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 ...

We apply Dirac’s gauge fixing procedure to (2+1)-gravity with vanishing cosmological constant. For general gauge fixing conditions based on two point particles, this yields explicit expressions for the Dirac bracket. We explain how gauge fixing is related to the introduction of an observer into the theory and show that the Dirac bracket is determined by a classical dynamical r-matrix. Its two d...