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

Research output: Contribution to journal › Article › peer-review

72 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

Access to Document

10.1007/BF02101513

Cite this

@article{6c70789fd75b4bf4ac140a8cd5fa7ce2,

title = "Perturbative expansion of Chern-Simons theory with non-compact gauge group",

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.",

author = "Dror Bar-Natan and Edward Witten",

year = "1991",

month = oct,

doi = "10.1007/BF02101513",

language = "English (US)",

volume = "141",

pages = "423--440",

journal = "Communications In Mathematical Physics",

issn = "0010-3616",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Perturbative expansion of Chern-Simons theory with non-compact gauge group

AU - Bar-Natan, Dror

AU - Witten, Edward

PY - 1991/10

Y1 - 1991/10

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0342885396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0342885396&partnerID=8YFLogxK

U2 - 10.1007/BF02101513

DO - 10.1007/BF02101513

M3 - Article

AN - SCOPUS:0342885396

SN - 0010-3616

VL - 141

SP - 423

EP - 440

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 2

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this