# Aktuelles

## Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Valter Moretti am 13.01.2021 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis

[13.01.2021]

Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 13. Januar 2021, um 14:30 Uhr,

Herr Prof. Dr. Valter Moretti (University of Trento, Italy)

einen Vortrag zum Thema

“An operational construction of the sum of two non-commuting observables in quantum theory and related constructions”.

Abstract: The existence of a real linear-space structure on the set of observables of a quantum system – i.e., the requirement that the linear combination of two generally non-commuting observables $A,B$ is an observable as well – is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable of the form $aA + bB (a, b \in \mathbb{R})$ if such measuring instruments are given for the addends observables $A$ and $B$ when they are incompatible observables. A mathematical version of this dilemma is how to construct the spectral measure of $f(aA + bB)$ out of the spectral measures of $A$ and $B$. We present such a construction with a formula which is valid for general unbounded selfadjoint operators $A$ and $B$, whose spectral measures may not commute, and a wide class of functions $f : \mathbb{R} \to \mathbb{C}$ . In the bounded case, we prove that the Jordan product of $A$ and $B$ (and suitably symmetrized polynomials of $A$ and $B$) can be constructed with the same procedure out of the spectral measures of $A$ and $B$. The formula turns out to have an interesting operational interpretation and, in particular cases, a nice interplay with the theory of Feynman path integration and the Feynman-Kac formula.

Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Dr. Mugnolo (delio.mugnolo@fernuni-hagen.de) melden.

mathinf.webteam | 18.12.2020