Communications in Mathematical Physics

, Volume 254, Issue 3, pp 581–601 | Cite as

Hamiltonian BRST and Batalin-Vilkovisky Formalisms for Second Quantization of Gauge Theories

  • Glenn BarnichEmail author
  • Maxim Grigoriev


Gauge theories that have been first quantized using the Hamiltonian BRST operator formalism are described as classical Hamiltonian BRST systems with a BRST charge of the form Open image in new window and with natural ghost and parity degrees for all fields. The associated proper solution of the classical Batalin-Vilkovisky master equation is constructed from first principles. Both of these formulations can be used as starting points for second quantization. In the case of time reparametrization invariant systems, the relation to the standard Open image in new window master action is established.


Neural Network Statistical Physic Complex System Gauge Theory Nonlinear Dynamics 
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  1. 1.
    Thorn, C.B.: Perturbation theory for quantized string fields. Nucl. Phys. B287, 61 (1987)Google Scholar
  2. 2.
    Bochicchio, M.: Gauge fixing for the field theory of the bosonic string. Phys. Lett. B193, 31 (1987)Google Scholar
  3. 3.
    Bochicchio, M.: String field theory in the Siegel gauge. Phys. Lett. B188, 330 (1987)Google Scholar
  4. 4.
    Thorn, C.B.: String field theory. Phys. Rept. 175, 1–101 (1989)Google Scholar
  5. 5.
    Siegel, W.: Introduction to string field theory. Singapore: World Scientific, 1988, and, 2001
  6. 6.
    Witten, E.: Noncommutative geometry and string field theory. Nucl. Phys. B268, 253 (1986)Google Scholar
  7. 7.
    Batalin, I.A., Vilkovisky, G.A.: Gauge algebra and quantization. Phys. Lett. B102, 27–31 (1981)Google Scholar
  8. 8.
    Batalin, I.A., Vilkovisky, G.A.: Feynman rules for reducible gauge theories. Phys. Lett. B120, 166–170 (1983)Google Scholar
  9. 9.
    Batalin, I.A., Vilkovisky, G.A.: Quantization of gauge theories with linearly dependent generators. Phys. Rev. D28, 2567–2582 (1983)Google Scholar
  10. 10.
    Batalin, I.A., Vilkovisky, G.A.: Closure of the gauge algebra, generalized Lie equations and Feynman rules. Nucl. Phys. B234, 106–124 (1984)Google Scholar
  11. 11.
    Batalin, I.A., Vilkovisky, G.A.: Existence theorem for gauge algebra. J. Math. Phys. 26, 172–184 (1985)Google Scholar
  12. 12.
    Henneaux, M., Teitelboim, C.: Quantization of Gauge Systems. Princeton, NJ: Princeton University Press, 1992Google Scholar
  13. 13.
    Gomis, J., París, J., Samuel, S.: Antibracket, antifields and gauge theory quantization. Phys. Rept. 259, 1–145 (1995)Google Scholar
  14. 14.
    Fradkin, E.S., Vilkovisky, G.A.: Quantization of relativistic systems with constraints. Phys. Lett. B55, 224 (1975)Google Scholar
  15. 15.
    Batalin, I.A., Vilkovisky, G.A.: Relativistic S matrix of dynamical systems with boson and fermion constraints. Phys. Lett. B69, 309–312 (1977)Google Scholar
  16. 16.
    Fradkin, E.S., Fradkina, T.E.: Quantization of relativistic systems with boson and fermion first and second class constraints. Phys. Lett. B72, 343 (1978)Google Scholar
  17. 17.
    Henneaux, M.: Hamiltonian form of the path integral for theories with a gauge freedom. Phys. Rept. 126, 1 (1985)Google Scholar
  18. 18.
    Kibble, T.W.B.: Geometrization of quantum mechanics. Commun. Math. Phys. 65, 189 (1979)Google Scholar
  19. 19.
    Heslot, A.: Quantum mechanics as a classical theory. Phys. Rev. D 31, 1341–1348 (1985)Google Scholar
  20. 20.
    Hatfield, B.: Quantum field theory of point particles and strings. Frontiers in physics. Redwood City, USA: Addison-Wesley, 1992, 75Google Scholar
  21. 21.
    Schilling, T.: Geometry of quantum mechanics. PhD thesis, The Pennsylvania State University, 1996Google Scholar
  22. 22.
    Ashtekar, A., Schilling, T.A.: Geometrical formulation of quantum mechanics. P. Harvey (ed.), Berlin: Springer-Verlag, 1998Google Scholar
  23. 23.
    Zwiebach, B.: Closed string field theory: Quantum action and the B-V master equation. Nucl. Phys. B390, 33–152 (1993)Google Scholar
  24. 24.
    Siegel, W.: Relation between Batalin-Vilkovisky and first quantized style BRST. Int. J. Mod. Phys. A4, 3705 (1989)Google Scholar
  25. 25.
    Dayi, O.F.: Gauge fixing of point particle and open bosonic string field theory actions of Neveu and West. Nuovo Cim. A101, 1 (1989)Google Scholar
  26. 26.
    Dayi, O.F.: A general solution of the BV master equation and BRST field theories. Mod. Phys. Lett. A8, 2087–2098 (1993)Google Scholar
  27. 27.
    Grigoriev, M.A., Semikhatov, A.M., Tipunin, I.Y.: BRST formalism and zero locus reduction. J. Math. Phys. 42, 3315–3333 (2001)Google Scholar
  28. 28.
    Batalin, I., Fradkin, E.: Operatorial quantization of dynamical systems subject to constraints. A further study of the construction. Ann. Inst. Henri Poincaré (Phys. Theor.) 49, 145–214 (1988)Google Scholar
  29. 29.
    Siegel, W.: Batalin-Vilkovisky from Hamiltonian BRST. Int. J. Mod. Phys. A4, 3951 (1989)Google Scholar
  30. 30.
    Batlle, C., Gomis, J., París, J., Roca, J.: Lagrangian and Hamiltonian BRST formalisms. Phys. Lett. B224, 288 (1989)Google Scholar
  31. 31.
    Fisch, J.M.L., Henneaux, M.: Antibracket - antifield formalism for constrained Hamiltonian systems. Phys. Lett. B226, 80 (1989)Google Scholar
  32. 32.
    Henneaux, M.: Elimination of the auxiliary fields in the antifield formalism. Phys. Lett. B238, 299 (1990)Google Scholar
  33. 33.
    Batlle, C., Gomis, J., París, J., Roca, J.: Field - antifield formalism and Hamiltonian BRST approach. Nucl. Phys. B329, 139–154 (1990)Google Scholar
  34. 34.
    Dresse, A., Grégoire, P., Henneaux, M.: Path integral equivalence between the extended and nonextended Hamiltonian formalisms. Phys. Lett. B245, 192 (1990)Google Scholar
  35. 35.
    Dresse, A., Fisch, J.M.L., Grégoire, P., Henneaux, M.: Equivalence of the Hamiltonian and Lagrangian path integrals for gauge theories. Nucl. Phys. B354, 191–217 (1991)Google Scholar
  36. 36.
    Grigorian, G.V., Grigorian, R.P., Tyutin, I.V.: Equivalence of Lagrangian and Hamiltonian BRST quantization. Systems with first-class constraints. Sov. J. Nucl. Phys. 53, 1058–1061 (1991)Google Scholar
  37. 37.
    Grigoriev, M.A., Damgaard, P.H.: Superfield BRST charge and the master action. Phys. Lett. B474, 323–330 (2000)Google Scholar
  38. 38.
    Siegel, W.: Boundary conditions in first quantization. Int. J. Mod. Phys. A6, 3997–4008 (1991)Google Scholar
  39. 39.
    Barnich, G., Henneaux, M.: Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket. J. Math. Phys. 37, 5273–5296 (1996)Google Scholar
  40. 40.
    Deligne, P., Morgan, W.: Quantum Fields and Strings: A Course for Mathematicians, Part I, Chapter-Notes on Supersymmetry. Providence, RI: American Mathematical Society, 1999, pp. 41–98Google Scholar
  41. 41.
    Gaberdiel, M.R., Zwiebach, B.: Tensor constructions of open string theories I: Foundations. Nucl. Phys. B505, 569–624 (1997)Google Scholar
  42. 42.
    Sen, A., Zwiebach, B.: A note on gauge transformations in Batalin-Vilkovisky theory. Phys. Lett. B320, 29–35 (1994)Google Scholar
  43. 43.
    Grigoriev, M.A., Semikhatov, A.M., Tipunin, I.Y.: Gauge symmetries of the master action in the Batalin- Vilkovisky formalism. J. Math. Phys. 40, 1792–1806 (1999)Google Scholar
  44. 44.
    Alexandrov, M., Kontsevich, M., Schwartz, A.: and O. Zaboronsky, The geometry of the master equation and topological quantum field theory. Int. J. Mod. Phys. A12, 1405–1430 (1997)Google Scholar
  45. 45.
    Cattaneo, A.S., Felder, G.: A path integral approach to the Kontsevich quantization formula. Commun. Math. Phys. 212, 591–611 (2000)CrossRefGoogle Scholar
  46. 46.
    Batalin, I., Marnelius, R.: Generalized Poisson sigma models. Phys. Lett. B512, 225–229 (2001)Google Scholar
  47. 47.
    Cattaneo, A.S., Felder, G.: On the AKSZ formulation of the Poisson sigma model. Lett. Math. Phys. 56, 163–179 (2001)Google Scholar
  48. 48.
    Kobayashi, S., Nomizu, K.: Foundations of differential geometry. Vol. II. New York: John Wiley & Sons, 1996 ed., Orig. published in 1969Google Scholar

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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Physique Théorique et Mathématique and International Solvay InstitutesUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Tamm Theory DepartmentLebedev Physical InstituteMoscowRussia

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