Abstract
We introduce a rigorous mathematical model of abelian quantized Chern Simons theory (C.S. theory) based on the theory of infinite dimensional oscillatory integrals developed by Albeverio and Høegh-Krohn. We construct a gauge-fixed C.S. path integral as a Fresnel integral in a certain Hilbert space. Wilson loop variables are defined as Fresnel integrable functions and it is shown in this context that the expectation value of products of Wilson loops w.r.t. the C.S. path integral is a topological invariant which can be computed in terms of pairwise linking numbers of the loops, as conjectured by Witten. We also propose a lattice C.S. action which converges to the continuum limit.
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References
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© 1992 Springer Science+Business Media Dordrecht
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Albeverio, S., Schäfer, J. (1992). Rigorous Approach to Abelian Chern-Simons Theory. In: Gielerak, R., Lukierski, J., Popowicz, Z. (eds) Groups and Related Topics. Mathematical Physics Studies, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2801-8_12
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DOI: https://doi.org/10.1007/978-94-011-2801-8_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5244-3
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