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Algebraic construction of models in Relativistic Quantum Field Theory and modular localization

Abstract

The objective of this project is to construct non-perturbative models in relativistic quantum field theory (QFT), at the level of rigor required by Mathematical Physics. By model, here, we mean a net $\calA(O)$ of operator algebras whose elements are interpreted as observables in the region$ $\calO$. The main mathematical tools employed are the modular theory of Tomita and Takesaki, non-commutative measure theory, particularly the theory of relative modular operators, the theory of Connes co-cycles, and the theory of unitary representations of the groups of Lorentz and Poincaré. The fundamental physical concept to implement the property of causality (Einstein's causality) is called modular localization, based on the Bisognano-Wichmann property. The models will be built in a first step within the de Sitter space, and then transferred to the Minkowski space through a suited limit scaling procedure. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
JAKEL, CHRISTIAN D.; MUND, JENS. The Haag-Kastler Axioms for the Model on the De Sitter Space. ANNALES HENRI POINCARE, v. 19, n. 3, p. 959-977, MAR 2018. Web of Science Citations: 0.
JAKEL, CHRISTIAN D.; MUND, JENS. Canonical interacting quantum fields on two-dimensional de Sitter space. Physics Letters B, v. 772, p. 786-790, SEP 10 2017. Web of Science Citations: 1.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.