Quantum Mathematics Seminar: Alastair Grant-Stuart (Brandeis)

Quantum Maths Seminar, external speaker:

Speaker: Alastair Grant-Stuart (Brandeis University)

Title: Spacetimes categories and disjointness for algebraic quantum field theory

Abstract: An algebraic quantum field theory (AQFT) may be expressed as a functor from a category of spacetimes to a category of algebras of observables. However, a generic category whose objects admit interpretation as spacetimes is not necessarily viable as the domain of an AQFT functor; often, additional constraints on morphisms must be imposed. We introduce disjointness relations, a generalisation of the orthogonality relations of Benini, Schenkel and Woike (2021). In any category equipped with a disjointness relation, we prescribe a subcategory which is suitable as the domain of an AQFT. We test this prescription in two familiar contexts: standard relativistic QFTs and chiral CFTs. In the former, the prescription reproduces the familiar domain category Loc used for locally covariant relativistic AQFTs. In the latter, it produces a domain category which we describe explicitly and compare to standard conformal-net-based descriptions of chiral CFT.

One hour talk, followed by informal discussion.

All are welcome. Please contact the seminar organizer to be added to the talk.