Lorentz invariance without trans-Planckian physics?

TL;DR

This paper investigates whether low-energy quantum field theory processes can preserve Lorentz invariance despite a Planck-scale cutoff, using a modified propagator and one-loop corrections to demonstrate potential invariance.

Contribution

It introduces a method to derive Lorentz-invariant results in quantum field theory with a Planck-scale cutoff by imposing cutoff independence on one-loop corrections.

Findings

Lorentz invariance can be maintained at low energies with a Planck-scale cutoff.

The derived correction resembles standard results with a cutoff at the Planck scale.

The approach suggests Lorentz symmetry may be preserved without trans-Planckian physics.

Abstract

We explore the possibility that, in a quantum field theory with Planck scale cutoff Lambda=Mp, observable quantities for low-energy processes respect the Lorentz symmetry. In particular, we compute the one-loop radiative correction Pi to the self-energy of a scalar field with lambda phi^4 interaction, using a modified (non-invariant) propagator which vanishes in the trans-Planckian regime, as expected in the "classicalization" scenario. We then show that, by imposing the result does not depend on Lambda (in the limit Lambda to Mp), an explicit (albeit not unique) expression for Pi can be derived, which is similar to the one simply obtained with the standard Feynman propagator and a cutoff Lambda=Mp.