Statistics of invertible topological excitations: a framework using operators and many-body Hilbert spaces

• URL: http://arxiv.org/abs/2412.07653v2
• Date: Sat, 01 Feb 2025 15:37:17 GMT
• Title: Statistics of invertible topological excitations: a framework using operators and many-body Hilbert spaces
• Authors: Hanyu Xue,
• Abstract summary: We develop a framework that generalizes the concept of anyon statistics, based on string operators and many-body Hilbert space, to invertible topological excitations of any dimensions. We present a computer program for computing statistics, which has yielded results consistent with traditional physical theories.
• Score: 0.48951183832371004
• License:
• Abstract: In this paper, we develop a mathematical framework that generalizes the concept of anyon statistics, based on string operators and many-body Hilbert space, to invertible topological excitations of any dimensions. This framework is only build on several fundamental facts in quantum mechanics, while providing a rigorous and systematic theory for statistics independent to topological order and field theory. Additionally, we propose several conjectures that may hold mathematical interest. We also present a computer program for computing statistics, which has yielded results consistent with traditional physical theories.

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