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Mathematical Physics Seminar

Gerald Goldin - Group-Theoretical Approach to Anyons, Topological Quantum Configurations, and Infinite Systems

Date & time: Thursday, 16 April 2020 at 12:00PM - 1:00PM

Gerald Goldin – Rutgers University

Thursday, April 16, 12:00pm

 "Group-Theoretical Approach to Anyons, Topological Quantum Configurations, and Infinite Systems"

Classification of unitary representations of the group of diffeomorphisms of physical space, and its semidirect products, provides a unifying description of diverse quantum systems, including N-particle quantum mechanics, ordinary and exotic quantum statistics (including anyons and nonabelian anyons in two-space), and infinite configurations in statistical mechanics. The braid group enters naturally in two-space, where anyonic creation and annihilation fields satisfy \(q\)-deformed commutation relations. The ideas  generalize to configurations of extended objects having nontrivial topology, albeit with various mathematically rigorous results remaining to be demonstrated. I shall review briefly the main findings, highlight some directions for investigation, and point toward a possible approach to relativistic theories based on spatial measurements in inertial reference frames. Much of this work is in collaboration with David Sharp at Los Alamos National Laboratory.

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