Chern-Simons field theory and quantum groups. (English) Zbl 0722.57003
Quantum groups, Proc. 8th Int. Workshop Math. Phys., Clausthal/Germ. 1989, Lect. Notes Phys. 370, 307-317 (1990).
Summary: [For the entire collection see Zbl 0713.00024.]
We study the Gauss constraint of the Chern-Simons theory in presence of sources. We solve this constraint in terms of a matrix-valued gauge connection. The associated holonomies define a representation of the braid group, which commutes with the action of a quantum group.
We study the Gauss constraint of the Chern-Simons theory in presence of sources. We solve this constraint in terms of a matrix-valued gauge connection. The associated holonomies define a representation of the braid group, which commutes with the action of a quantum group.
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 81R50 | Quantum groups and related algebraic methods applied to problems in quantum theory |
| 20F36 | Braid groups; Artin groups |
Keywords:
Gauss constraint; Chern-Simons theory; gauge connection; holonomies; braid group; quantum groupCitations:
Zbl 0713.00024References:
| [1] | . Nucl. phys. B 322, 629 (1989) |
| [2] | S. Elitzur, G. Moore, A. Schwimmer and N. Seiberg, Remarks on the canonical quantization of the Chern-Simons-Witten theory, preprint IASSNS-HEP-89/20. |
| [3] | Bos, M.; Nair, V. P.: Coherent state quantization of the Chern-Simons theory. Cu-tp-432 (1989) |
| [4] | Atiyah, M. F.: New invariants of three- and four-dimensional manifolds. Proc. symp. Pure math. 48 (1988) · Zbl 0667.57018 |
| [5] | P. Cotta-Ramusino, E. Guadagnini, M. Martellini and M. Mintchev, Quantum field theory and link invariants, preprint CERN-TH.5277/89, Nucl. Phys. B, to appear. |
| [6] | Wilson lines in Chern-Simons theory and link invariants, preprint CERN-TH.5420/89, Nucl. Phys. B, to appear. |
| [7] | Kohno, T.: Ann. inst. Fourier, Grenoble. 37, 139 (1987) |
| [8] | Dunne, G. V.; Jackiw, R.; Trugenberger, C. A.: Ann. phys.. 149, 197 (1989) |
| [9] | E. Guadagnini, M. Martellini and M. Mintchev, Braids and quantum group symmetry in Chern-Simons theory, preprint CERN-TH-5573/89. · Zbl 0957.81536 |
| [10] | Labastida, J. M. F.; Ramallo, A. V.: Phys. lett. B. 228, 214 (1989) |
| [11] | S. Carlip, Exact quantum scattering in 2+1 dimensional gravity, preprint IASSNS-HEP-89/4. |
| [12] | Knizhnik, V. G.; Zamolochikov, A. B.: Nucl. phys. B. 247, 83 (1984) |
| [13] | Kimbo, M.: Commun. math. Phys.. 102, 537 (1986) |
| [14] | N.Yu. Reshetikhin, Quantized universal enveloping algebras, the Yang-Baxter equation and invariants of links I and II, preprints LOMI E-4-87 and E-17-87. |
| [15] | H.J. De Vega, Yang-Baxter algebras, conformal invariant models and quantum groups, preprint PAR LPTHE 88-46. · Zbl 0695.17007 |
| [16] | J-L.-Gervais, the Quantum group structure of 2D gravity and minimal models, preprint LPTENS 89/14. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
