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Gamow Vectors and Time Asymmetry

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Abstract

We prove that Gamow vectors are important toolsin the quantum theory of irreversibility. We use themathematical formalism of rigged Hilbert spaces. Wediscuss some spectral formulas that include Gamow vectors as well as some results concerningGamow vectors. The role of the time-reversal operator isstudied. The formalism can be applied to formulate asense of irreversibility in cosmology.

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REFERENCES

  1. R. W. Zwanzig, J. Chem. Phys. 33, 1338 (1960).

    Google Scholar 

  2. R. W. Zwanzig, Statistical mechanics of irreversibility, in Quantum Statistical Mechanics, P. Meijer, ed. (Gordon and Breach, New York, 1966).

    Google Scholar 

  3. D. H. Zeh, The Physical Basis of the Direction of Time (Springer-Verlag, Berlin, 1989).

    Google Scholar 

  4. B. Misra, I. Prigogine, and M. Courbage, Physica A, 98, 1 (1979).

    Google Scholar 

  5. I. Prigogine, From Being to Becoming (Freeman, New York, 1980).

    Google Scholar 

  6. I. Prigogine and C. George, Proc. Natl. Acad. Sci. USA 80, 4590 (1983).

    Google Scholar 

  7. I. Antoniou and I. Prigogine, Physica A 192, 443 (1993); Antoniou, I., and Tasaki, S., Physica A 190, 303 (1992).

    Google Scholar 

  8. A. Bohm, Quantum Mechanics: Foundation and Applications (Springer-Verlag, Berlin, 1986).

    Google Scholar 

  9. A. Bohm, J. Math. Phys. 22, 2813 (1981).

    Google Scholar 

  10. A. Bohm and M. Gadella, Dirac kets, Gamow vectors and Gel' fand triplets, in Springer Lecture Notes in Physics, No. 348, A. Bohm and J. D. Dollard, eds. (Springer-Verlag, New York, 1989).

    Google Scholar 

  11. M. Castagnino and R. Laura, Phys. Rev. A 56, 198 (1997).

    Google Scholar 

  12. R. Laura and M. Castagnino, Phys. Rev. A 57, 4140 (1998).

    Google Scholar 

  13. A. Bohm, I. Antoniou, and P. Kilelanowski, J. Math. Phys. 36, 2593 (1995).

    Google Scholar 

  14. I. M. Gel'fand and G. F. Shilov, Generalized Functions, Vol. 4 (Academic Press, New York, 1967).

    Google Scholar 

  15. K. Maurin, Bull. Acad. Pol. Sci. Ser. Sci. Math. Astr. Phys. VII, 471 (1959).

    Google Scholar 

  16. K. Maurin, Generalized Eigenfunction Expansion and Unitary Representations of Topological Groups (Polish Scientific Publishers, Warsaw, 1968).

    Google Scholar 

  17. D. Friedricks, Rep. Math. Phys. 8, 277 (1975)

    Google Scholar 

  18. O. Melsheimer, J. Math. Phys. 15, 902 (1974).

    Google Scholar 

  19. J. P. Antoine, J. Math. Phys. 10, 53 (1969).

    Google Scholar 

  20. A. Bohm, The rigged Hilbert space in quantum physics, ICTP Report No 4, Trieste (1965).

  21. A. Bohm, Rigged Hilbert space and mathematical description of physical systems, in Boulder Lectures on Theoretical Physics, Vol. 9, O. A. Barut, ed. (1966).

  22. J. E. Roberts, Commun. Math. Phys. 3, 98 (1966).

    Google Scholar 

  23. A. Bohm, J. Math. Phys. 21, 1040 (1980).

    Google Scholar 

  24. M. Gadella, J. Math. Phys. 24, 1462 (1983).

    Google Scholar 

  25. T. Petrovski, I. Prigogine, and S. Tasaki, Physica A 173, 175 (1991).

    Google Scholar 

  26. W. O. Amrein, J. M. Jauch, and K. B. Sinha, Scattering Theory in Quantum Mechanics (Benjamin, New York, 1977).

    Google Scholar 

  27. M. Reed and B. Simon, Scattering Theory (Academic Press, New York, 1979).

    Google Scholar 

  28. R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York 1966).

    Google Scholar 

  29. H. M. Nussenzveig, Causality and Dispersion Relations (Academic Press, New York, 1972).

    Google Scholar 

  30. C. van Winter, Trans. Am. Math. Soc. 162, 103 (1971); C. van Winter, J. Math. Ann. 47, 633 (1974).

    Google Scholar 

  31. A. Bohm, I. Antoniou, and P. Kilelanowski, Phys. Lett. A 189, 442 (1995).

    Google Scholar 

  32. N. Nakanishi, Progr. Theor. Phys. 19, 607 (1958).

    Google Scholar 

  33. M. Castagnino, F. Gaioli, and E. Gunzig, Found. Cosmol. Phys. 16, 221 (1996).

    Google Scholar 

  34. M. Gadella and A. Ordóñez, Int. J. Theor. Phys., 38, 191 (1999).

    Google Scholar 

  35. I. Antoniou and I. Prigogine, Physica 192A, 443 (1993).

    Google Scholar 

  36. P. D. Lax and R. S. Phillips, Scattering Theory (Academic Press, New York, 1979).

    Google Scholar 

  37. G. Ludwig, Foundations of Quantum Mechanics (Springer-Verlag, New York, 1985).

    Google Scholar 

  38. E. P. Wigner, Group Theory (Academic Press, New York, 1968).

    Google Scholar 

  39. E. P. Wigner, In Group Theoretical Concepts and Methods in Elementary Particle Physics, F. Gürsey, ed. (Gordon and Breach, New York, 1994).

    Google Scholar 

  40. P. Exner, Open Quantum Systems and Feynman Integrals (Reidel, Dordrecht, 1985).

    Google Scholar 

  41. B. Misra and I. Prigogine, Lett. Math. Phys. 7, 421 (1983).

    Google Scholar 

  42. S. W. Hawking, Nucl. Phys. B 239, 257 (1984).

    Google Scholar 

  43. J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2690 (1983).

    Google Scholar 

  44. A. Vilenkin, Phys Rev. D 53, 3560 (1986).

    Google Scholar 

  45. A. Vilenkin, Phys. Rev. D 37, 888 (1988).

    Google Scholar 

  46. M. Castagnino, Phys. Rev. D 57, 750 (1998).

    Google Scholar 

  47. M. Castagnino, The global nature of time asymmetry and Bohm-Reichenbach diagram, in Proceeding G 21, Goslar 1997, A. Bohm, ed. (Springer Verlag, Berlin, 1998).

    Google Scholar 

  48. M. Castagnino, E. Gunzig, S. Iguri, and A. Ordoñez, Kolmogorov Lax-Phillips systems as branch systems of Reichenbach diagram, in Proceeding 7th International Workshop on Instabilities and Non-equilibrium Structures, Valponaiso, Chile, E. Tirapegui, ed. (1997).

  49. M. Castagnino, E. Gunzig, P. Nardone, I. Prigogine, and S. Tasaki, Quantum cosmology and large Poincaré systems, in Quantum Chaos and Cosmology, M. Namiki, ed. (AIP, New York, 1997).

    Google Scholar 

  50. M. Castagnino, and E. Gunzig, Minimal irreversible quantum mechanics: An axiomatic formalism, Int. J. Theor. Phys. 38, 47 (1999).

    Google Scholar 

  51. P. Koosis, Introduction to H p Spaces (Cambridge University Press, Cambridge, 1980).

    Google Scholar 

  52. P. L. Duren, Theory of H p Spaces (Academic Press, New York, 1970).

    Google Scholar 

  53. K. Hoffman, Banach Spaces of Analytic Functions (Prentice-Hall, Englewood Cliffs, New Jersey, 1962).

    Google Scholar 

  54. W. Rudin, Functional Analysis (McGraw-Hill, New York, 1973).

    Google Scholar 

  55. Vo-Khac Khoan, Distributions, Analyse de Fourier, Operateurs aux Derivées Partielles (Vuiber, Paris, 1972).

    Google Scholar 

  56. A. Bohm, Phys. Rev. A, 51, 1758 (1995).

    Google Scholar 

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Authors
  1. M. Castagnino
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  2. M. Gadella
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  3. F. Gaioli
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  4. R. Laura
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Castagnino, M., Gadella, M., Gaioli, F. et al. Gamow Vectors and Time Asymmetry. International Journal of Theoretical Physics 38, 2823–2865 (1999). https://doi.org/10.1023/A:1026643712614

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