Canonical quantization of lattice Chern-Simons theory

A bstract 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 deta...

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Bibliographic Details
Published in:The journal of high energy physics 2024-11, Vol.2024 (11), p.87-31, Article 87
Main Authors: Jacobson, Theodore, Sulejmanpasic, Tin
Format: Article
Language:English
Subjects:
Anyons
Chern-Simons Theories
Classical and Quantum Gravitation
Constraints
Elementary Particles
Field theory (physics)
Hilbert space
Lattice Quantum Field Theory
Lattice theory
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Quantum theory
Regular Article - Theoretical Physics
Relativity Theory
Spacetime
Spin structure
String Theory
Symmetry
Topological Field Theories
Toruses
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Summary:A bstract 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.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2024)087