Extended Connection in Yang-mills Theory
نویسنده
چکیده
The three fundamental geometric components of YangMills theory -gauge field, gauge fixing and ghost fieldare 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 connections curvature, we derive the relevant BRST transformations without imposing the usual horizontality conditions. We show that the gauge fields 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 Gribovs obstruction.
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