Extended connection in Yang-Mills theory
The three fundamental geometric components of Yang-Mills theory -gauge field, gauge fixing and ghost field- are unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to generalize the notion of gauge fixing by using a gauge fixing co...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
2008
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | The three fundamental geometric components of Yang-Mills theory -gauge field, gauge fixing and ghost field- are unified in a new object: an extended connection in a properly chosen principal fiber bundle. To do this, it is necessary to generalize the notion of gauge fixing by using a gauge fixing connection instead of a section. From the equations for the extended connection's curvature, we derive the relevant BRST transformations without imposing the usual horizontality conditions. We show that the gauge field's standard BRST transformation is only valid in a local trivialization and we obtain the corresponding global generalization. By using the Faddeev-Popov method, we apply the generalized gauge fixing to the path integral quantization of Yang-Mills theory. We show that the proposed gauge fixing can be used even in the presence of a Gribov's obstruction. © 2008 Springer-Verlag. |
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| Bibliografía: | Atiyah, M.F., Singer, I.M., Dirac operators coupled to vector potentials (1984) Proc. National Acad. Sci., 81, p. 2597 Baulieu, L., Bellon, M., P-forms and Supergravity: Gauge symmetries in curved space (1986) Nucl. Phys. B, 266, p. 75 Baulieu, L., Singer, I.M., Topological Yang-Mills symmetry (1988) Nucl. Phys., 5, p. 12. , Proc. Suppl Baulieu, L., Thierry-Mieg, J., The principle of BRST symmetry: An alternative approach to Yang-Mills theories (1982) Nucl. Phys. B, 197, p. 477 Birmingham, D., Blau, M., Rakowski, M., Thompson, G., Topological Field Theory (1991) Phys. Rep., 209, p. 129 Bonora, L., Cotta-Ramusino, P.L., Some remarks on BRS transformations, anomalies and the cohomology of the lie algebra of the group of gauge transformations (1983) Commun. Math. Phys., 87, p. 589 Choquet-Bruhat, Y., Dewitt-Morette, C., (1989) Analysis, Manifolds and Physics. Part II: 92 Applications, , New York: Elsevier Science Publishers B.V Cordes, S., Moore, G., Ramgoolam, S., Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories (1995) Nucl. Phys., 41, p. 184. , Proc Suppl Donaldson, S.K., Kronheimer, P.B., (1990) The Geometry of Four-manifolds, , Oxford University Press Oxford Dubois-Violette, M., The Weil-B.R.S. algebra of a Lie algebra and the anomalous terms in gauge theory (1986) J. Geom. Phys., 3, p. 525 Faddeev, L., Slavnov, A., (1991) Gauge Fields: An Introduction to Quantum Theory. Second Ed., , Frontiers in Physics, Cambridge: Perseus Books Gribov, V., Quantization of non-Abelian gauge theories (1978) Nucl. Phys. B, 139, p. 1 Guillemin, V., Sternberg, S., Guillemin, V.W., (1999) Supersymmetry and Equivariant de Rham Theory, , Berlin-Heidelberg-NewYork Spinger-Verlag Henneaux, M., Hamiltonian form of the path integral for theories with a gauge freedom (1985) Phys. Rep., 126, p. 1. , 1 Henneaux, M., Teitelboim, C., (1994) Quantization of Gauge Systems, , Princeton Univ. Press Princeton, NJ Kobayashi, S., Nomizu, K., (1963) Foundations of Differential Geometry. Vol. i, , Wiley New York Kriegl, A., Michor, P., It A convenient setting for global analysis (1997) Mathematical Surveys and Monographs, 53. , Amer. Math. Soc Michor, P., Gauge theory for fiber bundles (1991) Monographs and Textbooks in Physical Sciences, Lecture Notes, 19. , Napoli: Bibliopolis Narasimhan, M.S., Ramadas, T.R., Geometry of SU(2) Gauge Fields (1979) Commun. Math. Phys., 67, p. 121 Singer, I., Some remarks on the Gribov Ambiguity (1978) Commun. Math. Phys., 60, p. 7 Szabo, R., (2000) Equivariant Cohomology and Localization of Path Integrals, , Springer-Verlag Berlin-Heidelberg-NewYork Thierry-Mieg, J., Geometrical reinterpretation of Faddeev-Popov ghost particles and BRS transformations (1980) J. Math. Phys., 21, p. 2834 Witten, E., Topological quantum field theory (1988) Commun. Math. Phys., 117, p. 353 Witten, E., Dynamics of Quantum Field Theory (1999) Quantum Fields and Strings: A Course for Mathematicians, (2), pp. 1119-1424. , Providence, RI: Amer. Math. Soc |
| ISSN: | 00103616 |
| DOI: | 10.1007/s00220-008-0608-0 |