Explicit classical solutions and comments on Higher-Derivative Klein-Gordon equation in (1+1)-D
A. Cherman ª, L.G. Ferreira Filhob, L.L. Santos Guedesc and J.A. Helayël-Netod
ª Fundacão Planetário da Cidade do Rio de Janeiro, Rua Vice-Governador Rubens Berardo, 100, 22451-070, Rio de Janeiro, RJ, Brasil, and Centro Brasileiro de Pesquisas Físicas - CBPF, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brasil, e-mail: alexandre.cherman@planetario.rio.rj.gov.br
b FAT— UERJ/Resende, Estrada Resende-Riachuelo s/n, 27523-000, Resende, RJ, Brasil, e-mail: gonzaga@fat.uerj.br
c Fundacão Planetario da Cidade do Rio de Janeiro, e-mail: leandro.guedes@planetario.rio.rj.gov.br
]]> d Centro Brasileiro de Pesquisas Físicas - CBPF, e-mail: helayel@cbpf.br
Recibido el 30 de marzo de 2012;
Aceptado el 6 de junio de 2012
Abstract
We present a simple and general method to solve higher-power D'Alembert equation in (1+1) dimensions for a set of completely general initial conditions. Explicit solutions are written down for the cases of []2 and []3 and the singularity structure is manifest through the derivative terms of some of the initial-condition functions. The explicit solutions found out may be useful if one wishes to device external sources which may suppress the non-physical modes introduced by the higher derivatives.
Keywords: Higher-derivative theories; 2D theories; ghosts.
PACS: 03.50.Kk; 03.65.Pm; 03.65.Fd
]]>DESCARGAR ARTÍCULO EN FORMATO PDF
References
1. M. Ostrogradsky, Mémoire de l'Academie des Sciences de St. Petersburg 6 (1850) 385. [ Links ]
2. B. Podolski, Physical Review 62 (1942) 68. [ Links ]
3. B. Podolski, and C. Kikuchi, Physical Review 65 (1944) 228. [ Links ]
]]>4. B. Podolski, and P. Schwed, Review of Modern Physics 20 (1948) 40. [ Links ]
5. W. Thirring, Physical Review 77 (1950) 570. [ Links ]
6. H. J. Bhabha, Physical Review 77 (1950) 665. [ Links ]
7. A. Pais, and G. E. Uhlenbeck, Physical Review 79 (1950) 145. [ Links ]
8. W. Heisenberg, Nuclear Physics 4 (1957) 532. [ Links ]
]]>9. A. Gravielides, T. K. Kuo, and S. Y. Lee, Physical Review D13 (1976) 2912. [ Links ]
10. H. Narnhofer, and W. Thirring, Physics Letters 76B (1978) 428. [ Links ]
11. B. -G. Englert, J. Karkowski, and J. M. Rayski Jr., Physics Letters 83B (1979) 399. [ Links ]
12. J. J. Giambiagi, J. A. Nieto, and O. Obregon, CBPF-Notas de Física 53 (1994) and Nuovo Cimento B110 (1995) 101- [ Links ]108. [ Links ]
13. A. Gravielides, T. K. Kuo, and S. Y. Lee, Physical Review D12 (1975) 1829. [ Links ]
14. P. Havas, General Relativity and Gravitation 8 (1977) 631. [ Links ]
15. K. S. Stelle, General Relativity and Gravitation 9 (1978) 353. [ Links ]
16. C. Jankiewicz, Acta Physica Polonica B12 (1981) 859. [ Links ]
17. S. N. Solodukhin, Physical Review D 51 (1995) 591. [ Links ]
18. S. Mignemi, and H.-J. Schmidt, Classical and Quantum Gravity 12 (1995) 849. [ Links ]
19. S. Naftulin, and S. D. Odintsov, Modern Physics Letters A10 (1995) 2071. [ Links ]
20. A. Hindawi, B. A. Ovrut, and D. Waldram, Nuclear Physics B471 (1996) 409. [ Links ]
21. M. A. Namazie, Journal of Physics A 13 (1980) 713. [ Links ]
22. N. V. Krasnikov, A. B. Kyiatkin, and E. R.d Poppitz, Physics Letters B 222 (1989) 66. [ Links ]
23. B. A. Ovrut, Talk presented at STRING'95 (University of Southern California, EUA, 1995). hep-th/9506028. [ Links ]
24. A. Hindawi, B. A. Ovrut, and D. Waldram, Progress of Theoretical Physics Supplement 123 (1996) 397. [ Links ]
25 . A. Hindawi, B. A. Ovrut, and D. Waldram, Nuclear Physics B476 (1996) 175. [ Links ]
26. K. Forger, B. A. Ovrut, S. J. Theisen, and D. Waldram, Physics Letters B388 (1996) 1539. [ Links ]
27. S. Nojiri, and S. D. Odintsov, JHEP 0007 (2000) 49. [ Links ]
28. I. P. Neupane, JHEP 0009 (2000) 40. [ Links ]
29. S. Mukohyama, Physical Review D 65 (2002) 084036. [ Links ]
30. M. Parry, S. Pichler, and D. Deeg, (2005). hep-ph/0502048. [ Links ]
31. S. Nojiri, Gravitation and Cosmology 9 (2003) 71. [ Links ]
32. G. Berredo-Peixoto, and I. L. Shapiro, Physical Review D 71(2005) 064005. [ Links ]
33. Nojiri, S.; Odintsov, S. D. and Ogushi, S. Physical Review D 65 (2002) 023521. [ Links ]
34. J. Ronald Farias, Hadronic Journal 8 (1985) 227. [ Links ]
35. E. Pagani, G. Tecchiolli, and S. Zerbini, Letters in Mathematical Physics 14 (1987) 311. [ Links ]
36. T. Nakamura, and S. Hamamoto, Progress of Theoretical Physics 95 (1996) 469. [ Links ]
37. M. Borneas, and I. Damian, International Journal of Theoretical Physics 38 (1999) 2241. [ Links ]
38. I. Damian, International Journal of Theoretical Physics 39 (2000) 2141. [ Links ]
39. T. D. Bakeyev, and A. A. Slavnov, Modern Physics Letters A11 (1996) 1539. [ Links ]
40. T. D. Bakeyev, Theoretical and Mathematical Physics 122 (2000) 355. [ Links ]
]]>