Copertina Integrali
Gio 30 Nov
Seminari e Convegni

An operational construction of the sum of two non-commuting observables in Quantum Theory

The seminar will be explore, with Sonia Mazzucchi, Professor at the University of Trento, a fundamental postulate of Quantum Theory: the existence of a genuine linear-space structure on the set of observables of a quantum system.

It is not clear how to choose the measurement tool for a generic observable of the form aA+bB (with a, b real numbers) when measurement tools are provided for the incompatible observables A and B. A mathematical version of this dilemma concerns constructing the spectral measure of f(aA+bB) based on the spectral measures of A and B.
We present a construction addressing this issue with a formula applicable to general unbounded self-adjoint operators A and B, whose spectral measures may not commute, and a broad class of functions f: R --> C.

In the bounded case, we demonstrate that the Jordan product of A and B (and suitably symmetrized polynomials of A and B) can be constructed using the same procedure based on the spectral measures of A and B.
The formula has an interesting operational interpretation and, in specific cases, a delightful connection with the theory of Feynman path integration and the Feynman-Kac formula.

This work is based on joint research with N. Drago and V. Moretti.