Chern--Simons theory in the Schroedinger representation

Journal Article · Tue Aug 15 04:00:00 EDT 1989 · Annals of Physics (New York); (USA)

DOI:https://doi.org/10.1016/0003-4916(89)90036-5· OSTI ID:6828615

Dunne, G V; Jackiw, R; Trugenberger, C A ^[1]

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1. Center for Theoretical Physics, Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA (USA) Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA)

We quantize the (2+1)-dimensional Chern--Simons theory in the functional Schroedinger 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 Schroedinger representation. {copyright} 1989 Academic Press, Inc.

• OSTI ID: 6828615
• Journal Information: Annals of Physics (New York); (USA), Journal Name: Annals of Physics (New York); (USA) Vol. 194:1; ISSN APNYA; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

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INVARIANCE PRINCIPLES
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MATHEMATICS
QUANTIZATION
QUANTUM FIELD THEORY
SCHROEDINGER PICTURE
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