2024/01/17 by Theodore Jacobson, Jacobson, Theodore, Tin Sulejmanpašić +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.2401.09597
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.