Canonical quantization of lattice Chern-Simons theory

Canonical quantization of lattice Chern-Simons theory

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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 luce chandelier 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 Sneakers for Men - Grey - Canvas Mesh Athletic Running Shoes 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.