Renormalization group running of Newton's constant G: The static isotropic case

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 75, Issue 8, 2007, Pages

  Hamber, H W ^a,b   Williams, R M ^a,c  

^a CERN   (Switzerland)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34047255928     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.75.084014     Document Type: Article

References (81)

1. R.P. Feynman, Lectures on Gravitation, 1962-1963, edited by, F.B. Morinigo, and, W.G. Wagner, (California Institute of Technology, Pasadena, 1971).
2. G. 't Hooft and M. Veltman, Ann. Inst. Poincaré 20, 69 (1974).
3. S. Deser and P. van Nieuwenhuizen, Phys. Rev. D 10, 401 (1974); PRVDAQ 0556-2821 10.1103/PhysRevD.10.401
4. S. Deser, H.S. Tsao, and P. van Nieuwenhuizen, Phys. Rev. D 10, 3337 (1974). PRVDAQ 0556-2821 10.1103/PhysRevD.10.3337
5. K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975); RMPHAT 0034-6861 10.1103/RevModPhys.47.773
6. K.G. Wilson Rev. Mod. Phys. 55, 583 (1983); RMPHAT 0034-6861 10.1103/RevModPhys.55.583
7. K.G. Wilson and M. Fisher, Phys. Rev. Lett. 28, 240 (1972). PRLTAO 0031-9007 10.1103/PhysRevLett.28.240
8. K.G. Wilson, Phys. Rev. D 7, 2911 (1973). PRVDAQ 0556-2821 10.1103/PhysRevD.7.2911
9. G. Parisi, Lett. Nuovo Cimento 6, 450 (1973);
10. G. Parisi Nucl. Phys. NUPBBO 0550-3213 B100, 368 (1975); 10.1016/0550-3213(75)90624-0
11. G. Parisi Nucl. Phys. NUPBBO 0550-3213 B254, 58 (1985); 10.1016/0550-3213(85)90211-1
12. G. Parisi, in New Development in Quantum Field Theory and Statistical Mechanics, Cargese, 1976, edited by, M. Levy, and, P. Mitter, (Plenum Press, New York, 1977).
13. K. Symanzik, Commun. Math. Phys. CMPHAY 0010-3616 45, 79 (1975). 10.1007/BF01609868
14. S. Weinberg, in General Relativity-An Einstein Centenary Survey, edited by, S.W. Hawking, and, W. Israel, (Cambridge University Press, Cambridge, England, 1979).
15. S.W. Hawking, in General Relativity-An Einstein Centenary Survey, edited by, S.W. Hawking, and, W. Israel, (Cambridge University Press, Cambridge, England, 1979).
16. J.B. Hartle and S.W. Hawking, Phys. Rev. D 28, 2960 (1983). PRVDAQ 0556-2821 10.1103/PhysRevD.28.2960
17. J.B. Hartle, Theoretical Advanced Study Institute in Elementary Particle Physics, Yale University, 1985, Vol. 2, pp. 471-566.
18. H.W. Hamber and R.M. Williams, Phys. Rev. D 72, 044026 (2005); PRVDAQ 0556-2821 10.1103/PhysRevD.72.044026
19. H.W. Hamber R.M. Williams Mod. Phys. Lett. A 21, 735 (2006). MPLAEQ 0217-7323 10.1142/S0217732306019979
20. H.W. Hamber, Phys. Rev. D 45, 507 (1992); PRVDAQ 0556-2821 10.1103/PhysRevD.45.507
21. H.W. Hamber Phys. Rev. D 61, 124008 (2000). PRVDAQ 0556-2821 10.1103/PhysRevD.61.124008
22. H.W. Hamber and R.M. Williams, Phys. Rev. D 70, 124007 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.124007
23. H.W. Hamber and R.M. Williams, Phys. Rev. D 73, 044031 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.044031
24. T. Regge, Nuovo Cimento 19, 558 (1961). NUCIAD 0029-6341
25. M. Rocek and R.M. Williams, Phys. Lett. B 104, 31 (1981); PYLBAJ 0370-2693 10.1016/0370-2693(81)90848-0
26. M. Rocek R.M. Williams Z. Phys. C 21, 371 (1984). ZPCFD2 0170-9739 10.1007/BF01581603
27. J. Cheeger, W. Müller, and R. Schrader, in Proceedings of the Heisenberg Symposium on Unified Theories Of Elementary Particles München 1981 (Springer, New York, 1982), pp. 176-188.
28. T.D. Lee, in Proceedings of International School of Subnuclear Physics on Discrete Mechanics, Erice, 1983 (Plenum Press, New York 1985), Vol. 21, and references therein.
29. H.W. Hamber and R.M. Williams, Nucl. Phys. NUPBBO 0550-3213 B248, 392 (1984); 10.1016/0550-3213(84)90603-5
30. H.W. Hamber R.M. Williams Nucl. Phys. NUPBBO 0550-3213 B260, 747 (1985); 10.1016/0550-3213(85)90057-4
31. H.W. Hamber R.M. Williams Phys. Lett. B 157, 368 (1985); PYLBAJ 0370-2693 10.1016/0370-2693(85)90382-X
32. H.W. Hamber R.M. Williams Nucl. Phys. NUPBBO 0550-3213 B269, 712 (1986). 10.1016/0550-3213(86)90518-3
33. J.B. Hartle, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 26, 804 (1985); 10.1063/1.526571
34. J.B. Hartle J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 27, 287 (1986); 10.1063/1.527331
35. J.B. Hartle J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 30, 452 (1989). 10.1063/1.528410
36. B. Berg, Phys. Rev. Lett. 55, 904 (1985); PRLTAO 0031-9007 10.1103/PhysRevLett.55.904
37. B. Berg Phys. Lett. B 176, 39 (1986). PYLBAJ 0370-2693 10.1016/0370-2693(86)90921-4
38. H.W. Hamber and R.M. Williams, Nucl. Phys. NUPBBO 0550-3213 B267, 482 (1986). 10.1016/0550-3213(86)90401-3
39. H.W. Hamber and R.M. Williams, Phys. Rev. D 47, 510 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.47.510
40. H.W. Hamber, Phys. Rev. D 50, 3932 (1994). PRVDAQ 0556-2821 10.1103/PhysRevD.50.3932
41. H.W. Hamber, Nucl. Phys. NUPBBO 0550-3213 B400, 347 (1993). 10.1016/0550-3213(93)90409-I
42. H.W. Hamber and R.M. Williams, Nucl. Phys. NUPBBO 0550-3213 B435, 361 (1995); 10.1016/0550-3213(94)00495-Z
43. H.W. Hamber R.M. Williams Phys. Rev. D 59, 064014 (1999). PRVDAQ 0556-2821 10.1103/PhysRevD.59.064014
44. H.S. Tsao, Phys. Lett. B 68, 79 (1977). PYLBAJ 0370-2693 10.1016/0370-2693(77)90039-9
45. R. Gastmans, R. Kallosh, and C. Truffin, Nucl. Phys. NUPBBO 0550-3213 B133, 417 (1978); 10.1016/0550-3213(78)90234-1
46. S.M. Christensen and M.J. Duff, Phys. Lett. B 79, 213 (1978). PYLBAJ 0370-2693 10.1016/0370-2693(78)90225-3
47. H. Kawai and M. Ninomiya, Nucl. Phys. NUPBBO 0550-3213 B336, 115 (1990); 10.1016/0550-3213(90)90345-E
48. H. Kawai, Y. Kitazawa, and M. Ninomiya, Nucl. Phys. NUPBBO 0550-3213 B393, 280 (1993); 10.1016/0550-3213(93)90246-L
49. H. Kawai Y. Kitazawa M. Ninomiya Nucl. Phys. NUPBBO 0550-3213 B404, 684 (1993); 10.1016/0550-3213(93)90594-F
50. Y. Kitazawa and M. Ninomiya, Phys. Rev. D 55, 2076 (1997). PRVDAQ 0556-2821 10.1103/PhysRevD.55.2076
51. T. Aida and Y. Kitazawa, Nucl. Phys. NUPBBO 0550-3213 B491, 427 (1997). 10.1016/S0550-3213(97)00091-6
52. E. Brezin and J. Zinn-Justin, Phys. Rev. Lett. 36, 691 (1976); PRLTAO 0031-9007 10.1103/PhysRevLett.36.691
53. E. Brezin J. Zinn-Justin Phys. Rev. D 14, 2615 (1976); PRVDAQ 0556-2821 10.1103/PhysRevD.14.2615
54. E. Brezin J. Zinn-Justin Phys. Rev. B PLRBAQ 0556-2805 14, 3110 (1976); 10.1103/PhysRevB.14.3110
55. E. Brezin and S. Hikami, Report No. LPTENS-96-64 1996.
56. W.A. Bardeen, B.W. Lee, and R.E. Shrock, Phys. Rev. D 14, 985 (1976). PRVDAQ 0556-2821 10.1103/PhysRevD.14.985
57. S. Hikami and E. Brezin, J. Phys. A JPHAC5 0305-4470 11, 1141 (1978). 10.1088/0305-4470/11/6/015
58. G. Parisi, Statistical Field Theory (Addison Wesley, New York, 1988).
59. See, for example, J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, New York, 1996), 3rd ed..
60. E. Brezin, J.C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, M. Green, (Academic Press, London 1976), Vol. 6, pp. 125-247.
61. See, for example, M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory (Addison Wesley, Reading, Massachusetts, 1995), sec..
62. K.G. Wilson, Phys. Rev. D 10, 2445 (1974); PRVDAQ 0556-2821 10.1103/PhysRevD.10.2445
63. K.G. Wilson in Proceedings of New Phenomena In Subnuclear Physics, Erice 1975 (Plenum Press, New York, 1977).
64. G.A. Vilkovisky, Nucl. Phys. NUPBBO 0550-3213 B234, 125 (1984); 10.1016/0550-3213(84)90228-1
65. A.O. Barvinsky and G.A. Vilkovisky, Nucl. Phys. NUPBBO 0550-3213 B282, 163 (1987); 10.1016/0550-3213(87)90681-X
66. A.O. Barvinsky G.A. Vilkovisky Nucl. Phys. NUPBBO 0550-3213 B333, 471 (1990); 10.1016/0550-3213(90)90047-H
67. A.O. Barvinsky G.A. Vilkovisky Nucl. Phys. NUPBBO 0550-3213 B333, 512 (1990); 10.1016/0550-3213(90)90048-I
68. A.O. Barvinsky, Y.V. Gusev, V.V. Zhytnikov, and G.A. Vilkovisky, Manitoba Report No. Print-93-0274;
69. A.O. Barvinsky and G.A. Vilkovisky, Phys. Rep. PRPLCM 0370-1573 119, 1 (1985).
70. C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation (Freeman, New York, 1973).
71. E.A. Uehling, Phys. Rev. 48, 55 (1935). PHRVAO 0031-899X 10.1103/PhysRev.48.55
72. E. Wichmann and N. Kroll, Phys. Rev. 96, 232 (1954). PHRVAO 0031-899X 10.1103/PhysRev.96.232
73. A.D. Martin, J. Outhwaite, and M.G. Ryskin, Phys. Lett. B 492, 69 (2000). PYLBAJ 0370-2693 10.1016/S0370-2693(00)01083-2
74. J.B. Hartle, Gravity: an Introduction to Einstein's General Relativity (Addison-Wesley, New York, 2002).
75. R.C. Myers and M.J. Perry, Ann. Phys. (N.Y.) APNYA6 0003-4916 172, 304 (1986); 10.1016/0003-4916(86)90186-7
76. D.Y. Xu, Classical Quantum Gravity CQGRDG 0264-9381 5, 871 (1988). 10.1088/0264-9381/5/6/008
77. S. Capozziello, S. Carloni, and A. Troisi, Report No. RSP/AA/21-2003;
78. S.M. Carroll, V. Duvvuri, M. Trodden, and M.S. Turner, Phys. Rev. D 70, 043528 (2004); PRVDAQ 0556-2821 10.1103/PhysRevD.70.043528
79. E.E. Flanagan, Phys. Rev. Lett. 92, 071101 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.92.071101
80. J.W. Moffat, J. Cosmol. Astropart. Phys. 1475-7516 03 (2006) 004; 10.1088/1475-7516/2006/03/004
81. J.W. Moffat J. Cosmol. Astropart. Phys. 1475-7516 05 (2005) 003. 10.1088/1475-7516/2005/05/003