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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 5: Foundations of Quantum Mechanics I

AGPhil 5.1: Talk

Wednesday, March 12, 2025, 14:00–14:30, HS XVII

In Place of Quantization: A Universal Group-Theoretic Approach to Quantum Mechanics — •Gerald Goldin — Rutgers University, New Brunswick NJ, USA

This talk summarizes and expands on very recent results with David Sharp at Los Alamos, where we obtain a universal kinematical group for quantum mechanics directly from fundamental physical assumptions, without quantization in the usual sense. One then obtains distinct quantum systems with different configuration spaces, standard and exotic particle exchange statistics, and other properties, directly by classifying the inequivalent unitary representations of a single infinite-dimensional group. The method applies to arbitrary physical spaces, and does not seem limited to any particular space-time symmetry structure.

Here I explore whether such a unifying group-theoretic description can extend to dynamical as well as kinematical observables, and what that means. I also discuss some further ramifications and philosophical perspectives. Nature does not quantize classical dynamics; the latter merely approximates quantum phenomena in macroscopic domains. Quantization methods are essentially addressing an *inverse problem* regarding measurement, which is now more clearly characterized.

Reference: G. A. Goldin and D. H. Sharp, arXiv:20404.18274 [quant-ph]

Keywords: quantization; kinematics; Lie algebras; group representations; measurement