Table of Contents
Physics Research International
Volume 2012 (2012), Article ID 506285, 11 pages
http://dx.doi.org/10.1155/2012/506285
Research Article

On 𝑓(𝑅) Theories in Two-Dimensional Spacetime

Physics Department, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 22 June 2011; Revised 26 October 2011; Accepted 3 December 2011

Academic Editor: Ashok Chatterjee

Copyright © 2012 M. A. Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Weyl, Annalen der Physik, vol. 364, no. 10, pp. 101–133, 1919.
  2. A. S. Eddington, The Mathematical Theory of Relativity, Cambridge University Press, Cambridge, UK, 1923.
  3. R. Utiyama and B. S. DeWitt, “Renormalization of a classical gravitational field interacting with quantized matter fields,” Journal of Mathematical Physics, vol. 3, no. 4, pp. 608–618, 1962. View at Google Scholar
  4. K. S. Stelle, “Renormalization of higher-derivative quantum gravity,” Physical Review D, vol. 16, no. 4, pp. 953–969, 1977. View at Publisher · View at Google Scholar
  5. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Spacetime, Cambridge University Press, Cambridge, UK, 1982.
  6. I. L. Buchbinder, S. D. Odinstov, and I. L. Smapiro, Effective Actions in Quantum Gravity, IOP Publishing, Bristol, UK, 1992.
  7. A. de Felice and S. Tsujikawa, “f (R) theories,” Living Reviews in Relativity, vol. 13, no. 3, pp. 1–161, 2010. View at Google Scholar
  8. L. P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton, NJ, USA, 1949.
  9. D. Grumiller, W. Kummer, and D. V. Vassilevich, Physics Reports, vol. 369, no. 4, Article ID 104012, pp. 327–430, 2002.
  10. C. G. Callan, S. B. Giddings, J. A. Harvey, and A. Strominger, “Evanescent black holes,” Physical Review D, vol. 45, no. 4, pp. R1005–R1009, 1992. View at Publisher · View at Google Scholar · View at Scopus
  11. G. Mandal, A. M. Sengupta, and S. R. Wadia, “Classical solutions of two-dimensional string theory,” Modern Physics Letters A, vol. 6, pp. 1685–1692, 1991. View at Google Scholar
  12. E. Witten, “String theory and black holes,” Physical Review D, vol. 44, no. 2, pp. 314–324, 1991. View at Publisher · View at Google Scholar · View at Scopus
  13. M. A. Ahmed, “Classical and quantum cosmology in a model of two-dimensional dilaton gravity,” Physical Review D, vol. 61, no. 10, Article ID 104012, 8 pages, 2000. View at Publisher · View at Google Scholar
  14. M. A. Ahmed, “Cosmology in two-dimensional dilaton gravity theories,” Nuovo Cimento della Societa Italiana di Fisica B, vol. 121, no. 7, pp. 661–673, 2006. View at Publisher · View at Google Scholar · View at Scopus
  15. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York, NY, USA, 1972.
  16. K. C. K. Chan and R. B. Mann, “Cosmological models in two spacetime dimensions,” Classical and Quantum Gravity, vol. 10, no. 5, pp. 913–930, 1993. View at Publisher · View at Google Scholar
  17. A. Vilenkin, “Classical and quantum cosmology of the Starobinsky inflationary model,” Physical Review D, vol. 32, no. 10, pp. 2511–2521, 1985. View at Publisher · View at Google Scholar · View at Scopus
  18. M. P. Hobson, G. Efstathiou, and A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press, Cambridge, UK, 2006.
  19. A. R. Liddle and D. H. Lyth, Cosmological Inflation & Large Scale Structure, Cambridge University Press, Cambridge, UK, 2000.
  20. S. W. Hawking and J. C. Luttrell, “Higher derivatives in quantum cosmology. (I). The isotropic case,” Nuclear Physics, Section B, vol. 247, no. 1, pp. 250–260, 1984. View at Google Scholar
  21. K. W. Ford, D. L. Hill, M. Wakano, and J. A. Wheeler, “Quantum effects near a barrier maximum,” Annals of Physics, vol. 7, no. 3, pp. 239–258, 1959. View at Google Scholar · View at Scopus
  22. W. A. Friedman and C. J. Goebel, “Barrier-top resonances and heavy ion reactions,” Annals of Physics, vol. 104, no. 1, pp. 145–183, 1977. View at Google Scholar · View at Scopus
  23. G. Barton, “Quantum mechanics of the inverted oscillator potential,” Annals of Physics, vol. 166, no. 2, pp. 322–363, 1986. View at Google Scholar
  24. N. L. Balazs and A. Voros, “Wigner's function and tunneling,” Annals of Physics, vol. 199, no. 1, pp. 123–140, 1990. View at Google Scholar · View at Scopus
  25. D. Chruściński, “Quantum mechanics of damped systems. II. Damping and parabolic potential barrier,” Journal of Mathematical Physics, vol. 45, no. 3, pp. 841–854, 2004. View at Publisher · View at Google Scholar
  26. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1972.
  27. Z. X. Wong and D. R. Guo, Special Functions, World Scientific, Singapore, 1989.
  28. A. A. Starobinsky, “A new type of isotropic cosmological models without singularity,” Physics Letters B, vol. 91, no. 1, pp. 99–102, 1980. View at Google Scholar · View at Scopus