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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.

##### 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
##### References:
 [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.
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