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

DOI10.1007/BF02099464zbMATH Open0844.53059arXivhep-th/9405109OpenAlexW3103680067WikidataQ59307851 ScholiaQ59307851MaRDI QIDQ1903333

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Publication date: 27 August 1996

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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 $H_k(delta|d)$ in negative ghost degree $-k(k>0)$, where $delta$ is the Koszul-Tate differential associated with the stationary surface. The cohomological group $H_1(delta|d)$ 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 $H_k(delta|d)$ in form degree $n$ is isomorphic to the space of $n-k$ forms that are closed when the equations of motion hold. The groups $H_k(delta|d)$ $(k>2)$ are shown to vanish for standard irreducible gauge theories. The group $H_2(delta|d)$ 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

Full work available at URL: https://arxiv.org/abs/hep-th/9405109

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