Møller operators for Dirac fields with MIT boundary conditions

17.01.2022, 16:15  –  Online via zoom
Forschungsseminar Differentialgeometrie

Nicolò Drago (Trento)

Classical and quantum field theories are based on the study of the space of solutions to certain differential operators \(D\) (e.g. the Dirac operator) on globally hyperbolic spacetimes \((M,g)\) - either with or without a timelike boundary. Within the algebraic approach a suitable *-algebra of observables \(\mathcal{A}_D(M,g)\) is built out of these solutions.

In practise, it is often useful to discuss whether it is possible to deform the parameters of the underlying theory (e.g. the metric associated with the Dirac operator) in such a way that the resulting algebras \(\mathcal{A}_D(M,g)\), \(\mathcal{A}_{D'}(M,g')\) are *-isomorphic. This is done by introducing suitable maps , known with the name of Møller operators.

In this talk we will discuss Møller operators for Dirac fields coupled with MIT boundary conditions on globally hyperbolic manifolds with a timelike boundary. In particular, we will show that Møller operators lead to *-isomorphisms and that any Hadamard state can be pulled back along this -isomorphism preserving the singular structure of its two-point distribution.

Zoom access data are available at this moodle.