Topological quantum field theories, moduli spaces, and flat gauge connections

Journal Article · Sat Sep 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2080· OSTI ID:6227553

Sonnenschein, J ^[1]

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1. Stanford Linear Accelerator Center, Stanford University, Stanford, California 94309 (USA)

We show how to construct a topological quantum field theory which corresponds to a given moduli space. We apply this method to the case of flat gauge connections defined over a Riemann surface and discuss its relations with the Chern-Simons theory and conformal field theory. Geometrical properties are invoked to prove that the observables of those theories are not trivial. The case of the SO(2,1) group is separately discussed. A topological field theory is linked to the moduli space of self-dual'' connections over Riemann surfaces. Another relation between the Chern-Simons theory and topological quantum field theory in three dimensions is established. We present the theory which corresponds to three-dimensional gravity. Expressions for the Casson invariants are given. Possible generalizations are briefly discussed.

• DOE Contract Number: AC03-76SF00515
• OSTI ID: 6227553
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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645400* -- High Energy Physics-- Field Theory
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GRAVITATION
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
PARTICLE MODELS
PARTITION FUNCTIONS
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM GRAVITY
RIEMANN SPACE
SIGMA MODEL
SO GROUPS
SPACE
SPACE-TIME
SYMMETRY BREAKING
SYMMETRY GROUPS
THREE-DIMENSIONAL CALCULATIONS
TOPOLOGY
YANG-MILLS THEORY