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

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 Poincaré 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.