Communications in Mathematical Physics

, Volume 284, Issue 1, pp 93–116 | Cite as

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.

Keywords

Ghost Gauge Group Gauge Transformation Principal Bundle Universal Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Instituto de Astronomia y Fisica del EspacioCasilla de Correo 67Buenos AiresArgentina
  2. 2.Math. Dept. FCENUniversidad de Buenos Aires, Ciudad UniversitariaBuenos AiresArgentina

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