Renormalization group functional equations

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 83, Issue 6, 2011, Pages

  Curtright, Thomas L ^a,b   Zachos, Cosmas K ^c  

^a CERN   (Switzerland)

^b University of Miami   (United States)

^c ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79959658091     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.83.065019     Document Type: Article

References (38)

1. M. Gell-Mann and F.E. Low, Phys. Rev. 95, 1300 (1954). PHRVAO 0031-899X 10.1103/PhysRev.95.1300
2. E.C.G. Stueckelberg and A. Petermann, Helv. Phys. Acta 24, 317 (1951); HPACAK 0018-0238
3. E.C.G. Stueckelberg A. Petermann Helv. Phys. Acta 26, 499 (1953). HPACAK 0018-0238
4. E. Schröder, Ann. Math. 3, 296 (1870). ANMAAH 0003-486X 10.1007/BF01443992
5. T.D. Lee, Particle Physics and Introduction to Field Theory (Harwood Academic, Chur, Switzerland, 1981), p. 458.
6. M. Kuczma, Functional Equations in a Single Variable (P.W.N.-Polish Scientific, Warsaw, 1968);
7. M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations (Cambridge University Press, Cambridge, England, 1990).
8. S. Caracciolo, R.G. Edwards, S.J. Ferreira, A. Pelissetto, and A.D. Sokal, Phys. Rev. Lett. 74, 2969 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett. 74.2969
9. M. Lüscher, P. Weisz, and U. Wolff, Nucl. Phys. NUPBBO 0550-3213 B359, 221 (1991). 10.1016/0550-3213(91)90298-C
10. T. Curtright and C. Zachos, J. Phys. A JPHAC5 0305-4470 42, 485208 (2009). 10.1088/1751-8113/42/48/485208
11. T. Curtright and C. Zachos, J. Phys. A JPHAC5 0305-4470 43, 445101 (2010). 10.1088/1751-8113/43/44/445101
12. T. Curtright and A. Veitia, Phys. Lett. A PYLAAG 0375-9601 375, 276 (2011). 10.1016/j.physleta.2010.11.019
13. C.G. Callan, Phys. Rev. D PRVDAQ 0556-2821 2, 1541 (1970). 10.1103/PhysRevD.2.1541
14. K. Symanzik, Commun. Math. Phys. 18, 227 (1970); CMPHAY 0010-3616 10.1007/BF01649434
15. K. Symanzik Commun. Math. Phys. 23, 49 (1971). CMPHAY 0010-3616 10.1007/BF01877596
16. T. Appelquist, G.T. Fleming, and E.T. Neil, Phys. Rev. D PRVDAQ 1550-7998 79, 076010 (2009). 10.1103/PhysRevD.79.076010
17. A. LeClair, J.M. Román, and G. Sierra, Phys. Rev. B PRBMDO 0163-1829 69, 20505 (2004); 10.1103/PhysRevB.69.020505
18. A. LeClair J.M. Román G. Sierra Nucl. Phys. NUPBBO 0550-3213 B675, 584 (2003); 10.1016/j.nuclphysb.2003.09.032 (Pubitemid 37416808)
19. A. LeClair J.M. Román G. Sierra Nucl. Phys. NUPBBO 0550-3213 B700, 407 (2004). 10.1016/j.nuclphysb.2004.08.033 (Pubitemid 39436124)
20. E. Gardi, G. Grunberg, and M. Karliner, J. High Energy Phys. JHEPFG 1029-8479 07 (1998) 007. 10.1088/1126-6708/1998/07/007
21. J. Ellis, I. Jack, D.R.T. Jones, M. Karliner, and M.A. Samuel, Phys. Rev. D PRVDAQ 0556-2821 57, 2665 (1998). 10.1103/PhysRevD.57.2665
22. T.A. Ryttov and F. Sannino, Phys. Rev. D PRVDAQ 1550-7998 78, 065001 (2008). 10.1103/PhysRevD.78.065001
23. E. Braaten, T. Curtright, and C. Zachos, Nucl. Phys. B NUPBBO 0550-3213 260, 630 (1985). 10.1016/0550-3213(85)90053-7
24. S.D. Głazek and K.G. Wilson, Phys. Rev. Lett. 89, 230401 (2002); PRLTAO 0031-9007 10.1103/PhysRevLett.89.230401
25. S.D. Głazek K.G. Wilson Phys. Rev. Lett. 92, 139901(E) (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.139901
26. T. Curtright, arXiv:1011.6056.
27. Higher-order renormalization group differential equations have been encountered in models coupled to quantum gravity in two dimensions. We thank Sumit Das for bringing this to our attention. See S.R. Das, S. Naik, and S.R. Wadia, Mod. Phys. Lett. A 4, 1033 (1989); MPLAEQ 0217-7323 10.1142/ S0217732389001209
28. S.R. Das, A. Dhar, and S.R. Wadia, Mod. Phys. Lett. A 5, 799 (1990); MPLAEQ 0217-7323 10.1142/S0217732390000895
29. A.M. Polyakov, in Proceedings of the Jerusalem Winter School for Theoretical Physics, edited by, D.J. Gross, T. Piran, and, S. Weinberg, (World Scientific, Singapore, 1992), p. 175.
30. P. Collet and J.P. Eckmann, Iterated Maps on the Interval As Dynamical Systems (Birkhäuser, Boston, 1980).
31. R.L. Devaney, An Introduction to Chaotic Dynamical Systems (Addison-Wesley, Reading, MA, 1989).
32. K.G. Wilson, Phys. Rev. D PRVDAQ 0556-2821 3, 1818 (1971). 10.1103/PhysRevD.3.1818
33. K.G. Wilson and S.D. Głazek, Phys. Rev. B PRBMDO 0163-1829 69, 094304 (2004). 10.1103/PhysRevB.69.094304
34. J. Cardy, J. Stat. Mech. 1742-5468 2010, P10004 (2010). 10.1088/1742-5468/2010/10/P10004
35. A.B. Zamolodchikov, JETP Lett. 43, 730 (1986). JTPLA2 0021-3640
36. R.C. Myers and A. Sinha, Phys. Rev. D PRVDAQ 1550-7998, 82, 04606 (2010). 10.1103/PhysRevD.82.046006
37. A. LeClair and G. Sierra, J. Stat. Mech. 1742-5468 2004, P08004 (2004). 10.1088/1742-5468/2004/08/P08004
38. Sidney Coleman, a student of Gell-Mann, discusses renormalization group flows in one of his Erice lectures, using an analogy with the advection of bacteria moving down a pipe. See § 4.1 of Chap. 3 (Dilatations) in S. Coleman, Aspects of Symmetry (Cambridge University Press, Cambridge, England, 1985).