Canonical quantization of lattice Chern-Simons theory

Canonical quantization of lattice Chern-Simons theory

Blog Article

Abstract We discuss the canonical quantization of U(1) k Chern-Simons theory on a spatial lattice.In addition to the dwarf montmorency cherry tree for sale 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 pr30 (odd level) theories, describing in detail how the latter depends on a choice of spin structure.