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Canonical quantization of lattice Chern-Simons theory

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arxiv 2401.09597 v1 pith:SZUDRBSZ submitted 2024-01-17 hep-th hep-lat

Theodore Jacobson , Tin Sulejmanpasic This is my paper · ORCID
classification hep-thhep-lat
keywords latticeconstraintsspatialbosoniccanonicalchern-simonsgaugehilbert
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation

    hep-lat 2026-07 conditional novelty 7.0 of 10

    Lattice Villain Maxwell theory realizes the theta subgroup of SL(2,Z) via Hamiltonian operators S and T2, with charge exchange, the Witten effect, and a non-invertible defect with Tambara-Yamagami fusion.

  2. Exactly Solvable 1+1d Chiral Lattice Gauge Theories

    hep-th 2026-01 conditional novelty 7.0 of 10

    Anomaly-free chiral U(1) gauge theories in 1+1 dimensions can be written as quadratic, exactly solvable lattice Hamiltonians, with the 34-50 model as an explicit example.

  3. Bosonization versus the Nielsen-Ninomiya theorem

    hep-th 2026-07 conditional novelty 6.5 of 10

    The 2D modified Villain model's Weyl operators reproduce free Dirac correlations in the continuum, and their no-doubler Dirac kernel is non-local, showing exactly how bosonization evades the Nielsen-Ninomiya theorem.

  4. U(1)-gauged 2-flavor spin system in 3-D

    hep-lat 2025-02 conditional novelty 6.0 of 10

    A U(1)-gauged two-flavor spin model on a 3D lattice shows a transition that is likely weakly first order, passing near a multi-critical point, based on preliminary Monte Carlo data.

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