Local BRST cohomology in gauge theories

Physics Report

Volumn 338, Issue 5, 2000, Pages 439-569

  Barnich, Glenn ^a,b   Brandt, Friedemann ^c   Henneaux, Marc ^a,d  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UNIVERSITY OF VALENCIA   (Spain)

^c LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^d CENTRO DE ESTUDIOS CIENTÍFICOS CECS   (Chile)

Author keywords

Anomalies; BRST cohomology; Gauge field theories; Locality

Indexed keywords

EID: 0001098285     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(00)00049-1     Document Type: Review

References (232)

1. M. Alexandrov, M. Kontsevich, A. Schwartz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12 (1997) 1405 hep-th/9502010.
2. L. Alvarez-Gaumé, E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269.
3. S.C. Anco, New spin-one gauge theory in three dimensions, J. Math. Phys. 36 (1995) 6553.
4. S.C. Anco, Novel generalization of three-dimensional Yang-Mills theory, J. Math. Phys. 38 (1997) 3399.
5. I.M. Anderson, T. Duchamp, On the existence of global variational principles, Am. J. Math. 102 (1980) 781.
6. I.M. Anderson, Introduction to the variational bicomplex, Contemp. Math. 132 (1992) 51.
7. D. Anselmi, Removal of divergences with the Batalin-Vilkovisky formalism, Class. Quant. Grav. 11 (1994) 2181.
8. D. Anselmi, More on the subtraction algorithm, Class. Quant. Grav. 12 (1995) 319 hep-th/9407023.
9. R. Arnowitt, S. Deser, Interaction between gauge vector fields, Nucl. Phys. 49 (1963) 133.
10. B. Geyer, P.M. Lavrov, D. Mülsch, Osp (1, 1)-covariant quantization of reducible massive gauge theories, J. Math. Phys. 40 (1999) 6189, hep-th/9806117.
11. G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 1, classical theory and the properties of ghost states, Ann. Inst. Henri Poincaré Phys. Theor. 28 (1978) 225.*
12. G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 2, renormalization, Ann. Inst. Henri Poincaré Phys. Theor. 28 (1978) 255.*
13. G. Bandelloni, Yang-Mills cohomology in four-dimensions, J. Math. Phys. 27 (1986) 2551.
14. G. Bandelloni, Nonpolynomial Yang-Mills Local Cohomology, J. Math. Phys. 28 (1987) 2775.
15. G. Bandelloni, S. Lazzarini, Diffeomorphism cohomology in Beltrami parametrization, J. Math. Phys. 34 (1993) 5413.
16. G. Bandelloni, S. Lazzarini, Diffeomorphism cohomology in Beltrami parametrization. 2: the 1 forms, J. Math. Phys. 36 (1995) 1 (hep-th/9410190).
17. W.A. Bardeen, Anomalous ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848.
18. W.A. Bardeen, B. Zumino, Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B 244 (1984) 421.
19. G. Barnich, M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 (hep-th/9304057).
20. G. Barnich, M. Henneaux, R. Tatar, Consistent interactions between gauge fields and local BRST cohomology: the example of Yang-Mills models, Int. J. Mod. Phys. D 3 (1994) 139 (hep-th/9307155).
21. G. Barnich, M. Henneaux, Renormalization of gauge invariant operators and anomalies in Yang-Mills theory, Phys. Rev. Lett. 72 (1994) 1588 (hep-th/9312206).
22. G. Barnich, F. Brandt, M. Henneaux, Conserved currents and gauge invariance in Yang-Mills theory, Phys. Lett. B 346 (1995) 81 (hep-th/9411202).
23. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. I. General theorems, Commun. Math. Phys. 174 (1995) 57 (hep-th/9405109).
24. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory, Commun. Math. Phys. 174 (1995) 93 (hep-th/9405194).
25. G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in Einstein Yang-Mills theory, Nucl. Phys. B 455 (1995) 357 (hep-th/9505173).
26. G. Barnich, M. Henneaux, T. Hurth, K. Skenderis, Cohomological analysis of gauged-fixed gauge theories, (hep-th/9910201) to appear in Phys. Lett. B.
27. I.A. Batalin, G.A. Vilkovisky, Relativistic S matrix of dynamical systems with Boson and fermion constraints, Phys. Lett. 69 B (1977) 309.
28. I.A. Batalin, G.A. Vilkovisky, Gauge algebra and quantization, Phys. Lett. 102 B (1981) 27***.
29. I.A. Batalin, G.A. Vilkovisky, Feynman rules for reducible gauge theories, Phys. Lett. B 120 (1983) 166.
30. I.A. Batalin, G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567*.
31. I.A. Batalin, E.S. Fradkin, A generalized canonical formalism and quantization of reducible gauge theories, Phys. Lett. 122 B (1983) 157.
32. I.A. Batalin, G.A. Vilkovisky, Closure of the gauge algebra, generalized Lie equations and Feynman rules, Nucl. Phys. B 234 (1984) 106.
33. I.A. Batalin, G.A. Vilkovisky, Existence theorem for gauge algebra, J. Math. Phys. 26 (1985) 172.*
34. I.A. Batalin, P.M. Lavrov, I.V. Tyutin, Remarks on the Sp(2) covariant lagrangian quantization of gauge theories, J. Math. Phys. 32 (1991) 2513.
35. I.A. Batalin, K. Bering, P.H. Damgaard, Gauge independence of the Lagrangian path integral in a higher-order formalism Phys. Lett. B 389 (1996) 673 (hep-th/9609037).
36. I. Batalin, R. Marnelius, General quantum antibrackets, hep-th/9905083.
37. I. Batalin, R. Marnelius, Open group transformations within the Sp(2)-formalism, hep-th/9909223.
38. L. Baulieu, J. Thierry-Mieg, Algebraic structure of quantum gravity and the classification of the gravitational anomalies, Phys. Lett. B 145 (1984) 53.
39. L. Baulieu, Algebraic construction of gauge invariant theories, PAR-LPTHE 84/4 Based on lectures given at Cargèse Summer School: Particles and Fields, Cargèse, France, July 6-22, 1983.*
40. L. Baulieu, Anomalies and gauge symmetry, Nucl. Phys. B 241 (1984) 557.
41. L. Baulieu, Perturbative gauge theories, Phys. Rep. 129 (1985) 1.
42. L. Baulieu, C. Becchi, R. Stora, On the covariant quantization of the free bosonic string, Phys. Lett. B 180 (1986) 55.
43. L. Baulieu, M. Bellon, R. Grimm, BRS symmetry of supergravity in superspace and its projection to component formalism, Nucl. Phys. B 294 (1987) 279.
44. L. Baulieu, M. Bellon, Beltrami parametrization and string theory, Phys. Lett. B 196 (1987) 142.
45. C. Becchi, A. Rouet, R. Stora, The Abelian Higgs-Kibble model, unitarity of the S operator, Phys. Lett. B 52 (1974) 344.
46. C. Becchi, A. Rouet, R. Stora, Renormalization of the Abelian Higgs-Kibble model, Commun. Math. Phys. 42 (1975) 127.
47. C. Becchi, A. Rouet, R. Stora, Renormalization of gauge theories, Ann. Phys. 98 (1976) 287.***
48. C. Becchi, A. Rouet, R. Stora, Renormalizable theories with symmetry breaking, in: E. Tirapegui (Ed.), Field Theory Quantization and Statistical Physics, Reidel, Dordrecht, 1981 (preprint dated 1975).
49. C. Becchi, On the covariant quantization of the free string: the conformal structure, Nucl. Phys. B 304 (1988) 513.
50. F.A. Berends, G.J. Burgers, H. van Dam, On the theoretical problems in constructing interactions involving higher spin massless particles, Nucl. Phys. B 260 (1985) 295.*
51. K. Bering, P.H. Damgaard, J. Alfaro, Algebra of Higher Antibrackets, Nucl. Phys. B 478 (1996) 459 (hep-th/9604027).
52. R.A. Bertlmann, Anomalies in quantum field theory, Clarendon Press, Oxford, UK, 1996, 566 p. (International Series of Monographs on Physics, Vol. 91).
53. P.A. Blaga, L. Tǎtaru, I.V. Vancea, BRST cohomology for 2D gravity, Rom. J. Phys. 40 (1995) 773 (hep-th/9504037).
54. G. Bonneau, Some fundamental but elementary facts on renormalization and regularization: a critical review of the eighties, Int. J. Mod. Phys. A 5 (1990) 3831.
55. L. Bonora, P. Cotta-Ramusino, Some remarks On BRS transformations, anomalies and the cohomology of the lie algebra of the group of gauge transformations, Commun. Math. Phys. 87 (1983) 589.**
56. L. Bonora, P. Cotta-Ramusino, C. Reina, Conformal anomaly and cohomology, Phys. Lett. B 126 (1983) 305.
57. L. Bonora, P. Pasti, M. Tonin, The anomaly structure of theories with external gravity, J. Math. Phys. 27 (1986) 2259.
58. L. Bonora, P. Pasti, M. Bregola, Weyl Cocycles, Class. Quant. Gray. 3 (1986) 635.
59. L. Bonora, P. Pasti, M. Tonin, The chiral anomaly in supersymmetric gauge theories coupled to supergravity, Phys. Lett. B 167 (1986) 191.
60. N. Bourbaki, Groupes et Algèbres de Lie I, Hermann, Paris, 1960.
61. F. Brandt, N. Dragon, M. Kreuzer, All consistent Yang-Mills Anomalies, Phys. Lett. B 231 (1989) 263.
62. F. Brandt, N. Dragon, M. Kreuzer, Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B 332 (1990) 224.
63. F. Brandt, N. Dragon, M. Kreuzer, Lie algebra cohomology, Nucl. Phys. B 332 (1990) 250.
64. F. Brandt, N. Dragon, M. Kreuzer, The gravitational anomalies, Nucl. Phys. B 340 (1990) 187.
65. F. Brandt, Antifield dependence of anomalies Phys. Lett. B 320 (1994) 57 (hep-th/9310080).
66. F. Brandt, Anomaly candidates and invariants of D = 4, N = 1 supergravity theories, Class. Quant. Grav. 11 (1994) 849 (hep-th/9306054).
67. F. Brandt, W. Troost, A. Van Proeyen, The BRST-antibracket cohomology of 2d gravity, Nucl. Phys. B 464 (1996) 353 (hep-th/9509035).
68. F. Brandt, W. Troost, A. Van Proeyen, Background charges and consistent continuous deformations of 2d gravity theories, Phys. Lett. B 374 (1996) 31 (hep-th/9510195).
69. F. Brandt, Local BRST cohomology in minimal D = 4, N = 1 supergravity, Annals Phys. 259 (1997) 253 (hep-th/9609192).
70. F. Brandt, J. Gomis, J. Simón, Cohomological analysis of bosonic D-strings and 2d sigma models coupled to abelian gauge fields, Nucl. Phys. B 523 (1998) 623 (hep-th/9712125).
71. A.D. Browning, D. McMullan, The Batalin, Fradkin, and Vilkovisky formalism for higher order theories, J. Math. Phys. 28 (1987) 438.
72. R.L. Bryant, P.A. Griffiths, Characteristic cohomology of differential systems I: general theory, J. Am. Math. Soc. 8 (1995) 507.
73. I.L. Buchbinder, B.R. Mistchuk, V.D. Pershin, BRST - BFV analysis of anomalies in bosonic string theory interacting with background gravitational field, Phys. Lett. B 353 (1995) 457 (hep-th/9502087).
74. D.M. Capper, M.J. Duff, Trace anomalies in dimensional regularization, Nuovo Cim. 23 A (1974) 173.
75. M. Carvalho, L.C. Vilar, C.A. Sasaki, S.P. Sorella, BRS cohomology of zero curvature systems I, the complete ladder case, J. Math. Phys. 37 (1996) 5310 (hep-th/9509047).
76. C. Chevalley, S. Eilenberg, Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc. 63 (1948) 85.
77. J.C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion, University Press, Cambridge, UK, 1984, 380 pp. (Chapter 12.6).
78. J.C. Collins, R.J. Scalise, The renormalization of composite operators in Yang-Mills theories using general covariant gauge, Phys. Rev. D 50 (1994) 4117 (hep-ph/9403231).
79. S. Deser, M.J. Duff, C.J. Isham, Nonlocal conformal anomalies, Nucl. Phys. B 111 (1976) 45.
80. S. Deser, R. Jackiw, S. Templeton, Three-dimensional massive gauge theories, Phys. Rev. Lett. 48 (1982) 975.
81. S. Deser, A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 (hep-th/9302047).
82. M. De Wilde, On the local chevalley cohomology of the dynamical lie algebra of a symplectic manifold, Lett. Math. Phys. 5 (1981) 351.
83. B. de Wit, J.W. van Holten, Covariant quantization of gauge theories with open gauge algebra, Phys. Lett. 79 B (1978) 389.*
84. B.S. DeWitt, Quantum theory of gravity II, the manifestly covariant theory, Phys. Rev. 162 (1967) 1195.
85. L.A. Dickey, On exactness of the variational bicomplex, Contemp. Math. 132 (1992) 307.
86. J.A. Dixon, J.C. Taylor, Renormalization of Wilson operators in gauge theories, Nucl. Phys. B 78 (1974) 552.
87. J.A. Dixon, Field redefinition and renormalization in gauge theories, Nucl. Phys. B 99 (1975) 420.*
88. J.A. Dixon, Cohomology and renormalization of gauge theories, 1, unpublished preprint.
89. J.A. Dixon, Cohomology and renormalization of gauge theories, 2, HUTMP 78/B64.
90. W.S. Deans, J.A. Dixon, Theory of gauge invariant operators: their renormalization and S matrix elements, Phys. Rev. D 18 (1978) 1113.
91. J. Dixon, M. Ramon Medrano, Anomalies of higher-dimension composite fields, Phys. Rev. D 22 (1980) 429.
92. J.A. Dixon, Calculation of BRS cohomology with spectral sequences, Commun. Math. Phys. 139 (1991) 495.**
93. N. Dragon, Regular gravitational Lagrangians, Phys. Lett. B 276 (1992) 31.
94. N. Dragon, BRS symmetry and cohomology, Lectures given at First National Summer School for Graduate Students, Saalburg 1995, hep-th/9602163.*
95. N. Dragon, T. Hurth, P. van Nieuwenhuizen, Polynomial form of the Stueckelberg model, Nucl. Phys. Proc. Suppl. 56 B (1997) 318 (hep-th/9703017).
96. M. Dubois-Violette, M. Talon, C.M. Viallet, New results on BRS cohomology in gauge theory, Phys. Lett. 158 B (1985) 231.
97. M. Dubois-Violette, M. Talon, C.M. Viallet, BRS algebras: analysis of the consistency equations in gauge theory, Commun. Math. Phys. 102 (1985) 105.**
98. M. Dubois-Violette, M. Talon, C.M. Viallet, Anomalous terms in gauge theory: relevance of the structure group, Ann. Inst. Henri Poincaré Phys. Theor. 44 (1986) 103.
99. M. Dubois-Violette, Systèmes dynamiques contraints: l'approche homologique, Ann. Inst. Fourier 37 (1987) 45.
100. M. Dubois-Violette, M. Henneaux, M. Talon, C. Viallet, Some results on local cohomologies in field theory, Phys. Lett. B 267 (1991) 81.
101. M. Dubois-Violette, M. Henneaux, M. Talon, C. Viallet, General solution of the consistency equation, Phys. Lett. B 289 (1992) 361 (hep-th/9206106).
102. L.D. Faddeev, V.N. Popov, Feynman diagrams for the Yang-Mills field, Phys. Lett. B 25 (1967) 29.
103. R. Ferrari, P.A. Grassi, Constructive algebraic renormalization of the Abelian Higgs-Kibble model, Phys. Rev. D 60 (1999) 065010 (hep-th/9807191).
104. R.P. Feynman, Quantum theory of gravitation, Acta Phys. Polon. 24 (1963) 697.
105. J. Fisch, M. Henneaux, J. Stasheff, C. Teitelboim, Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts, Commun. Math. Phys. 120 (1989) 379.
106. J.M.L. Fisch, M. Henneaux, Homological perturbation theory and the algebraic structure of the antifield - antibracket formalism for gauge theories, Commun. Math. Phys. 128 (1990) 627.
107. E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints, Phys. Lett. B 55 (1975) 224.
108. E.S. Fradkin, M.A. Vasilev, Hamiltonian formalism, quantization and S matrix for supergravity, Phys. Lett. B 72 (1977) 70.
109. E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN-TH-2332.
110. E.S. Fradkin, T.E. Fradkina, Quantization of relativistic systems with boson and fermion first and second class constraints, Phys. Lett. 72 B (1978) 343.
111. D.Z. Freedman, P.K. Townsend, Antisymmetric tensor gauge theories and nonlinear sigma models, Nucl. Phys. B 177 (1981) 282.
112. T. Fujiwara, H. Suzuki, K. Wu, Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories, hep-lat/9906015.
113. J.A. Garcia, B. Knaepen, Couplings between generalized gauge fields, Phys. Lett. B 441 (1998) 198 (hep-th/9807016).
114. I.M. Gel'fand, I.Ya. Dorfman, Hamiltonian operators and associated algebraic structures, Funct. Anal. Appl. 13 (1979) 174.
115. H. Georgi, Thoughts on effective field theory, Nucl. Phys. Proc. Suppl. 29 BC (1992) 1.
116. J. Gomis, J. París, S. Samuel, Antibracket, antifields and gauge theory quantization Phys. Rep. 259 (1995) 1 (hep-th/9412228].*
117. J. Gomis, J. París, Perturbation theory and locality in the field - antifield formalism, J. Math. Phys. 34 (1993) 2132.
118. J. Gomis, S. Weinberg, Are nonrenormalizable gauge theories renormalizable? Nucl. Phys. B 469 (1996) 473 (hep-th/9510087).**
119. P.A. Grassi, T. Hurth, M. Steinhauser, Practical algebraic renormalization, hep-ph/9907426.
120. W. Greub, S. Halperin, R. Vanstone, in: S. Eilenberg, H. Bass (Eds.), Connections, Curvature and Cohomology, Vol. III: Cohomology of Principal Bundles and Homogeneous Spaces, Pure and Applied Mathematics, (A Series of Monographs and Textbooks), Vol. 47, Academic Press, New York, 1976.
121. M.A. Grigorev, P.H. Damgaard, Superfield BRST charge and the master action, hep-th/9911092.
122. M.A. Grigorev, A.M. Semikhatov, I.Y. Tipunin, BRST formalism and zero locus reduction, hep-th/0001081.
123. V.K.A.M. Gugenheim, J.P. May, On the theory and applications of torsion products, Mem. AMS 142 (1974).
124. V.K.A.M. Gugenheim, On a perturbation theory for the homology of a loop space, J. Pure Appl. Alg. 25 (1982) 197.
125. ∞ -structures, Bull. Soc. Math. Belgique 38 (1986) 237.
126. V.K.A.M. Gugenheim, L. Lambe, Applications of perturbation theory to differential homological algebra, Ill. J. Math. 33 (1989) 556.
127. V.K.A.M. Gugenheim, L. Lambe, J.D. Stasheff, Applications of perturbation theory to differential homological algebra II, Ill. J. Math. 34 (1990) 485.
128. B.W. Harris, J. Smith, Anomalous dimension of the gluon operator in pure Yang-Mills theory, Phys. Rev. D 51 (1995) 4550 (hep-ph/9409405).
129. M. Henneaux, Hamiltonian form of the path integral for theories with a gauge freedom, Phys. Rep. 126 (1985) 1.
130. M. Henneaux, C. Teitelboim, BRST cohomology in classical mechanics, Commun. Math. Phys. 115 (1988) 213.
131. M. Henneaux, Lectures on the antifield - BRST formalism for gauge theories, Lectures given at 20th GIFT Int. Seminar on Theoretical Physics, Jaca, Spain, Jun 5-9, 1989, and at CECS, Santiago, Chile, June/July 1989, Nucl. Phys. B (Proc. Suppl.) A 18 (1990) 47.
132. M. Henneaux, Space-time locality of the BRST formalism, Commun. Math. Phys. 140 (1991) 1.
133. M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, University Press, Princeton, USA, 1992, 520 pp.
134. M. Henneaux, Remarks on the renormalization of gauge invariant operators in Yang-Mills theory, Phys. Lett. B 313 (1993) 35 (hep-th/9306101).
135. M. Henneaux, On the gauge-fixed BRST cohomology, Phys. Lett. B 367 (1996) 163 (hep-th/9510116).
136. M. Henneaux, Consistent interactions between gauge fields: the cohomological approach, Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 93 (hep-th/9712226).
137. M. Henneaux, B. Knaepen, C. Schomblond, Characteristic cohomology of p-form gauge theories, Commun. Math. Phys. 186 (1997) 137 (hep-th/9606181).
138. M. Henneaux, B. Knaepen, C. Schomblond, BRST cohomology of the Chapline-Manton model, Lett. Math. Phys. 42 (1997) 337 (hep-th/9702042).
139. M. Henneaux, B. Knaepen, All consistent interactions for exterior form gauge fields, Phys. Rev. D 56 (1997) 6076 (hep-th/9706119).
140. M. Henneaux, A. Wilch, Local BRST cohomology of the gauged principal non-linear sigma model, Phys. Rev. D 58 (1998) 025017 (hep-th/9802118).
141. M. Henneaux, B. Knaepen, The Wess-Zumino consistency condition for p-form gauge theories, Nucl. Phys. B 548 (1999) 491 (hep-th/9812140).
142. M. Henneaux, A. Wilch, Semi-invariant terms for gauged non-linear sigma-models, Phys. Lett. B 471 (2000) 373 (hep-th/9906121).
143. G. Hirsch, Sur les groups d'homologie des espaces fibrés, Bull. Soc. Math. Belgique 6 (1953) 79.
144. G. 't Hooft, Renormalization of massless Yang-Mills fields, Nucl. Phys. B 33 (1971) 173.
145. G. 't Hooft, Renormalizable lagrangians for massive Yang-Mills fields, Nucl. Phys. B 35 (1971) 167.
146. G. 't Hooft, M. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189.
147. G. 't Hooft, M. Veltman, Combinatorics of gauge fields, Nucl. Phys. B 50 (1972) 318.
148. P.S. Howe, U. Lindström, P. White, Anomalies and renormalization in the BRST-BV framework, Phys. Lett. B 246 (1990) 430.*
149. T. Hurth, K. Skenderis, Quantum Noether method, Nucl. Phys. B 541 (1999) 566, hep-th/9803030.
150. T. Hurth, K. Skenderis, The quantum Noether condition in terms of interacting fields (hep-th/9811231).
151. S.D. Joglekar, B.W. Lee, General theory of renormalization of gauge invariant operators, Ann. Phys. 97 (1976) 160.**
152. R.E. Kallosh, Gauge invariance in supergravitation, Pisma Zh. Eksp. Teor. Fiz. 26 (1977) 575 (in Russian).
153. R.E. Kallosh, Modified Feynman rules in supergravity, Nucl. Phys. B 141 (1978) 141.
154. D.B. Kaplan, Effective field theories, Lectures at the Seventh Summer School in Nuclear Physics: Symmetries, Seattle, 1995, nucl-th/9506035.
155. H. Kluberg-Stern, J.B. Zuber, Ward identities and some clues to the renormalization of gauge invariant operators, Phys. Rev. D 12 (1975) 467.
156. H. Kluberg-Stern, J.B. Zuber, Renormalization of Nonabelian gauge theories in a background field gauge, 1, green functions, Phys. Rev. D 12 (1975) 482.
157. H. Kluberg-Stern, J.B. Zuber, Renormalization of Nonabelian gauge theories in a background field gauge, 2, gauge invariant operators, Phys. Rev. D 12 (1975) 3159.**
158. O.M. Khudaverdian, A.P. Nersessian, On the geometry of the Batalin-Vilkovsky formalism, Mod. Phys. Lett. A 8 (1993) 2377 (hep-th/9303136).
159. B. Knaepen, Local BRST cohomology for p-form gauge theories, hep-th/9912021.
160. S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vol. II, section 12, Wiley, New York, 1996.
161. J.-L. Koszul, Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France 78 (1950) 65-127.
162. Y.P. Lam, Perturbation Lagrangian theory for scalar fields: Ward-Takahasi identity and current algebra, Phys. Rev. D 6 (1972) 2145.
163. Y.P. Lam, Equivalence theorem on Bogoliubov-Parasiuk-Hepp-Zimmermann renormalized lagrangian field theories, Phys. Rev. D 7 (1973) 2943.
164. L. Lambe, J.D. Stasheff, Applications of perturbation theory to iterated fibrations, Manus. Math. 58 (1987) 363.
165. F. Langouche, T. Schücker, R. Stora, Gravitational anomalies of the Adler-Bardeen type, Phys. Lett. B 145 (1984) 342.
166. P.M. Lavrov, I.V. Tyutin, Effective action in general gauge theories, Sov. J. Nucl. Phys. 41 (1985) 1049.
167. B.W. Lee, J. Zinn-Justin, Spontaneously broken gauge symmetries. I. Preliminaries, Phys. Rev. D 5 (1972) 3121.
168. B.W. Lee, J. Zinn-Justin, Spontaneously broken gauge symmetries. II. Perturbation theory and renormalization, Phys. Rev. D 5 (1972) 3137.
169. B.W. Lee, J. Zinn-Justin, Spontaneously broken gauge symmetries. III. Equivalence, Phys. Rev. D 5 (1972) 3155.
170. B.W. Lee, J. Zinn-Justin, Spontaneously broken gauge symmetries. IV. General gauge formulation, Phys. Rev. D 7 (1973) 1049.
171. J.H. Lowenstein, Differential vertex operations in lagrangian field theory, Commun. Math. Phys. 24 (1971) 1.
172. M. Lüscher, Topology and the axial anomaly in abelian lattice gauge theories, Nucl. Phys. B 538 (1999) 515.
173. J. Mañes, R. Stora, B. Zumino, Algebraic study of chiral anomalies, Commun. Math. Phys. 102 (1985) 157.
174. A.V. Manohar, Effective field theories, Lectures at the 1996 Schladming Winter School, hep-ph/9606222.
175. D. McMullan, Yang-Mills theory and the Batalin-Fradkin-Vilkovisky formalism, J. Math. Phys. 28 (1987) 428.
176. C.W. Misner, J.A. Wheeler, Classical physics as geometry: gravitation, electromagnetism, unquantized charge and mass as properties of curved empty space, Ann. Phys. (NY) 2 (1957) 525.
177. P.J. Olver, Applications of Lie Groups to Differential Equations, Springer, New York, 1986.
178. B. Zumino, Chiral anomalies and differential geometry, in: B.S. DeWitt, R. Stora (Eds.), Lectures given at Les Houches Summer School on Theoretical Physics, Les Houches, France, August 8-September 2, 1983, published in Relativity, Groups and Topology II, North-Holland, Amsterdam, 1984.
179. A. Pich, Effective field theory: course, in: Talk given at Les Houches Summer School in Theoretical Physics, Session 68: Probing the Standard Model of Particle Interactions, Les Houches, France, 28 July-5 September 1997, hep-ph/9806303.
180. O. Piguet, A. Rouet, Symmetries in perturbative quantum field theory, Phys. Rep. 76 (1981) 1.
181. O. Piguet, S.P. Sorella, Algebraic renormalization: perturbative renormalization, symmetries and anomalies, Lecture Notes in Physics: m28, Springer, Berlin, Germany, 1995, 134 pp.*
182. O. Piguet, S. Wolf, The supercurrent trace identities of the N = 1, D = 4 super-Yang-Mills theory in the Wess-Zumino gauge, JHEP 9804 (1998) 001 (hep-th/9802027).
183. J. Polchinski, Effective field theory and the Fermi surface, Lectures presented at TASI92, Boulder, CO, June 3-28, 1992, Published in Boulder TASI 92:0235-276 (hep-th/9210046).
184. B. Zumino, Y. Wu, A. Zee, Chiral anomalies, higher dimensions, and differential geometry, Nucl. Phys. B 239 (1984) 477.**.
185. D.J. Saunders, The Geometry of Jet Bundles, Cambridge University Press, Cambridge, 1989.
186. T. Schücker, The cohomological proof of Stora's solutions, Commun. Math. Phys. 109 (1987) 167.
187. A.A. Slavnov, Ward identities in gauge theories, Theor. Math. Phys. 10 (1972) 99.***
188. J. Stasheff, Homological (ghost) approach to constrained Hamiltonian systems, hep-th/9112002.
189. J. Stasheff, Deformation theory and the Batalin-Vilkovisky master equation, q-alg/9702012.
190. G. Sterman, P.K. Townsend, P. van Nieuwenhuizen, Unitarity, ward identities, and new quantization rules of supergravity, Phys. Rev. D 17 (1978) 1501.
191. R. Stora, Continuum gauge theories, in: M. Levy, P. Mitter (Eds.), Lectures given at Summer Institute for Theoretical Physics, Cargése, France, July 12-31, 1976, published in New Developments in Quantum Field Theory and statistical Physics, NATO ASI Series B 26, Plenum Press, New York, 1977.**
192. R. Stora, Algebraic structure and topological origin of anomalies, in: 't Hooft et al. (Eds.), Seminar given at Cargèse Summer Institute September 1-15, 1983, published in Progress in Gauge Field Theory, Plenum Press, New York, 1984.**
193. D. Sullivan, Infinitesimal computations in topology, Pub. Math. IHES 47 (1977) 269.
194. F. Takens, A global version of the inverse problem to the calculus of variations, J. Differential Geometry 14 (1979) 543.
195. H. Suzuki, Anomaly cancellation condition in lattice gauge theory, hep-lat/0002009.
196. M. Talon, Algebra of anomalies, PAR-LPTHE-85/37, Presented at Cargèse Summer School, Cargèse, France, July 15-31, 1985.
197. L. Tǎtaru, I.V. Vancea, BRST cohomology in Beltrami parametrization, Int. J. Mod. Phys. A 11 (1996) 375 (hep-th/9504036).
198. L. Tǎtaru, R. Tǎtar, Koszul-Tate cohomology for an Sp(2)-covariant quantization of gauge theories with linearly dependent generators, Int. J. Mod. Phys. A 13 (1998) 1981 (hep-th/9708159).
199. J.C. Taylor, Ward identities and charge renormalization of the Yang-Mills field, Nucl. Phys. B 33 (1971) 436.***
200. J. Thierry-Mieg, Classification of the Yang-Mills anomalies in even and odd dimension, Phys. Lett. B 147 (1984) 430.
201. M. Tonin, Dimensional regularization and anomalies in chiral gauge theories, Nucl. Phys. Proc. Suppl. 29 BC (1992) 137.
202. C.G. Torre, Natural symmetries of the Yang-Mills equations, J. Math. Phys. 36 (1995) 2113 (hep-th/9407129).
203. W. Troost, P. van Nieuwenhuizen, A. Van Proeyen, Anomalies and the Batalin-Vilkovisky Lagrangian formalism, Nucl. Phys. B 333 (1990) 727.*
204. W. Troost, A. Van Proeyen, Regularization, the BV method, and the antibracket cohomology, hep-th/9410162.
205. W. Troost, A. Van Proeyen, Regularization and the BV formalism, hep-th/9307126.
206. T. Tsujishita, On variational bicomplexes associated to differential equations, Osaka J. Math. 19 (1982) 311.
207. W.M. Tulczyjew, The Euler-Lagrange Resolution, Lecture Notes in Mathematics, Vol. 836, Springer, Berlin, 1980, 22 pp.
208. I.V. Tyutin, Gauge invariance in field theory and statistical physics in operator formalism, LEBEDEV-75-39.
209. I.V. Tyutin, B.L. Voronov, Renormalization of general gauge theories, in: Proceedings, Quantum Gravity*, Moscow 1981, pp. 481-501.
210. W.G. Unruh, Excluded possibilities of geometrodynamical analog to electric charge, Gen. Relativ. Gravit. 2 (1971) 27.
211. J.W. van Holten, On the construction of supergravity theories, Ph.D. Thesis, University of Leiden, 1980.
212. A. Verbovetsky, Notes on the horizontal cohomology, in: Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 211 (math.dg/9803115).
213. A.M. Vinogradov, On the algebra-geometric foundations of Lagrangian field theory, Sov. Math. Dokl. 18 (1977) 1200.
214. A.M. Vinogradov, A spectral sequence associated with a nonlinear differential equation and algebra-geometric foundations of Lagrangian field theory with constraints, Sov. Math. Dokl. 19 (1978) 144.
215. A.M. Vinogradov, The script C sign-spectral sequence, Lagrangian formalism, and conservation laws, I, the linear theory. II. The non linear theory, J. Math. Anal. Appl. 100 (1984) 1.
216. B.L. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, I, Theor. Math. Phys. 50 (1982) 218.**
217. B.I. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, II, gauge invariant renormalizability and renormalization structure, Theor. Math. Phys. 52 (1982) 628.**
218. B.L. Voronov, P.M. Lavrov, I.V. Tyutin, Canonical transformations and the gauge dependence in general gauge theories, Sov. J. Nucl. Phys. 36 (1982) 292.
219. R.M. Wald, Spin-two fields and general covariance, Phys. Rev. D 33 (1986) 3613.
220. R.M. Wald, On identically closed forms locally constructed from a field, J. Math. Phys. 31 (1990) 2378.
221. S. Weinberg, Phenomenological lagrangians, Physica 96 A (1979) 327.
222. S. Weinberg, The quantum theory of fields. Vol. 1: Foundations, University Press, Cambridge, UK, 1995, 609 pp.
223. S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, University Press, Cambridge, UK, 1996, 489 pp.
224. S. Weinberg, What is quantum field theory, and what did we think it was?, hep-th/9702027.
225. M. Werneck de Oliveira, M. Schweda, S.P. Sorella, Supersymmetric structure of the bosonic string theory in the Beltrami parametrization, Phys. Lett. B 315 (1993) 93 (hep-th/9305148).
226. J. Wess, B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95.***
227. E. Witten, A note on the antibracket formalism, Mod. Phys. Lett. A 5 (1990) 487.
228. C.N. Yang, R.L. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96 (1954) 191.
229. D.P. Želobenko, in: Compact Lie Groups and their Representations, Translations of Mathematical Monographs, Vol. 40, American Mathematical Society, Providence, RI, 1973.
230. J. Zinn-Justin, Renormalization of gauge theories, in: H. Rollnik, K. Dietz (Eds.), Lectures given at International Summer Institute for Theoretical Physics, July 29-August 9, 1974, Bonn, West Germany, published in Trends in Elementary Particle Physics, Lectures Notes in Physics, Vol. 37, Springer, Berlin, 1975.***
231. J. Zinn-Justin, Quantum field theory and critical phenomena, Clarendon press, Oxford, UK, 1989, 914 pp. (International Series of Monographs on Physics, Vol. 77. 3rd Edition 1996 (chapter 21)).
232. J. Zinn-Justin, Renormalization of gauge theories and master equation, Mod. Phys. Lett. A 14 (1999) 1227, hep-th/9906115.