Local BRST cohomology in the antifield formalism: I. General theorems

We establish general theorems on the cohomologyH ^* (s/d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of localp-forms depending on the fields and the antifields (=sources for the BRST variations). It is shown thatH ^–k (s/d) is isomorphic toH _k (/d) in negative ghost degree–k (k>0), where is the Koszul-Tate differential associated with the stationary surface. The cohomology groupH ₁ (/d) in form degreen is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether's theorem. More generally, the groupH _k (/d) in form degreen is isomorphic to the space ofn–k forms that are closed when the equations of motion hold. The groupsH _k (/d)(k>2) are shown to vanish for standard irreducible gauge theories. The groupH ₂ (/d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groupsH ^k (s/d) under the introduction of non-minimal variables and of auxiliary fields is also demonstrated. In a companion paper, the general formalism is applied to the calculation ofH ^k (s/d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group.Supported by Deutsche Forschungsgemeinschaft