@article{TMF_1992_93_3_a6,
author = {P. Loll},
title = {Loop approaches to gauge field theories},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {481--505},
year = {1992},
volume = {93},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a6/}
}
P. Loll. Loop approaches to gauge field theories. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 3, pp. 481-505. http://geodesic.mathdoc.fr/item/TMF_1992_93_3_a6/
[1] Gu C.-H., “On classical Yang-Mills fields”, Phys. Rep., 80 (1981), 251–337 | DOI | MR
[2] Migdal A. A., “Loop equations and $1/N$ expansion”, Phys. Rep., 102 (1983), 199–290 | DOI
[3] Kogut J., Susskind L., “Hamiltonian formulation of Wilson's lattice gauge theories”, Phys. Rev. D, 11 (1975), 395–408 | DOI
[4] Fort H., Gambini R., “Lattice QED with lignt fermions in $P$ representation”, Phys. Rev. D, 44 (1991), 1257–1262 | DOI | MR
[5] Yang C. N., “Integral formalism for gauge fields”, Phys. Rev. Lett., 33 (1974), 445–447 | DOI | MR | Zbl
[6] Kobayashi S., Nomizu K., Foundations of differential geometry, v. 1, Interscience, New York, 1969 | MR | Zbl
[7] Lichnerowicz A., Global theory of connections and holonomy groups, Noordhoff International Publishing, 1976 | MR | Zbl
[8] Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M., Analysis, manifolds and physics, revised edition, North-Holland, Amsterdam, 1982 | MR | Zbl
[9] Wilson K., “Confinement of quarks”, Phys. Rev. D, 10 (1974), 2445–2459 | DOI
[10] Kauffman L. H., On knots, Princeton University Press, 1987 | MR | Zbl
[11] Kauffman L. H., Knots and Physics, World Scientific, Singapore, 1991 | MR
[12] Gambini R., Trias A., “Chiral formulation of Yang–Mills equations: A geometric approach”, Phys. Rev. D, 27 (1983), 2935–2939 | DOI | MR
[13] Adams J. F., Infinite loop spaces, Princeton University Press, 1978 | MR | Zbl
[14] Michor P. W., Manifolds of differentiable mappings, Shiva Publishing Limited, Orpington, 1980 | MR | Zbl
[15] Lipschutz S., General topology, McGraw-Hill, New York, 1965
[16] Ashtekar A., Isham C. J., Representations of the holonomy algebras of gravity and non-Abelian gauge theories, preprint Imperial/TP/91-92/14 and SU-GP-91-12-2, 1991 | MR
[17] Isham C. J., “Loop algebras and canonical quantum gravity”, Proceedings of the 1991 AMS Summer Research Conference on Mathematical Methods in Classical Field Theory, to appear | MR
[18] Mensky M. B., “Group of parallel transports and description of particles in curved spacetime”, Lett. Math. Phys., 2 (1978), 175–180 | DOI | MR
[19] Mensky M. B., “Application of the group of paths to the gauge theory and quarks”, Lett. Math. Phys., 3 (1979), 513–520 | DOI | MR
[20] Mensky M. B., The group of paths, Nauka, Moscow, 1983 (Russian) | MR
[21] Stasheff J., Differential graded Lie algebras, Quasi-Hopf algebras and higher homotopy algebras, preprint UNC-MATH-91-3 | MR
[22] Brylinski J. M., The Kaehler geometry of the space of knots in a smooth threefold, Penn State pure mathematics report No PM93, 1990
[23] Schäper U., Geometry of loop spaces. I. A Kaluza–Klein type point of view, preprint Freiburg THEP 91/3, march 1991
[24] Gambini R., Trias A., “Geometrical origin of gauge theories”, Phys. Rev. D, 23 (1981), 553–555 | DOI | MR
[25] Jackiw R., “Gauge-covariant conformal transformations”, Phys. Rev. Lett., 41 (1978), 1635–1638 | DOI
[26] Durhuus B., Leinaas J. M., “On the loop space formulation of gauge theories”, Physica Scripta, 25 (1982), 504–510 | DOI | MR | Zbl
[27] Gliozzi F., Virasoro M. A., “The interaction among dual strings as a manifestation of the gauge group”, Nucl. Phys. B, 164 (1980), 141–151 | DOI | MR
[28] Gambini R., Trias A., “Gauge dynamics in the $C$-representation”, Nucl. Phys. B, 278 (1986), 436–448 | DOI | MR
[29] Giles R., “Reconstruction of gauge potentials from Wilson loops”, Phys. Rev. D, 24 (1981), 2160–2168 | DOI | MR
[30] Goldberg J. N., Lewandowski J., Stomaiolo C., “Degeneracy in loop variables”, Comm. Math. Phys., to appear | MR
[31] Polyakov A. M., Gauge fields and strings, Harwood Academic Publishers, Chur, 1987 | MR
[32] Polyakov A. M., “Gauge fields as rings of glue”, Nucl. Phys. B, 164 (1979), 171–188 | DOI | MR
[33] Mandelstam S., “Quantum electrodynamics without potentials”, Ann. Phys., 19 (1962), 1–24 | DOI | MR | Zbl
[34] Bialnycki-Birula I., “Gauge-invariant variables in the Yang–Mills theory”, Bull. Acad. Polon. Sci., 11 (1963), 135–138 | MR
[35] Mandelstam S., “Feynman rules for electromagnetic and Yang–Mills fields from the gauge-independent field-theoretic formalism”, Phys. Rev., 175 (1968), 1580–1603 | DOI
[36] Polyakov A. M., “String representations and hidden symmetries for gauge fields”, Phys. Lett. B, 82 (1979), 247–250 | DOI | MR
[37] Aref'eva I. Ya., “The gauge field as chiral field on the path and its integrability”, Lett. Math. Phys., 3 (1979), 241–247 | DOI | MR
[38] Aref'eva I. Ya., “Quantum contour field equations”, Phys. Lett. B, 93 (1980), 347–353 | DOI | MR
[39] Aref'eva I. Ya., The integral formulation of gauge theories - strings, bags or something else, lectures given at the 17-th Karpacz Winter School, 1980
[40] Gu C.-H., Wang L.-L.Ch., “Loop-space formulation of gauge theories”, Phys. Rev. Lett., 25 (1980), 2004–2007
[41] Mandelstam S., “Charge-monopole duality and the phases of non-Abelian gauge theories”, Phys. Rev. D, 19 (1979), 2391–2409 | DOI
[42] Blencowe M. P., “The Hamiltonian constraint in quantum gravity”, Nucl. Phys. B, 341 (1990), 213–251 | DOI | MR | Zbl
[43] Brügmann B., Pullin J., On the constraint of quantum gravity in the loop representation, preprint Syracuse SU-GP-91/8-5 | MR
[44] Durhuus B., Olesen P., “Eigenvalues of the Wilson operator in multicolor QCD”, Nucl. Phys. B, 184 (1981), 406–428 | DOI
[45] Furmanski W., Kolawa A., “Yang–Mills vacuum: An attempt at lattice loop calculus”, Nucl. Phys. B, 291 (1987), 594–628 | DOI | MR
[46] Gambini R., Leal L., Trias A., “Loop calculus for lattice gauge theories”, Phys. Rev. D, 39 (1989), 3127–3135 | DOI | MR
[47] Rovelli C., Smolin L., Loop representation for lattice gauge theory, preprint Pittsburgh and Syracuse, 1990 | MR
[48] Brügmann B., “The method of loops applied to lattice gauge theory”, Phys. Rev. D, 43 (1991), 566–579 | DOI | MR
[49] Loll R., “Independent $SU(2)$-loop variables and the reduced configuration space of $SU(2)$-lattice gauge theory”, Nucl. Phys. B, 368 (1992), 121–142 | DOI | MR
[50] Loll R., Yang–Mills theory without Mandelstam constraints, Syracuse preprint SUGP-92 | MR
[51] Rovelli C., Smolin L., “Loop space representation of quantum general relativity”, Nucl. Phys. B, 331 (1990), 80–152 | DOI | MR
[52] Rovelli C., “Ashtekar formulation of general relativity and loop-space non-perturbative quantum gravity: A report”, Class. Quantum Grav., 1991, 1613–1675 | DOI | MR | Zbl
[53] Loll R., “A new quantum representation for canonical gravity and $SU(2)$ Yang–Mills theory”, Nucl. Phys. B, 350 (1991), 831–860 | DOI | MR
[54] 't Hooft G., “On the phase transition towards permanent quark confinement”, Nucl. Phys. B, 138 (1978), 1–25 | DOI | MR
[55] 't Hooft G., “A property of electric and magnetic flux in non-Abelian gauge theories”, Nucl. Phys. B, 153 (1979), 141–160 | DOI | MR
[56] Gambini R., Trias A., “On confinement in pure Yang–Mills theory”, Phys. Lett. B, 141 (1984), 403–406 | DOI | MR
[57] Hosoya A., “Duality for the Lorentz force in loop space”, Phys. Lett. B, 92 (1980), 331–332 | DOI | MR
[58] Hosoya A., Shigemoto K., “Dual potential and magnetic loop operator”, Prog. Theor. Phys., 65 (1981), 2008–2022 | DOI
[59] Aldaya V., Navarro-Salas J., “New solutions of the Hamiltonian and diffeomorphism constraints of quantum gravity from a highest weight loop representation”, Phys. Lett. B, 259 (1991), 249–255 | DOI | MR
[60] Rayner D., “Hermitian operators on quantum general relativity loop space”, Class. Quant. Grav., 7 (1990), 651–661 | DOI | MR | Zbl
[61] Ashtekar A., Isham C. J., “Inequivalent observable algebras: another ambiguity in field quantisation”, Phys. Lett. B, 274 (1992), 393–398 | DOI | MR