Perturbative expansion of Chern-Simons theory with non-compact gauge group

Dror Bar-Natan; Edward Witten

doi:10.1007/BF02101513

Perturbative expansion of Chern-Simons theory with non-compact gauge group

Dror Bar-Natan, Edward Witten

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74 Scopus citations

Abstract

Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly "unitary" format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified.

Original language	English (US)
Pages (from-to)	423-440
Number of pages	18
Journal	Communications In Mathematical Physics
Volume	141
Issue number	2
DOIs	https://doi.org/10.1007/BF02101513
State	Published - Oct 1991
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF02101513

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abstract = "Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly {"}unitary{"} format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified.",

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AB - Naive imitation of the usual formulas for compact gauge group in quantizing three dimensional Chern-Simons gauge theory with non-compact gauge group leads to formulas that are wrong or unilluminating. In this paper, an appropriate modification is described, which puts the perturbative expansion in a standard manifestly "unitary" format. The one loop contributions (which differ from naive extrapolation from the case of compact gauge group) are computed, and their topological invariance is verified.

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Perturbative expansion of Chern-Simons theory with non-compact gauge group

Abstract

All Science Journal Classification (ASJC) codes

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