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Extended Connection in Yang-Mills Theory

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Abstract

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.

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Authors and Affiliations

  1. Instituto de Astronomia y Fisica del Espacio, Casilla de Correo 67, Sucursal 28, 1428, Buenos Aires, Argentina

    Gabriel Catren

  2. Math. Dept. FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellon 1, 1428, Buenos Aires, Argentina

    Jorge Devoto

Authors
  1. Gabriel Catren
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  2. Jorge Devoto
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Correspondence to Gabriel Catren.

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Communicated by N.A. Nekrasov

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Catren, G., Devoto, J. Extended Connection in Yang-Mills Theory. Commun. Math. Phys. 284, 93–116 (2008). https://doi.org/10.1007/s00220-008-0608-0

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  • DOI: https://doi.org/10.1007/s00220-008-0608-0

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