Communications in Mathematical Physics

, Volume 174, Issue 1, pp 93–116 | Cite as

Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory

  • Glenn Barnich
  • Friedemann Brandt
  • Marc Henneaux


Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differentials modulo the exterior space-time derivatived for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditionssa+db=0 depending non-trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency conditionsa+db=0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature or Chern-Simons terms.


Ghost Gauge Group Quantum Computing Companion Paper High Derivative 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barnich, G., Brandt, F., Henneaux, M.: Local BRST cohomology in the antifield formalism: I. General theorems. Commun. Math. Phys.174, 57–91 (1995)Google Scholar
  2. 2.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems. Princeton, NJ: Princeton University Press, 1992Google Scholar
  3. 3.
    Henneaux, M.: Phys. Lett.B313, 35 (1993)Google Scholar
  4. 4.
    Dixon, J.A.: Cohomology and Renormalization of Gauge Theories I, II, III, Unpublished preprints (1976–1979); Commun. Math. Phys.139, 495 (1991)Google Scholar
  5. 5.
    Bandelloni, G.: J. Math. Phys.27, 2551 (1986),28, 2775 (1987)Google Scholar
  6. 6.
    Brandt, F., Dragon, N., Kreuzer, M.: Phys. Lett.B231, 263 (1989)Google Scholar
  7. 7.
    Brandt, F., Dragon, N., Kreuzer, M.: Nucl. Phys.B332, 224 (1990)Google Scholar
  8. 8.
    Brandt, F., Dragon, N., Kreuzer, M.: Nucl. Phys.B332, 250 (1990)Google Scholar
  9. 9.
    Dubois-Violette, M., Henneaux, M., Talon, M., Viallet, C.M.: Phys. Lett.B289, 361 (1992)Google Scholar
  10. 10.
    Joglekar, S.D., Lee, B.W.: Ann. Phys. (NY)97, 160 (1976)Google Scholar
  11. 11.
    Collins, J.C.: Renormalization. Cambridge: Cambridge U.P., 1984Google Scholar
  12. 12.
    Collins, J.C., Scalise, R.J.: The renormalization of composite operators in Yang-Mills theories using general covariant gauge. Phys. Rev.D50, 4117 (1994)Google Scholar
  13. 13.
    Brandt, F.: Phys. Lett.B320, 57 (1994)Google Scholar
  14. 14.
    Kluberg-Stern, H., Zuber, J.B.: Phys. Rev.D12, 467, 482, 3159 (1975)Google Scholar
  15. 15.
    Zinn-Justin, J.: Quantum Field Theory and Critical Phenomena. 2 ed. Oxford: Clarendon Press 1993Google Scholar
  16. 16.
    Barnich, G., Henneaux, M.: Phys. Rev. Lett.72, 1588 (1994)Google Scholar
  17. 17.
    Becchi, C., Rouet, A., Stora, R.: Commun. Math. Phys.42, 127 (1975); Ann. Phys. (N.Y.)98, 287 (1976)Google Scholar
  18. 18.
    Tyutin, I.V.: Gauge Invariance in Field Theory and Statistical Mechanics. Lebedev preprint FIAN n0 39 (1975)Google Scholar
  19. 19.
    Henneaux, M.: Commun. Math. Phys.140, 1 (1991)Google Scholar
  20. 20.
    Stora, R.: Continuum Gauge Theories. In: New Developments in Quantum Field Theory and Statistical Mechanics, Lévy M., Mitter, P. (eds.) London: Plenum, 1977; Algebraic Structure and Topological Origin of Anomalies. In: Progress in Gauge Field Theory, G. 't Hooft et al. (eds.) London: Plenum, 1984.Google Scholar
  21. 21.
    Zumino, B.: Chiral Anomalies and Differential Geometry in Relativity, Groups and Topology II. B.S. De Witt, R. Stora Amsterdam (eds.) North-Holland, 1984Google Scholar
  22. 22.
    Baulieu, L.: Phys. Rep.129, 1 (1985)Google Scholar
  23. 23.
    Dubois-Violette, M., Talon, M., Viallet, C.M.: Phys. Lett.B158, 231 (1985); Commun. Math. Phys.102, 105 (1985)Google Scholar
  24. 24.
    Barnich, G., Henneaux, M.: Phys. Lett.B311, 123 (1993)Google Scholar
  25. 25.
    Chevalley, C., Eilenberg, S.: Trans. Am. Math. Soc.63, 589 (1953); Koszul, J.L.: Bull. Soc. Math. France78, 65 (1950); Hochschild, G., Serre, J.P.: Ann. Math.57, 59 (1953)Google Scholar
  26. 26.
    Barnich, G., Brandt, F., Henneaux, M.: Conserved currents and gauge invariance in Yang-Mills theory. Phys. Lett.B346, 81 (1995)Google Scholar
  27. 27.
    Delduc, F., Lucchesi, C., Piguet, O., Sorella, S.P.: Nucl. Phys.B346, 313 (1990); Blasi, A., Piguet, O., Sorella, S.P.: Nucl. Phys.B356, 154 (1991); Lucchesi, C., Piguet, O.: Nucl. Phys.B381, 281 (1992)Google Scholar
  28. 28.
    Bandelloni, G., Blasi, A., Becchi, C., Collina, R.: Ann. Inst. Henri Poincaré28, 225, 255 (1978)Google Scholar
  29. 29.
    Bonora, L., Cotta-Ramusino, P.: Commun. Math. Phys.87, 589 (1983)Google Scholar
  30. 30.
    Baulieu, L., Thierry-Mieg, J.: Nucl. Phys.187, 477 (1982); Baulieu, L.: Nucl. Phys.B241, 557 (1984)Google Scholar
  31. 31.
    Thierry-Mieg, J.: Phys. Lett147B, 430 (1984)Google Scholar
  32. 32.
    Barnich, G., Brandt, F., Henneaux, M.: Local BRST cohomology in Einstein-Yang-Mills theory, to appear in Nucl. Phys. BGoogle Scholar
  33. 33.
    Anderson, I.M.: The variational bicomplex. Boston HA: Academic Press 1994; Contemp. Math132, 51 (1992)Google Scholar

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

Personalised recommendations