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


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.


Gauge Theory Ghost Gauge Group Companion Paper General Theorem 
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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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