OSMU 2024 TALK 3 by Maurice De Gosson, 22nd March 2024

OSMU 2024
22/03/24
Speaker: Maurice De Gosson
Title: The sympletctic camel, quantum blobs, and the metatron: exploring the interplay of symplectic mechanics and quantum principles
School: Faculty of Mathematics (NuHAG) University of Vienna, Austria
Abstract:
In this talk, we begin by delving into the realm of symplectic mechanics, exploring in an elementary way some of the profound implications of Gromov's non-squeezing theorem, a cornerstone in modern symplectic topology. Building upon our previous work, we thereafter introduce the concept of "quantum blob," the smallest phase space unit consistent with the indeterminacy principle of quantum mechanics. Contrary to conventional expectations, these quantum blobs are characterized not by volume but by the Gromov width, always equating to half of the quantum of action. This novel characterization facilitates an intrinsic symplectically invariant topological formulation of the principle of quantum indeterminacy. We establish a bijective correspondence between our quantum blobs and the generalized Gaussian states of quantum mechanics. We draw connections to the geometric notion of symplectic polarity between convex bodies in phase We finally show how Schrödinger's equation ca be rigorously derived from symplectic geometry.