AG Lie-Gruppen: J. Schober, FAU: Standard subspaces, reflection positivity, Pick functions and how to pass from one to the other

Standard subspaces, reflection positivity, Pick functions and how to pass from
one to the other – Vortragender: Jonas Schober, FAU Erlangen – Einladender:
Karl-Hermann Neeb

Abstract: Motivated by the Haag-Kastler theory of local observables in Quantum
Field Theory, one is interested in unitary endomorphisms of standard
subspaces. Classical results in this context are given in the works of
Borchers and Longo/Witten. In my PhD project I focus on one-parameter
semigroups of these unitary endomorphisms. In the context of Borchers theorem
a natural approach is to pass from one-parameter semigroups of unitary
endomorphisms of standard subspaces to reflection positive unitary one-
parameter groups, while in the context of Longo/Witten one thinks of these
one-parameter semigroups as one-parameter semigroups of inner functions which
are infinitesimally generated by Pick functions. In this talk I will show how
to pass from one picture to the other.