| Grant number: | 14/24522-9 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - Brazil |
| Start date: | February 01, 2015 |
| End date: | April 30, 2015 |
| Field of knowledge: | Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields |
| Principal Investigator: | João Carlos Alves Barata |
| Grantee: | João Carlos Alves Barata |
| Visiting researcher: | Jens Karl Heinz Mund |
| Visiting researcher institution: | Universidade Federal de Juiz de Fora (UFJF). Instituto de Ciências Exatas, Brazil |
| Host Institution: | Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
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)
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