Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories

TL;DR

This paper introduces warped convolutions, a new deformation method for quantum field theories that produces wedge-localized operators with non-trivial scattering matrices, expanding the toolkit for constructing and analyzing quantum fields.

Contribution

It extends the deformation procedure to general quantum field theories, creating wedge-localized operators with covariance and non-trivial scattering, while breaking Lorentz symmetry.

Findings

Constructed wedge-localized operators with covariance.

Produced non-trivial scattering matrices.

Broken Lorentz symmetry in the deformed theories.

Abstract

Recently, Grosse and Lechner introduced a novel deformation procedure for non-interacting quantum field theories, giving rise to interesting examples of wedge-localized quantum fields with a non-trivial scattering matrix. In the present article we outline an extension of this procedure to the general framework of quantum field theory by introducing the concept of warped convolutions: given a theory, this construction provides wedge-localized operators which commute at spacelike distances, transform covariantly under the underlying representation of the Poincare group and admit a scattering theory. The corresponding scattering matrix is nontrivial but breaks the Lorentz symmetry, in spite of the covariance and wedge-locality properties of the deformed operators.