IWOTA 2019, International Workshop on Operator Theory and its Applications, July 22-26,2019, Lisbon, Portugal
Sprache des Tagungstitel:
Despite the fact that the observables are the basic quantities in quantum field theory, there is no adequate theory to carry over the basic methods of real and complex analysis to this context. We are particularly interested in the notions of holomorphic functions between spaces of observables and of operator-valued distributions. It is our intention in this talk to present such a treatment. It is based on a natural representation of the space of observables as a generalised spectrum of an algebra of functions on the real line, resp., the complex plane which is used to give it the structure of a polish space (when the underlying Hilbert space is separable). We use this fact to define various spaces of distributions with values in the space of observables and of holomorphic functions into or between them, whereby we employ methods developed for the classical case by J. Sebastião e Silva, G. Köthe and A. Grothendieck on the relations between duality and tensor products of spaces of test functions or analytic functions, resp., their vector-valued versions. In order to emphasise the naturalness of our approach we shall emphasise its axiomatic and functorial properties, rather than the technical details of the constructions.