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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 7: Quantum field theory
MP 7.1: Talk
Wednesday, March 23, 2022, 16:45–17:05, MP-H5
Fermionic integrable models and graded Borchers triples — •Henning Bostelmann1 and Daniela Cadamuro2 — 1University of York, Department of Mathematics, York YO10 5DD, United Kingdom — 2Universität Leipzig, Institut für Theoretische Physik, Brüderstraße 16, 04103 Leipzig, Germany
The operator-algebraic construction of 1+1-dimensional integrable quantum field theories has received substantial attention over the past decade. These models are characterized by their asymptotic particle spectrum and their two-particle S-matrix; so far, those particles have been bosonic. By contrast, we consider the case of asymptotic fermions. Abstractly, they arise from a grading of the underlying operator algebraic structures (Borchers triples). Many of the technical methods required can be carried over from the bosonic case, mutatis mutandis; most importantly, existing results on the technically hard part of the construction (i.e., establishing the modular nuclearity condition) do not require modification.
Thus we are lead to a new family of rigorously constructed quantum field theories which are physically distinct from the bosonic case (with a different net of local algebras and a different scattering theory). Their local operators fulfill modified form factor axioms, consistent with the physics literature.