Chern-Simons Theory in the Schrodinger Representation
Mar, 198928 pages
Published in:
- Annals Phys. 194 (1989) 197
Report number:
- MIT-CTP-1711
Citations per year
Abstract: (Elsevier)
We quantize the (2 + 1)-dimensional Chern-Simons theory in the functional Schrödinger representation. The realization of gauge transformations on states involves a 1-cocycle. We determine this cocycle; we show how solving the Gauss law constraint in the non-Abelian theory requires quantizing the parameter that normalizes the action; we trivialize the 1-cocycle with a spatially non-local cochain related to a 2-dimensional fermion determinant and we find the physical states that satisfy the Gauss law constraint. The quantum holonomy of physical states involves a contribution that is missed when the constraint is solved before quantization. We compute this quantity for the Abelian theory in Minkowski space, where it exhibits an interesting group theoretic structure. (In a note added in proof the corresponding non-Abelian computation is presented.) Also we consider coupling to external sources and offer yet another derivation of the anomalous statistics and spin of the charge and flux carrying particles —a calculation which is especially simple in the functional Schrödinger representation.Note:
- In Memorium Heinz Pagels
- GAUGE FIELD THEORY: THREE-DIMENSIONAL
- FIELD THEORY: CHERN-SIMONS TERM
- FIELD THEORY: GAUSS LAW
- QUANTIZATION
- TRANSFORMATION: GAUGE
- CHARGE: TOPOLOGICAL
- ALGEBRA: LIE
- commutation relations
- REPRESENTATION: SCHROEDINGER
- TENSOR: ENERGY-MOMENTUM
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