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

Detlev Buchholz, Stephen J. Summers
June 02, 2008
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.
open access link doi:10.1142/9789812833556_0007
@inproceedings{Buchholz:2008rd, author = "Buchholz, Detlev and Summers, Stephen J.", title = "{Warped Convolutions: A Novel Tool in the Construction of Quantum Field Theories}", booktitle = "{Quantum field theory and beyond: Essays in honor of Wolfhart Zimmermann. Proceedings, Symposium in Honor of Wolfhart Zimmermann's 80th Birthday, Tegernsee, Germany, February 3-6, 2008}", year = "2008", pages = "107-121", eprint = "0806.0349", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:0806.0349;%%" }