Statistical Interpretation in the Schwinger’s picture of Quantum Mechanics

Abstract: In this talk I will illustrate some ideas about the statistical interpretation in the Schwinger’s picture of Quantum Mechanics. After a brief introduction on the postulates assumed in this framework, I will recall the basic ingredients of Connes’ non commutative integration theory. This language allows me to define, on one hand quantum measures on the groupoid associated with the quantum systems, and on the other weights on the corresponding groupoid von-Neumann algebra. In particular, quantum measures are a generalization of measures on sigma-algebras which is suited for the description of interference phenomena. Then, the final part of the talk will be devoted to the statistical interpretation associated with both situations.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

( video )

Comments: First part of a double session, followed by a 20 minute break for coffee and discussion, before the second speaker, Pedro Resende.

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Topological Quantum Field Theory Club (IST, Lisbon)

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