1994/05/17 by Glenn Barnich, G. Barnich, Friedemann Brandt +3 · 1 voice
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1007/bf02099464
arxiv published 1994/05/17 · arxiv updated 1994/06/13 · openalex publication_date 1995/11/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Hk(δ|d) in negative ghost degree -k (k>0), where δ is the Koszul-Tate differential associated with the stationary surface. The cohomological group H1(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 Hk(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 Hk(δ|d) (k>2) are shown to vanish for standard irreducible gauge theories. The group H2(δ|d) is then calculated explicitly for electromagnetism, Yang-Mills models and Einstein gravity. The invariance of the groups Hk(s|d) under the introduction of non minimal variables and of auxiliary