Local BRST cohomology in the antifield formalism. Pt. 1. General theorems

摘要

We establish general theorems on the cohomology H(sup *)(svertical stroke d) of the BRST differential modulo the spacetime exterior derivative, acting in the algebra of local p-forms depending on the fields and the antifields (= sources for the BRST variations). It is shown that H(sup -k)(svertical stroke d) is isomorphic H(sub k)((delta)vertical stroke d) in negative ghost degree -k (k > 0), where (delta) is the Koszul-Tate differential associated with the stationary surface. The cohomological group H(sub 1)((delta)vertical stroke d) in form degree n is proved to be isomorphic to the space of constants of the motion, thereby providing a cohomological reformulation of Noether theorem. More generally, the group H(sub k)((delta)vertical stroke d) in form degree n is isomorphic to the space of n - k forms that are closed when the equations of motion hold. The groups H(sub k)((delta)vertical stroke d) (k > 2) are shown to vanish for standard irreducible gauge theories. The group H(sub 2)((delta)vertical stroke d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups H(sup k)(svertical stroke 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 of H(sup k)(svertical stroke d) in Yang-Mills theory, which is carried out in detail for an arbitrary compact gauge group. (orig.). (Atomindex citation 27:011790)