On the spectrum of anomalous dimensions of composite operators in the scalar field theory
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 136-169 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the one-loop approximation the problem of the diagonalization of the mixing matrix is equivalent some quantum mechanical eigenvalue problem. For the illustration of this technik we consider two simplest examples of the scalar field theories. Bibl. – 27 titles.
@article{ZNSL_2010_374_a8,
     author = {S. E. Derkachov and A. N. Manashov},
     title = {On the spectrum of anomalous dimensions of composite operators in the scalar field theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {136--169},
     year = {2010},
     volume = {374},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a8/}
}
TY  - JOUR
AU  - S. E. Derkachov
AU  - A. N. Manashov
TI  - On the spectrum of anomalous dimensions of composite operators in the scalar field theory
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2010
SP  - 136
EP  - 169
VL  - 374
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a8/
LA  - ru
ID  - ZNSL_2010_374_a8
ER  - 
%0 Journal Article
%A S. E. Derkachov
%A A. N. Manashov
%T On the spectrum of anomalous dimensions of composite operators in the scalar field theory
%J Zapiski Nauchnykh Seminarov POMI
%D 2010
%P 136-169
%V 374
%U http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a8/
%G ru
%F ZNSL_2010_374_a8
S. E. Derkachov; A. N. Manashov. On the spectrum of anomalous dimensions of composite operators in the scalar field theory. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 136-169. http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a8/

[1] V. E. Kravtsov, I. V. Lerner, V. I. Yudson, Phys. Lett. A, 134 (1989), 245 | DOI

[2] F. Wegner, Z. Phys. B, 78 (1990), 33 | DOI | MR

[3] G. E. Castilla, S. Chakravarty, Nucl. Phys. B, 485 (1997), 613 | DOI

[4] E. Brezin, S. Hikami, Fancy and facts in the $(d-2)$ expansion of nonlinear sigma models, arXiv: cond-mat/9612016

[5] S. E. Derkachov, A. N. Manashov, Phys. Rev. Lett., 79 (1997), 1423 | DOI

[6] A. P. Bukhvostov, G. V. Frolov, L. N. Lipatov, E. A. Kuraev, Nucl. Phys. B, 258 (1985), 601 | DOI

[7] I. I. Balitsky, V. M. Braun, Nucl. Phys. B, 311 (1989), 541 | DOI

[8] V. M. Braun, G. P. Korchemsky, D. Mueller, Prog. Part. Nucl. Phys., 51 (2003), 311 | DOI

[9] V. M. Braun, S. E. Derkachov, A. N. Manashov, Phys. Rev. Lett., 81 (1998), 2020 | DOI

[10] J. M. Maldacena, Adv. Theor. Math. Phys., 2 (1998), 231 ; Int. J. Theor. Phys., 38 (1999), 1113 | MR | Zbl | DOI | MR | Zbl

[11] N. Beisert, Nucl. Phys. B, 676 (2004), 3 | DOI | MR | Zbl

[12] S. E. Derkachov, A. N. Manashov, Nucl. Phys. B, 455 (1995), 685 | DOI

[13] S. E. Derkachov, A. N. Manashov, J. Phys. A, 29 (1996), 8011 | DOI | MR | Zbl

[14] S. E. Derkachov, S. K. Kehrein, A. N. Manashov, Nucl. Phys. B, 493 (1997), 660 | DOI | MR | Zbl

[15] V. M. Braun, S. E. Derkachov, G. P. Korchemsky, A. N. Manashov, Nucl. Phys. B, 553 (1999), 355 | DOI

[16] V. M. Braun, G. P. Korchemsky, A. N. Manashov, Nucl. Phys. B, 603 (2001), 69 | DOI | Zbl

[17] A. V. Belitsky, S. E. Derkachov, G. P. Korchemsky, A. N. Manashov, Phys. Lett. B, 594 (2004), 385 | DOI | MR | Zbl

[18] S. K. Kehrein, F. J. Wegner, Y. M. Pis'mak, Nucl. Phys. B, 402 (1993), 669 | DOI | MR | Zbl

[19] S. K. Kehrein, F. J. Wegner, Nucl. Phys. B, 424 (1994), 521 | DOI | MR | Zbl

[20] S. K. Kehrein, Nucl. Phys. B, 453 (1995), 777 | DOI

[21] D. C. Collins, Renormalization, Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[22] A. N. Vasilev, Kvantovopolevaya renormgruppa v teorii kritichesskogo povedeniya i stokhasticheskoi dinamike, Izd-vo PIYaF, Sankt-Peterburg, 1998

[23] Yu. M. Makeenko, Sov. J. Nucl. Phys., 33 (1981), 440 | MR

[24] I. M. Gelfand, M. I. Graev, N. Ya. Vilenkin, Generalized functions, v. 5, Integral geometry and representation theory, NY Academic Press, New York, 1966 | Zbl

[25] T. Ohrndorf, Nucl. Phys. B, 198 (1982), 26 | DOI

[26] A. M. Polyakov, JETP Lett., 12 (1970), 381 ; Pisma Zh. Eksp. Teor. Fiz., 12 (1970), 538; Zh. Eksp. Teor. Fiz., 66 (1974), 23 | MR

[27] C. F. Dunkl, Trans. Amer. Math. Soc., 311 (1989), 167 | DOI | MR | Zbl