An algebraic interpretation of quantized gauge interactions and BRS transformations

Summary

In an algebraic approach, nonlinear gauge interactions and Becchi-Rouet-Stora transformations arise as two isomorphic aspects of a gauge algebra—consisting of the homogeneous and inhomogeneous structures in the tangent algebra of a Lie group. The quantized representatives are formulated in the associated quantum algebra which has to be of Bose and Fermi type for the gauge vectors and the Faddeev-Popov vectors, respectively. The implementation of the time reflection (hermiticity) properties requires a doubling for the Faddeev-Popov sector of the theory or—equivalently—a 2nd-order time derivative formalism.