Canonical quantization of lattice Chern-Simons theory

Jacobson, Theodore; Sulejmanpasic, Tin

Abstract

We discuss the canonical quantization of U(1)k Chern-Simons theory on a spatial lattice. In addition to the usual local Gauss law constraints, the physical Hilbert space is defined by 1-form gauge constraints implementing the compactness of the U(1) gauge group, and (depending on the details of the spatial lattice) non-local constraints which project out unframed Wilson loops. Though the ingredients of the lattice model are bosonic, the physical Hilbert space is finite-dimensional, with exactly k ground states on a spatial torus. We quantize both the bosonic (even level) and fermionic (odd level) theories, describing in detail how the latter depends on a choice of spin structure.

Citation

Jacobson, T., & Sulejmanpasic, T. (2024). Canonical quantization of lattice Chern-Simons theory. Journal of High Energy Physics, 2024(11), Article 87. https://doi.org/10.1007/jhep11%282024%29087

• Journal Article Type: Article
• Acceptance Date: Oct 18, 2024
• Online Publication Date: Nov 14, 2024
• Publication Date: Nov 14, 2024
• Deposit Date: Nov 19, 2024
• Publicly Available Date: Nov 19, 2024
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2024
• Issue: 11
• Article Number: 87
• DOI: https://doi.org/10.1007/jhep11%282024%29087
• Keywords: Lattice Quantum Field Theory, Chern-Simons Theories, Topological Field Theories, Anyons
• Public URL: https://durham-repository.worktribe.com/output/3098620