Abstract
A rigorous algebraic proof of the full finiteness in all orders of perturbation theory is given for the Yang–Mills–Chern–Simons theory in a general three-dimensional Riemannian manifold. We show the validity of a trace identity, playing the role of a local form of the Callan–Symanzik equation, in all loop orders, which yields the vanishing of the β-functions associated to the topological mass and gauge coupling constant as well as the anomalous dimensions of the fields.
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Deser, S., Jackiw, R. and Templeton, S.: Ann. Phys. (N.Y.) 140 (1982), 372.
Pisarski, R. D. and Rao, S.: Phys. Rev. D 32 (1985), 2081.
Deser, S., Jackiw, R. and Templeton, S.: Ann. Phys. (N.Y.) 185 (1988), 406.
Martin, C. P.: Phys. Lett. B 241 (1990), 513.
Giavarini, G., Martin, C. P. and Ruiz Ruiz, F.: Nuclear Phys. B 381 (1992), 222.
Ruiz Ruiz, F. and van Nieuwenhuizen, P.: Nuclear Phys. B 486 (1997), 443.
Maggiore, N., Piguet, O. and Ribordy, M.: Helv. Phys. Acta 68 (1995), 265.
Blasi, A. and Collina, R.: Nuclear Phys. B 345 (1990), 472; Delduc, F., Lucchesi, C., Piguet, O. and Sorella, S. P.: Nuclear Phys. B 346 (1990), 313; Lucchesi, C. and Piguet, O.: Nuclear Phys. B 381 (1992), 281.
Lemes, V. E. R., Linhares de Jesus, C., Sasaki, C. A. G., Sorella, S. P., Ventura, O. S. and Vilar, L. C. Q.: Phys. Lett. B 418 (1998), 324.
Lemes, V. E. R., Linhares de Jesus, C., Sorella, S. P., Ventura, O. S. and Vilar, L.C.Q.: Preprint CBPF-NF-078/97, hep-th/9801021.
Barnich, G.: Preprint ULB-TH-98/08, hep-th/9805030.
Del Cima, O. M., Franco, D. H. T., Helayël-Neto, J. A. and Piguet, O.: J. High Energy Phys. 2 (1998), 2, hep-th/9711191.
Del Cima, O. M., Franco, D. H. T., Helayël-Neto, J. A. and Piguet, O.: J. High Energy Phys. 4 (1998), 10, hep-th/9803247.
Becchi, C., Rouet, A. and Stora, R.: Comm. Math. Phys. 42 (1975), 127; Ann. Phys. (N.Y.) 98 (1976), 287; Piguet, O. and Rouet, A.: Phys. Rep. 76 (1981), 1.
Piguet, O.: Renormalisation en théorie quantique des champs and Renormalisation des théories de jauge, lectures of the Troisième cycle de la physique en Suisse Romande (1982–1983).
Piguet, O. and Sorella, S. P.: Algebraic Renormalization, Lecture Notes in Phys. 28, Springer-Verlag, Berlin, 1995.
Lowenstein, J. H.: Phys. Rev. D 4 (1971), 2281; Comm. Math. Phys. 24 (1971), 1; Lam, Y. M. P.: Phys. Rev. D 6 (1972), 2145; Phys. Rev. D 7 (1973), 2943; Clark, T. E. and Lowenstein, J. H.: Nuclear Phys. B 113 (1976), 109.
Zimmermann, W.: in S. Deser, M. Grisaru and H. Pendleton (eds), Lectures on Elementary Particles and Quantum Field Theory (1970 Brandeis Lectures), MIT Press, Cambridge, Mass, 1970; Ann. Phys. (N.Y.) 77 (1973), 536.
Blasi, A., Piguet, O. and Sorella, S. P.: Nuclear Phys. B 356 (1991), 154.
Brandt, F., Dragon, N. and Kreuzer, M.: Nuclear Phys. B 340 (1990), 187.
Barnich, G., Brandt, F. and Henneaux, M.: Nuclear Phys. B 455 (1995), 357.
Barnich, G. and Henneaux, M.: Phys. Rev. Lett. 72 (1994), 1588.
Bandelloni, G., Becchi, C., Blasi, A. and Collina, R.: Ann. Inst. Henri Poincaré 28 (1978), 225, 255.
Iorio, A., O'Raifeartaigh, L., Sachs, I. and Wiesendager, C.: Nuclear Phys. B 495 (1997), 433.
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Del Cima, O.M., Franco, D.H.T., Helayël-Neto, J.A. et al. An Algebraic Proof on the Finiteness of Yang–Mills–Chern–Simons Theory in D=3. Letters in Mathematical Physics 47, 265–273 (1999). https://doi.org/10.1023/A:1007595121742
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DOI: https://doi.org/10.1023/A:1007595121742