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

G. Barnich; F. Brandt; M. Henneaux

doi:10.1007/BF02099464

paper

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

arXiv:hep-th/9405109 · doi:10.1007/BF02099464

Abstract

We establish general theorems on the cohomology $H^{*} (s ∣ d)$ 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 $H^{- k} (s ∣ d)$ is isomorphic to $H_{k} (δ ∣ d)$ in negative ghost degree $- k (k > 0)$ , where $δ$ is the Koszul-Tate differential associated with the stationary surface. The cohomological group $H_{1} (δ ∣ d)$ 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 $H_{k} (δ ∣ d)$ in form degree $n$ is isomorphic to the space of $n - k$ forms that are closed when the equations of motion hold. The groups $H_{k} (δ ∣ d)$ $(k > 2)$ are shown to vanish for standard irreducible gauge theories. The group $H_{2} (δ ∣ d)$ is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups $H^{k} (s ∣ d)$ under the introduction of non minimal variables and of auxiliary

48 pages LaTeX file, ULB-PMIF-94/06 NIKEF-H 94-13 (minor changes in section 10)

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

Abstract

References in corpus (8)

Cited by in corpus (196)