Gauge Theories: Geometry and Cohomological Invariants

We develop a geometrical structure of themanifolds and associated, respectively, withgauge symmetry and BRST symmetry. Then, we show that , where is the group of BRST transformations, is endowed with the structureof a principal fiber bundle over the base manifold. Furthermore, in this geometricalsetup, due to the nilpotency of the BRST operator, weprove that the effective action of a gauge theory is aBRST-exact term up to the classical action. Then, weconclude that the effective action where only the gaugesymmetry is fixed is cohomologically equivalent to the action where the gauge and the BRSTsymmetries are fixed.