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BIMSA TQFT and Higher Symmetries Seminar
Definition for statistics of invertible quasi-particles and extended excitations using operators on many-body Hilbert space
Definition for statistics of invertible quasi-particles and extended excitations using operators on many-body Hilbert space
Organizers
Speaker
Hanyu Xue
Time
Monday, January 6, 2025 1:30 PM - 4:00 PM
Venue
A3-3-201
Online
Zoom 518 868 7656
(BIMSA)
Abstract
We develop a mathematical framework that generalizes the definition of statistics for Abelian anyons, based on string operators in many-body Hilbert space, to arbitrary dimensions of invertible topological excitations on arbitrary manifolds. This theory is rigorous, systematic, and provides a general framework for understanding and proving the properties of statistics. Additionally, we propose several conjectures that may hold mathematical interest. We also present a computer program for calculating statistics, which has yielded results consistent with predictions from other physical theories. The talk is based on 2412.07653.