Quantum field theory with varying couplings

TL;DR

This paper investigates a quantum scalar field theory with spacetime-dependent couplings, revealing that momentum conservation can be restored at the quantum level despite classical translation symmetry breaking, with implications for Lorentz symmetry and fractional theories.

Contribution

It demonstrates that specific spacetime-dependent couplings can preserve momentum conservation quantum mechanically and explores the renormalization of fractional field theories.

Findings

Momentum conservation recovered at quantum level for certain couplings

Calculated tree and one-loop diagrams in specific cases

Lorentz symmetry violation not enhanced quantum mechanically

Abstract

A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific choice of the coupling's profile for any finite-order perturbative expansion. For one of these cases, some tree and one-loop diagrams are calculated. This is an example of a theory where violation of Lorentz symmetry is not enhanced at the quantum level. We draw some consequences for the renormalization properties of certain classes of fractional field theories.