Unbounded self-adjoint operators play the role of the real numbers in quantum mechanics, normal operators that of complex
ones. Key tools of theoretical physicists in this context are distributions with values in the space of observables (quantum field theory) and analytic functions therein (perturbation methods). Despite this fact the literature provides no rigorous definition of these concepts or (at best) woefully inadequate ones. In our talk we present a theoretical basis for a rigorous
approach to spaces of observable-valued tempered distributions and holomorphic functions. We show how the regular toolbox of theoretical physics (Fourier transform, Hermite expansions, McLaurin series) carries over to this situation and use this to display some non-trivial examples.
Sprache der Kurzfassung:
Hauptvortrag / Eingeladener Vortrag auf einer Tagung