×

zbMATH — the first resource for mathematics

All order I.R. finite expansion for short distance behavior of massless theories perturbed by a relevant operator. (English) Zbl 1003.81514
Summary: We consider here renormalizable theories without relevant couplings and present an I.R. consistent technique to study corrections to short distance behavior (Wilson O.P.E. coefficients) due to a relevant perturbation. Our method is the result of a complete reformulation of recent works on the field, and is characterized by a more orthodox treatment of U.V. divergences that allows for simpler formulae and consequently an explicit all order (regularization invariant) I.R. finiteness proof. Underlying hypotheses are discussed in detail and found to be satisfied in conformal theories that constitute a natural field of application of this approach.

MSC:
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Jackiw, R.; Templeton, S.; Bergére, M.C.; David, F., Phys. rev. D, Ann. phys., 142, 416, (1982)
[2] Saleur, H.; Itzykson, C.; Dotsenko, Vl.S.; Cappelli, A.; Latorre, J.I., J. of stat. phys., Nucl. phys. B, Nucl. phys. B, 340, 659, (1990)
[3] Belavin, A.A.; Polyakov, A.M.; Zamolodchikov, A.B., Nucl. phys. B, 241, 333, (1984)
[4] ()
[5] Zamolodchikov, A.B.; Ludwig, A.A.; Cardy, J.L., Sov. J. nucl. phys., Nucl. phys. B, 285, 687, (1987)
[6] Zamolodchikov, A.B.; Zamolodchikov, Al.B., Ann. phys., 120, 253, (1979)
[7] Cardy, J.L.; Zamolodchikov, A.B., Fields, strings and critical phenomena, (), Rev. math. phys., 1, 197, (1990)
[8] Zamolodchikov, Al.B., Nucl. phys. B, 348, 619, (1991)
[9] Sonoda, H.; Sonoda, H., Nucl. phys. B, Nucl. phys. B, 394, 302, (1993)
[10] Mikhak, B.; Zarkesh, A.M., Nucl. phys. B, 430, 656, (1994), [FS]
[11] Wilson, K.G., Phys. rev., 179, 1499, (1969)
[12] Wegner, F., J. phys. A, 8, 710, (1975)
[13] Broadhurst, D.J.; Generalis, S.C., Open university report no. OUT-4102-12, (1984), unpublished
[14] Generalis, S.G.; Generalis, S.G.; Chetyrkin, K.; Spiridonov, K.G.; Jamin, M.; Munz, M., J. phys. G, J. phys. G, Sov. J. nucl. phys., Z. phys. C, 60, 569, (1993)
[15] Sonoda, H.; Sonoda, H., Nucl. phys. B, Nucl. phys. B, 352, 601, (1991)
[16] Schwinger, J.; Schwinger, J., Phys. rev., Phys. rev., 91, 713, (1953)
[17] Lowenstein, J.H.; Lam, Y.M.P.; Lam, Y.M.P.; Clark, T.E.; Lowenstein, J.H., Commun. math. phys., Phys. rev. D, Phys. rev. D, Nucl. phys. B, 113, 109, (1976)
[18] Breitenlohner, P.; Maison, D.; Breitenlohner, P.; Maison, D.; Breitenlohner, P.; Maison, D.; Bergére, M.C.; Lam, Y.M.P., Commun. math. phys., Commun. math. phys., Commun. math. phys., J. math. phys., 17, 1546, (1976)
[19] Speer, E.R., ()
[20] Smirnov, V.A., Z. phys. C, 67, 531, (1995)
[21] ’t Hooft, G.; Veltman, M.; Collins, J.C., Nucl. phys. B, Nucl. phys. B, 80, 341, (1974)
[22] Chetyrkin, K.G.; Gorishny, S.G.; Tkachov, F.V.; Gorishny, S.G.; Larin, S.A.; Tkachov, F.V.; Smith, C.H.Llewellyn; de Vries, J.P., Phys. lett. B, Phys. lett. B, Nucl. phys. B, 296, 991, (1988)
[23] Polyakov, A.M.; Mack, G., Sov. phys. JETP, Nucl. phys. B, 118, 445, (1977)
[24] Mack, G., Commun. math. phys., 53, 155, (1977)
[25] Wilson, K.G.; Zimmermann, W., Commun. math. phys., 24, 87, (1972)
[26] Zimmermann, W.; Clark, T.E.; Collecott, P.S., Ann. phys., Nucl. phys. B, Ann. phys., 113, 461, (1978)
[27] Bogoliubov, N.N.; Shirkov, O.V.; Hepp, K.; Epstein, H.; Glaser, V., Introduction to the theory of quantized fields, Commun. math. phys., Ann. inst. Poincaré, XIX, 211, (1973), Wiley New York
[28] Becchi, C.M., Fields and particles, ()
[29] Collecott, P.S., Nucl. phys. B, 135, 167, (1978)
[30] Zinn-Justin, J., Quantum field theory and critical phenomena, (1989), Clarendon Press Oxford
[31] Shore, G.M., Nucl. phys. B, 362, 85, (1991)
[32] ’t Hooft, G., Acta phys. austriaca, 22, 531, (1980)
[33] Kutasov, D.; Lässig, M., Phys. lett. B, Nucl. phys. B, 334, 647, (1990)
[34] H. Sonoda, Connections on the theory space, hep-th/9306119
[35] Collins, J.C., Renormalization, (1984), Cambridge Univ. Press Cambridge
[36] Di Francesco, P.; Saleur, H.; Zuber, J.-B., Nucl. phys. B, 290, 527, (1987)
[37] Wu, T.T.; McCoy, B.M.; Tracy, C.A.; Barouch, E., Phys. rev. B, 13, 316, (1976)
[38] Chetyrkin, K.G.; Kataev, A.L.; Tkachov, F.V.; Chetyrkin, K.G.; Kataev, A.L.; Tkachov, F.V.; Freedman, D.Z.; Johnson, K.; Latorre, J.I., Phys. lett. B, Nucl. phys. B, Nucl. phys. B, 371, 353, (1992), see also
[39] Gorishny, S.G.; Larin, S.A., Nucl. phys. B, 287, 452, (1987)
[40] Smirnov, V.A., Renormalization and asymptotic expansions, () · Zbl 0744.46072
[41] Schwartz, L., Théorie des distributions, tome I, (1966), Hermann Paris
[42] Gelfand, I.M.; Shilow, G.E., ()
[43] I.S. Gradshtein and I.M. Ryzhik, Tables of integrals, series and products (Academic Press, New York.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.