Institut für Mathematik


Konferenz: Symposium in Mathematical Physics

Algebraic quantum field theory meets homotopy theory and operads

Vortrag von Dr. Marco Benini
Datum: 25.04.17   Zeit: 13.00 - 13.45   Raum: Y27H46

Algebraic quantum field theory (AQFT) formalizes QFTs on Lorentzian manifolds as functors assigning algebras (of observables) to spacetimes, subject to physical axioms (e.g. Einstein causality). Despite its successful applications, AQFT exhibits some limitations: 1) The range of constructions is restricted by the current (non-optimal) formulation of AQFT; 2) Locality, i.e. the process of "gluing" local algebras to obtain a global one, is not fully understood; 3) The AQFT axioms lack the flexibility needed for their homotopical extension, crucial for gauge theories. While reviewing the structure of AQFT, I will highlight these limitations and propose a solution based on a novel approach to AQFT that combines homotopy theory (in the sense of model categories à la Quillen) and operads to 1) provide new, more flexible constructions, 2) offer a satisfactory implementation of locality, and 3) lead to a natural homotopical extension of AQFT, resulting in a good axiomatic framework for quantum gauge theories on Lorentzian manifolds.