Gerald Goldin – Rutgers University
Date/Time/Location
Thursday, November 20th, 2025, 12:10 pm; Hill Center 705
A Universal Kinematical Group for Quantum Mechanics and Some Consequent Anyonic Structures
This talk first describes recent results with David Sharp (Los Alamos), where we obtain a universal kinematical group for quantum mechanics directly from a few fundamental physical assumptions, without quantizing any classical phase-space. One obtains directly the kinematics of all possible quantum systems having mass or charge, by classifying the group’s inequivalent continuous unitary representations. This describes all possible configuration spaces, together with standard and exotic particle exchange statistics. The method applies to arbitrary physical spaces, and does not seem limited to any particular space-time symmetry structure. Quantization methods thus essentially address a variety of “inverse problems” regarding measurement. This makes concrete the idea that nature does not quantize classical dynamics; classical systems merely approximate quantum phenomena in macroscopic domains.
Our early predictions of anyonic exchange statistics, and of nonabelian anyons, followed from modeling this group on two-dimensional space. Interesting intermediate quantum phases can arise from theoretically possible internal multipole structures, independent of the exchange statistics of such particle-like configurations. These new results are in collaboration with Hongyi Shen at Rutgers University, and form a part of his Ph.D. thesis in progress.
Reference: G. A. Goldin and D. H. Sharp, J. Math. Phys. 66, 082103 (2025), https://doi.org/10.1063/5.021162