Hamiltonian formalism in the presence of higher derivatives

Theoretical and Mathematical Physics

Volumn 157, Issue 2, 2008, Pages 1542-1549

  Morozov, A Yu ^a  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

Author keywords

Hamiltonian mechanics; Higher derivative theory; Reparameterization invariance

Indexed keywords

EID: 58149216230     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-008-0128-2     Document Type: Article

References (45)

1. E. Fradkin A. Tseytlin 1985 Nucl. Phys. B 261 1 27
2. M. Reuter and F. Saueressig, "Functional renormalization group equations, asymptotic safety, and quantum Einstein gravity," arXiv:0708.1317v1 (2007).
3. A. Garrett Lisi, "An exeptionally simple theory of everything," arXiv:0711.0770v1 (2007).
4. N. Arkani-Hamed S. Dimopoulos G. Dvali 1998 Phys. Lett. B 429 263 272
5. B. Kosyakov, Introduction to the Classical Theory of Particles and Fields, Springer, Berlin (2007); D. V. Gal'tsov, Phys. Rev. D, 66, 025016 (2002); arXiv:hep-th/0112110v1 (2001); P. O. Kazinski, S. L. Lyakhovich, and A. A. Sharapov, Phys. Rev. D, 66, 025017 (2002); arXiv:hep-th/0201046v3 (2002); Yu. Yaremko, SIGMA, 0501, 012 (2005); arXiv:math-ph/0511075v1 (2005); P. O. Kazinskii, "Effective dynamics of singular sources in classical field theory," Candidate dissertation, Tomsk State Univ., Tomsk (2007); A. D. Mironov and A. Yu. Morozov, "The problem of radiation friction beyond four and six dimensions," arXiv:0710.5676v1 (2007); A. D. Mironov and A. Yu. Morozov, JETP Lett., 85, 6-11 (2007); arXiv:hep-ph/0612074v1 (2006); Theor. Math. Phys., 156, 1209-1217 (2008); arXiv:hep-th/0703097v1 (2007); D. Galakhov, JETP Lett., 87, 452-458 (2008); arXiv:0710.5688v3 (2007).
6. A. Slavnov 1975 Nucl. Phys. B 97 155 164
7. R. Woodard, Phys. Rev. A, 62, 052105 (2000); arXiv:hep-th/0006207v2 (2000).
8. K. Bering, "A note on non-locality and Ostrogradski's construction," arXiv:hep-th/0007192v1 (2000).
9. R. Miron, D. Hrimiue, H. Shimada, and S. V. Sabau, The Geometry of Hamilton and Lagrange Spaces (Fund. Theories Phys., Vol. 118), Kluwer, Dordrecht (2001).
10. S. Hawking and T. Hertog, Phys. Rev. D, 65, 103515 (2002); arXiv:hep-th/0107088v2 (2001).
11. T.-C. Cheng, P.-M. Ho, and M.-C. Yeh, Phys. Rev. D, 66, 085015 (2002); arXiv:hep-th/0206077v2 (2002).
12. J. Gomis K. Kamimura T. Ramirez 2004 Nucl. Phys. B 696 263 291
13. A. Smilga 2006 Phys. Lett. B 632 433 438
14. M. S. Plyushchay 2006 EJTP 3 10 17 31
15. I. Cortese J. A. Garcia 2006 Phys. Lett. A 358 327 333
16. S. L. Lyakhovich A. A. Sharapov 2007 JHEP 0701 047
17. K. Bolonek P. Kosi'nski 2007 J. Phys. A 40 11561 11567
18. C. S. Acatrinei 2007 J. Phys. A 40 F929 F933
19. K. Andrzejewski, J. Gonera, and P. Maslanka, "A note on the Hamiltonian formalism for higher-derivative theories," arXiv:0710.2976v1 (2007).
20. M. V. Ostrogradskii, Complete Collected Works [in Russian], Vol. 2, Akad. Nauk Ukrain. SSR, Kiev (1961).
21. E. T. Wittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: With an Introduction to the Problem of Three Bodies, Cambridge Univ. Press, New York (1988).
22. A. Pais G. Uhlenbeck 1950 Phys. Rev. 79 145 165
23. P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Grad. Sch. Sci. Monographs Series, Vol. 2), Belfer Grad. Sch. Sci., New York (1967).
24. A. Slavnov 1971 Nucl. Phys. B 31 301 315
25. A. A. Slavnov and L. D. Faddeev, Introduction to the Quantum Theory of Gauge Fields [in Russian], Nauka, Moscow (1978); English transl.: L. D. Faddeev and A. A. Slavnov Gauge Fields: Introduction to Quantum Theory (Front. Phys., Vol. 83), Benjamin, Reading, Mass. (1990).
26. B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry: Methods and Applications [in Russian], Vol. 2, The Geometry and Topology of Manifolds, URSS, Moscow (2001); English transl.: B. A. Dubrovin, A. T. Fomenko, and S. P. Novikov, Modern Geometry - Methods and Applications: Part II. The Geometry and Topology of Manifolds (Grad. Texts Math., Vol. 93), 1991, Springer.
27. D. M. Gitman and I. V. Tyutin, Canonical Quantization of Fields with Constraints [in Russian], Nauka, Moscow (1986); English transl.: Quantization of Fields with Constraints, Springer, Berlin (1990).
28. D. Eliezer R. Woodard 1989 Nucl. Phys. B 325 389 469
29. M. Plyushchay 1989 Modern Phys. Lett. A 4 837 847
30. J. M. Pons 1989 Lett. Math. Phys. 17 181 189
31. J. Z. Simon 1990 Phys. Rev. D 41 3720 3733
32. M. Kreuzer 1990 Class. Q. Grav. 7 1303 1317
33. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton Univ. Press, Princeton, N. J. (1992).
34. J. Govaerts and M. S. Rashid, "The Hamiltonian formulation of higher order dynamical systems," arXiv:hepth/ 9403009v2 (1994).
35. J. Llosa J. Vives 1994 J. Math. Phys. 35 2856 2877
36. H.-J. Schmidt 1994 Phys. Rev. D 49 6354 6366
37. T. Nakamura S. Hamamoto 1996 Progr. Theoret. Phys. 95 469 484
38. A. Yu. Morozov 1986 Sov. Phys. Usp. 29 993 1039
39. V. V. Dolotin A. Yu. Morozov Sh. R. Shakirov 2007 Phys. Lett. B 651 71 73
40. I. Gelfand, M. Kapranov, and A. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, Birkhäuser, Boston, Mass. (1994); V. Dolotin and A. Morozov, Introduction to Non-Linear Algebra, World Scientific, Hackensack, N. J. (2007); arXiv:hep-th/0609022v4 (2006).
41. D. Fairlie J. Govaerts A. Morozov 1992 Nucl. Phys. B 373 214 232
42. V. Dolotin and A. Stoyanovskii, "Talks at ITEP seminars," (2006-2007).
43. P. Dunin-Barkowski and A. Sleptsov, "Geometric Hamiltonian formalism for reparametrization-invariant theories with higher derivatives," Theor. Math. Phys. (to appear); arXiv:0801.4293v2 (2008).
44. L. D. Landau and E. M. Lifshits, Mechanics [in Russian] (Vol. 1 of Course of Theoretical Physics), Nauka, Moscow (1957); English transl., Pergamon, Oxford (1960).
45. A. Yu. Morozov 1994 Sov. Phys. Uspekhi 37 1 55