Algebraic constructive quantum field theory: Integrable models and deformation techniques

Gandalf Lechner
March 12, 2015
Several related operator-algebraic constructions for quantum field theory models on Minkowski spacetime are reviewed. The common theme of these constructions is that of a Borchers triple, capturing the structure of observables localized in a Rindler wedge. After reviewing the abstract setting, we discuss in this framework i) the construction of free field theories from standard pairs, ii) the inverse scattering construction of integrable QFT models on two-dimensional Minkowski space, and iii) the warped convolution deformation of QFT models in arbitrary dimension, inspired from non-commutative Minkowski space.
open access link
@incollection{Lechner:2015yxa, author = "Lechner, Gandalf", title = "{Algebraic constructive quantum field theory: Integrable models and deformation techniques}", editor = "Brunetti, Romeo and Dappiaggi, Claudio and Fredenhagen, Klaus and Yngvason, Jakob", booktitle = "Advances in algebraic quantum field theory", pages = "397-448", doi = "10.1007/978-3-319-21353-8_10", year = "2015", eprint = "1503.03822", archivePrefix = "arXiv", primaryClass = "math-ph", SLACcitation = "%%CITATION = ARXIV:1503.03822;%%" }

Keywords: 
constructive AQFT, constructive quantum field theory, integrable models, deformations of quantum field theories