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Communications in Mathematical Physics

, Volume 174, Issue 1, pp 57–91 | Cite as

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

  • Glenn Barnich
  • Friedemann Brandt
  • Marc Henneaux
Article

Abstract

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 thatHk(s/d) is isomorphic toH k (δ/d) in negative ghost degree−k (k>0), where δ is the Koszul-Tate differential associated with the stationary surface. The cohomology groupH1(δ/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 (δ/d) in form degreen is isomorphic to the space ofn−k forms that are closed when the equations of motion hold. The groupsH k (δ/d)(k>2) are shown to vanish for standard irreducible gauge theories. The groupH2(δ/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.

Keywords

Gauge Theory Ghost Gauge Group Companion Paper General Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Glenn Barnich
    • 1
  • Friedemann Brandt
    • 2
  • Marc Henneaux
    • 1
  1. 1.Faculté des SciencesUniversité Libre de BruxellesBruxellesBelgium
  2. 2.NIKHEF-HAmsterdamThe Netherlands

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