A gauge invariant exact renormalization group II

Journal of High Energy Physics

Volumn 4, Issue 12, 2000, Pages

  Morris, Tim R ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Gauge Symmetry; Renormalization Regularization and Renormalons

Indexed keywords

EID: 7544226856     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/12/012     Document Type: Article

References (65)

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21. V.N. Gribov, Quantization of nonabelian gauge theories, Nucl. Phys. B 139 (1978) 1; I.M. Singer, Some remarks on the Gribov ambiguity, Comm. Math. Phys. 60 (1978) 7 See e.g. P. van Baal, Gribov ambiguities and the fundamental domain, hep-th/9711070 M. Asorey and F. Falceto, Global aspects of covariant quantization of gauge theories, Ann. Phys. (NY) 196 (1989) 209 K. Fujikawa, Brst symmetric formulation of a theory with Gribov-type copies, Nucl. Phys. B 468 (1996) 355 [hep-th/9510111].
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23. For other approaches to evade the Gribov problem see e.g. V.M. Villanueva, J. Govaerts and J-L. Lucio-Martinez, Quantization without gauge fixing: avoiding Gribov ambiguities through the physical projector, J. Phys. A33 (2000) 4183 [hep-th/9909033] S.V. Shabanov and J.R. Klauder, Towards a nonperturbative path integral in gauge theories, Phys. Lett. B 456 (1999) 38 [hep-th/9902017].
24. For other approaches to evade the Gribov problem see e.g. V.M. Villanueva, J. Govaerts and J-L. Lucio-Martinez, Quantization without gauge fixing: avoiding Gribov ambiguities through the physical projector, J. Phys. A33 (2000) 4183 [hep-th/9909033] S.V. Shabanov and J.R. Klauder, Towards a nonperturbative path integral in gauge theories, Phys. Lett. B 456 (1999) 38 [hep-th/9902017].
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28. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
29. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
30. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
31. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
32. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
33. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
34. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
35. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
36. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
37. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
38. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
39. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
40. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
41. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
42. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
43. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
44. C. Becchi, On the construction of renormalized gauge theories using renormalization group techniques, in Elementary particles, field theory and statistical mechanics, Parma, 1993 hep-th/9607188 M. Bonini, M. D'Attanasio and G. Marchesini, Perturbative renormalization and infrared finiteness in the Wilson renormalization group: the massless scalar case, Nucl. Phys. B 409 (1993) 441 [hep-th/9301114]; Ward identities and wilson renormalization group for QED, Nucl. Phys. B 418 (1994) 429 [hep-th/9307174]; Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance, Nucl. Phys. B 421 (1994) 81 [hep-th/9312114]; Brs symmetry for Yang-Mills theory with exact renormalization group, Nucl. Phys. B 437 (1995) 163 [hep-th/9410138] U. Ellwanger, Flow equations and brs invariance for Yang-Mills theories, Phys. Lett. B 335 (1994) 364 [hep-th/9402077] U. Ellwanger, M. Hirsch and A. Weber, Flow equations for the relevant part of the pure Yang-Mills action, Z. Physik C 69 (1996) 687 [hep-th/9506019] M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181; Exact evolution equation for scalar electrodynamics, Nucl. Phys. B 427 (1994) 291 M. D'Attanasio and T.R. Morris, Gauge invariance, the quantum action principle and the renormalization group, Phys. Lett. B 378 (1996) 213 [hep-th/9602156] K.-I. Aoki, K.-I. Morikawa, J.-I. Sumi, H. Terao and M. Tomoyose, Nonperturbative renormalization group analysis of the chiral critical behaviors in QED, Prog. Theor. Phys. 97 (1997) 479 [hep-ph/9612459]; Wilson renormalization group equations for the critical dynamics of chiral symmetry, Prog. Theor. Phys. 102 (1999) 1151 [hep-th/9908042]; Analysis of the wilsonian effective potentials in dynamical chiral symmetry breaking, Phys. Rev. D 61 (2000) 045008 [hep-th/9908043] K.-I. Kubota and H. Terao, Nonperturbative renormalization group and renormalizability of gauged NJL model, Prog. Theor. Phys. 102 (1999) 1163 M. Pernici, M. Raciti and F. Riva, Hard-soft renormalization and the exact renormalization group, Nucl. Phys. B 520 (1998) 469 [hep-th/9710145] D.F. Litim and J.M. Pawlowski, Flow equations for Yang-Mills theories in general axial gauges, Phys. Lett. B 435 (1998) 181 [hep-th/9802064] M. Simionato, Gauge consistent Wilson renormalization group: abelian case, Int. J. Mod. Phys. A 15 (2000) 2121 [hep-th/9809004]; Gauge consistent wilson renormalization group, 2. Nonabelian case, Int. J. Mod. Phys. A 15 (2000) 2153 [hep-th/9810117]; On the consistency of the exact renormalization group approach applied to gauge theories in algebraic non-covariant gauges, Int. J. Mod. Phys. A 15 (2000) 4811 [hep-th/0005083].
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