Superfiber bundle structure of gauge theories with Faddeev–Popov fields

Abstract

In this work the mathematical structure of principal superfiber bundle Ps is used to give a geometrical description of gauge theories. The base space of Ps is an S4,2-supermanifold Xs (four commuting and two anticommuting variables), and the structure group an Sn,0 supergroup Gs, where n is the dimension of the gauge group for the classical theory. The body of Ps is the usual principal fiber bundle P of gauge theories. Gauge and Faddeev–Popov fields arise as superfields, components of the connections in Ps, in a local coordinate system. BRS (Becchi, Rouet, and Stora) and anti-BRS transformations are gauge transformations, in Ps, of parameters the ghost and antighost superfields, respectively. In the case of soul-flat connections, which are connections in Ps coming from connections in P, the BRS and anti-BRS transformations are finite translations along the anticommuting directions of Xs, and generate an S0,2-supergroup.