Instability of classical dynamics in theories with higher derivatives

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 75, Issue 8, 2007, Pages

  Nesterenko, V V ^a  

^a JOINT INSTITUTE FOR NUCLEAR RESEARCH   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34247490098     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.75.087703     Document Type: Article

References (43)

1. A. Pais and G.E. Uhlenbeck, Phys. Rev. 79, 145 (1950). PHRVAO 0031-899X 10.1103/PhysRev.79.145
2. B. Podolski and P. Schwed, Rev. Mod. Phys. 20, 40 (1948). RMPHAT 0034-6861 10.1103/RevModPhys.20.40
3. M. Kaku, Phys. Rev. D 27, 2809 (1983). PRVDAQ 0556-2821 10.1103/PhysRevD.27.2809
4. I.L. Buchbinder, S.D. Odintsov, and I.L. Shapiro, Effective Action in Quantum Gravity (I.O.P. Publishing, Boston and Philadelphia, 1992).
5. K.S. Stelle, Phys. Rev. D 16, 953 (1977); PRVDAQ 0556-2821 10.1103/PhysRevD.16.953
6. K.S. Stelle Gen. Relativ. Gravit. GRGVA8 0001-7701 9, 353 (1978). 10.1007/BF00760427
7. E. Tomboulis, Phys. Lett. B 97, 77 (1980). PYLBAJ 0370-2693 10.1016/0370-2693(80)90550-X
8. E.S. Fradkin and A.A. Tseytlin, Nucl. Phys. B NUPBBO 0550-3213 201, 469 (1982). 10.1016/0550-3213(82)90444-8
9. D.G. Boulware and S. Deser, Phys. Rev. Lett. 55, 2656 (1985). PRLTAO 0031-9007 10.1103/PhysRevLett.55.2656
10. B. Zwiebach, Phys. Lett. B 156, 315 (1985). PYLBAJ 0370-2693 10.1016/0370-2693(85)91616-8
11. D.G. Boulware in Quantum Theory of Gravity, edited by, S. Christensen, (Hilger, Bristol, 1984), p. 267.
12. S.W. Hawking in Quantum Field Theory and Quantum Statistics, edited by I.A. Batalin, C.J. Isham, and, G.A. Vilkovisky, (Hilger, Bristol, 1987), Vol. 2, p. 129.
13. S.W. Hawking and T. Hertog, Phys. Rev. D 65, 103515 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.65.103515
14. R.P. Woodard, in Proceedings of the 3rd Aegean Summer School, Chios, Greece, 2005;
15. R.P. Woodard astro-ph/0601672.
16. V.V. Nesterenko, J. Phys. A JPHAC5 0305-4470 22, 1673 (1989); 10.1088/0305-4470/22/10/021
17. V.V. Nesterenko J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 32, 3315 (1991); 10.1063/1.529494
18. V.V. Nesterenko Class. Quant. Grav. CQGRDG 0264-9381 9, 1101 (1992); 10.1088/0264-9381/9/4/020
19. V.V. Nesterenko Mod. Phys. Lett. A 6, 719 (1991); MPLAEQ 0217-7323 10.1142/S0217732391000749
20. V.V. Nesterenko Int. J. Mod. Phys. A 6, 3989 (1991); IMPAEF 0217-751X 10.1142/S0217751X91001945
21. V.V. Nesterenko J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 34, 5589 (1993); 10.1063/1.530271
22. V.V. Nesterenko Phys. Lett. B 327, 50 (1994). PYLBAJ 0370-2693 10.1016/0370-2693(94)91527-X
23. M.S. Plyushchay, Int. J. Mod. Phys. A 4, 3851 (1989); IMPAEF 0217-751X 10.1142/S0217751X89001564
24. M.S. Plyushchay Phys. Lett. B 243, 383 (1990); PYLBAJ 0370-2693 10.1016/0370-2693(90)91401-V
25. M.S. Plyushchay Nucl. Phys. NUPBBO 0550-3213 B362, 54 (1991); 10.1016/0550-3213(91)90555-C
26. Yu.A. Kuznetsov and M.S. Plyushchay, Nucl. Phys. NUPBBO 0550-3213 B389, 181 (1993). 10.1016/0550-3213(93)90290-6
27. V.V. Nesterenko and Nguyen Suan Han, Int. J. Mod. Phys. A 3, 2315 (1988). IMPAEF 0217-751X 10.1142/S0217751X88000977
28. W. Thirring, Phys. Rev. 77, 570 (1950). PHRVAO 0031-899X 10.1103/PhysRev.77.570
29. A.V. Smilga, Nucl. Phys. NUPBBO 0550-3213 B706, 598 (2005); 10.1016/j.nuclphysb.2004.10.037
30. A.V. Smilga Phys. Lett. B 632, 433 (2006). PYLBAJ 0370-2693 10.1016/j.physletb.2005.10.014
31. D. Robert and A.V. Smilga, hep-th/0611096.
32. P.D. Mannheim, Astrophys. J. 561, 1 (2001). ASJOAB 0004-637X 10.1086/323206
33. W. Heisenberg, Nucl. Phys. NUPHA7 0029-5582 4, 532 (1957).
34. A.M. Chervyakov and V.V. Nesterenko, Phys. Rev. D 48, 5811 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.48.5811
35. E. Pagani, G. Tecchiolli, and S. Zerbini, Lett. Math. Phys. 14, 311 (1987). LMPHDY 0377-9017 10.1007/BF00402140
36. P.D. Mannheim, hep-th/0608154;
37. P.D. Mannheim and A. Davidson, Phys. Rev. A 71, 042110 (2005); PLRAAN 1050-2947 10.1103/PhysRevA.71.042110
38. P.D. Mannheim A. Davidson hep-th/0001115.
39. M.V. Ostrogradski, Mem. Acad. Sci. St. Petersbourg VI 4, 385 (1850);
40. See also E.T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies (Cambridge University Press, Cambridge, England, 1959).
41. N.G. Stephen, J. Sound Vib. JSVIAG 0022-460X 292, 372 (2006); 10.1016/j.jsv.2005.08.003
42. On the Ostrogradski instability for higher-order derivative theories and a pseudo-mechanical energy (unpublished).
43. V.V. Nesterenko, J. Appl. Math. Mech. 57, 669 (1993). JAMMAR 0021-8928 10.1016/0021-8928(93)90036-L