proposal is based on the idea, appearing for example in Deformed Special Relativity, that momentum space could be curved rather than flat. This idea is implemented by introducing a fifth dimension and imposing an extra constraint on physical field configurations in addition to the mass shell constraint. It is shown that a deformed interacting scalar field theory is unitary. Also, a deformed version of QED is argued to give scattering amplitudes that reproduce the usual ones in the leading order. Possibilities for experimental signatures are discussed, but more work on the framework's consistency and interpretation is necessary to make concrete predictions.