Advertisement

Il Nuovo Cimento B (1971-1996)

, Volume 106, Issue 3, pp 253–261 | Cite as

Computing the normalized dirac wave function for oblique electric and magnetic fields

  • F. Melia
  • M. Fatuzzo
Article
  • 18 Downloads

Summary

Interactions taking place in superstrong gravitational and magnetic fields can account for a wide variety of spectral emissions from compact objects such as neutron stars. A quantum treatment of the particle transport in these environments,e.g., needed to calculate the anisotropic electrical conductivity, depends on the evaluation of matrix elements with solutions to the Dirac equation in oblique electric (E) and magnetic (H) fields. However, due to the complexity of the bispinors, these overlap integrals are often extremely difficult to compute. Indeed, no normalized wave function yet exists. Here we show that, in the special case whenE/H≲10−4, a simplification of the matrix elements permits an analytic integration that yields explicit expressions for the normalization constant and other overlap integrals. Physical quantities, such as the conductivity tensor, that depend directly on these matrix elements may then be computed in a straightforward way.

References

PACS 3.50.De Maxwell theory: general mathematical aspects PACS 11.10.Qr Relativistic wave equations PACS 52.40.Mj Particle beam interactions in plasma (including intese charged-particle beams) PACS 97.10.Ld Magnetic and electric fields polarization and starlight 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    E. P. Liang andV. Petrosian:Gamma-Ray Bursts (AIP, New York, N.Y., 1986).Google Scholar
  2. [2]
    E. P. Mazets, S. V. Golenetskii, R. L. Aptekar’, Yu. A. Gur’Yan andV. N. Il’inskii:Nature,290, 378 (1981).ADSCrossRefGoogle Scholar
  3. [3]
    G. J. Hueter: inHigh Energy Transients in Astrophysics, edited byS. E. Woosley (AIP, New York, N. Y., 1984), p. 373.Google Scholar
  4. [4]
    M. A. Ruderman: inXIII Texas Symposium on Relativistic Astrophysics, edited byM. P. Ulmer (World Scientific, Singapore, 1987), p. 448.Google Scholar
  5. [5]
    T. Murakami, M. Fujii, K. Hayashida, M. Itoh, J. Nishimura, T. Yamagami, J. P. Conner, W. D. Evans, E. E. Fenimore, R. W. Klebesadel, A. Yoshida, I. Kondo andN. Kawai:Nature,335, 234 (1988).ADSCrossRefGoogle Scholar
  6. [6]
    F. Melia:Astrophys. J.,334, L9 (1988).ADSCrossRefGoogle Scholar
  7. [7]
    E. E. Fenimore, J. P. Conner, R. I. Epstein, R. W. Klebesadel, J. G. Laros, A. Yoshida, M. Fujii, K. Hayashida, M. Itoh, T. Murakami, J. Nishimura, T. Yamagami, I. Kondo andN. Kawai:Astrophys. J.,335, L71 (1988).ADSCrossRefGoogle Scholar
  8. [8]
    J. C. L. Wang, D. Q. Lamb, T. J. Loredo, I. Wasserman andE. E. Fenimore:Bull. Am. Astron. Soc.,20, 1054 (1989).ADSGoogle Scholar
  9. [9]
    A. K. Harding andR. D. Preece:Astrophys. J.,338, L21 (1989).ADSCrossRefGoogle Scholar
  10. [10]
    F. Melia andM. Fatuzzo:Astrophys. J.,346, 378 (1989).ADSCrossRefGoogle Scholar
  11. [11]
    A. G. R. Lyne, R. N. Manchester andJ. H. Taylor:Mon. Not. R. Astron. Soc.,213, 613 (1985).ADSCrossRefGoogle Scholar
  12. [12]
    S. Rappaport andP. C. Joss:Nature,266, 683 (1977).ADSCrossRefGoogle Scholar
  13. [13]
    J. Trümper, W. Pietsch, C. Reppin, W. Voges, R. Staubert andE. Kendziorra:Astrophys. J.,219, L105 (1978).ADSCrossRefGoogle Scholar
  14. [14]
    W. A. Wheaton, J. P. Doty, F. A. Primini, B. A. Cooke, C. A. Dobson, A. Goldman, M. Hecht, J. A. Hoffman, S. K. Howe, A. Sheepmaker, E. Y. Tsiang, W. H. G. Lewin, J. L. Matteson, D. E. Gruber, W. A. Baity, R. Rothschild, F. K. Knight, P. Nolan andL. E. Peterson:Nature,282, 240 (1979).ADSCrossRefGoogle Scholar
  15. [15]
    F. Melia andM. Fatuzzo:Astrophys. J., in press (1991).Google Scholar
  16. [16]
    V. Canuto andC. Chiuderi:Lett. Nuovo Cimento,2, 223 (1969).ADSCrossRefGoogle Scholar
  17. [17]
    A. Holz:Lett. Nuovo Cimento,4, 26 (1970).CrossRefGoogle Scholar
  18. [18]
    V. Canuto andH. Y. Chiu:Space. Sci. Rev.,12, 755 (1971).CrossRefGoogle Scholar
  19. [19]
    D. B. Melrose andA. J. Parle:Aust. J. Phys.,36, 755 (1983).ADSCrossRefGoogle Scholar
  20. [20]
    A. A. Sokolov andI. M. Ternov:Synchrotron Radiation (Pergamon Press, Oxford, 1968).Google Scholar
  21. [21]
    M. H. Johnson andB. A. Lippmann:Phys. Rev.,76, 828 (1949).MathSciNetADSCrossRefMATHGoogle Scholar
  22. [22]
    F. Melia andM. Fatuzzo:Phys. Rev., in press (1991).Google Scholar

Copyright information

© Società Italiana di Fisica 1991

Authors and Affiliations

  • F. Melia
    • 1
  • M. Fatuzzo
    • 1
  1. 1.Department of Physics and AstronomyNorthwestern UniversityEvanstonUSA

Personalised recommendations