HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 67 (1982) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 67 No. 2 (1982) pp. 357-374

[ Full Text PDF : FREE ACCESS (730K) ]

Theory of Relativistic Top and Electromagnetic Interaction

Takehiko Takabayasi

Department of Physics, Nagoya University, Nagoya 464

(Received July 22, 1981)

Abstract:

The classical theory of an (generally) asymmetric relativistic top is given on the basis of a singular Lagrangian. The theory corresponds to covariant generalization of the non-relativistic theory of rigid body and leads to the relativization of Euler's equation for rigid body motion and to the standard mass formula for a top. The theory can be reinterpreted in terms of a quadrilocal model with rigidity constraints. In practice we give the theory for free case in two equivalent Lagrangian formalisms, of which the one is more flexible than the other and is employed for the extension of theory to the case when electromagnetic field is acting. This really given in a simple and natural manner in conformity with all the standard equations for relativistic particle with internal degrees moving in electromagnetic field. The theory is put equivalently in the constrained Hamiltonian formalism. For the case when the g-factor is two the theory gains a special simplicity. Quantum theory is deferred to a subsequent paper.


URL : http://ptp.ipap.jp/link?PTP/67/357/
DOI : 10.1143/PTP.67.357

[ Full Text PDF : FREE ACCESS (730K) ] Citation:

References:

  1. M. Born, Ann. der Phys. 30 (1909), 1.
    G. Herglotz, Ann. der Phys. 31 (1910), 393; ibid. 36 (1911), 493.
  2. L. H. Thomas, Phil. Mag. 3 (1927), 1.
  3. J. Frenkel. Z. Phys. 37 (1926), 243.
  4. H. B. G. Casimir, Rotation of a Rigid Body in Quantum Mechanics (Groningen, 1931).
  5. T. Nakano, Prog. Theor. Phys. 15 (1956), 333[PTP].
  6. T. Takabayasi, Nuovo Cim. 7 (1958), 118; C. R. Acad. Sci. Paris 246 (1958), 64.
  7. T. Takabayasi, Prog. Theor. Phys. 23 (1960), 915[PTP]; Nuovo Cim. 13 (1959), 532.
  8. T. Takabayasi, Soryushiron Kenkyu (Kyoto), 21 (1960), 723.
  9. D. Finkelstein, Phys. Rev. 100 (1955), 924[APS].
    F. Halbwachs, P. Hillion and J. P. Vigier, Nuovo Cim. 10 (1958), 817.
    H. Fukutome, Soryushiron Kenkyu (Kyoto), 26 (1962), 311.
    Y. Katayama, J. P. Vigier and H. Yukawa, Prog. Theor. Phys. 29 (1963), 468[PTP].
  10. D. Bohm, P. Hillion, T. Takabayasi and J. P. Vigier, Prog. Theor. Phys. 23 (1960), 496[PTP].
  11. O. Hara and T. Goto, Prog. Theor. Phys. Suppl. Extra Number (1965), 193[PTP]; ibid. No. 41 (1968), 56[PTP].
  12. T. Takabayasi, Prog. Theor. Phys. 36 (1966), 185[PTP]; ibid. 36 (1966), 187[PTP]; ibid. 36 (1966), 660[PTP]; ibid. 36 (1966), 662[PTP].
  13. T. Takabayasi, Prog. Theor. Phys. 38 (1967), 285[PTP]; ibid. 38 (1967), 287[PTP].
  14. T. Takabayasi, Prog. Theor. Phys. Suppl. No. 41 (1968), 130[PTP].
  15. H. Fukutome, Prog. Theor. Phys. 28 (1962), 731[PTP].
  16. T. Takabayasi, Prog. Theor. Phys. Suppl. Extra Number (1965), 339[PTP].
  17. T. Goto, Extended Pictures of Elementary particles (Iwanami, 1978).
    A. Barducci and L. Lusanna, Nuovo Cim. B 47 (1978), 54.
  18. T. Takabayasi, Prog. Theor. Phys. 57 (1977), 329[PTP].
  19. H. C. Corben, Classical and Quantum Theories of Spinning Particles (Holden-Day, 1968), which also contains numerous literature.
  20. A. J. Hanson and T. Regge, Ann. of Phys. 87 (1974), 498[CrossRef].
  21. S. Tanaka, Prog. Theor. Phys. Suppl. No. 67 (1979), 282[PTP].
  22. J. L. Synge, Relativity: The Special Theory (North-Holland, 1965).
  23. T. Takabayasi, Prog. Theor. Phys. 58 (1977), 1299[PTP]. (See §7 thereof.)
  24. T. Takabayasi, Prog. Theor. Phys. Suppl. No. 67 (1979), 1[PTP]. (See p. 63 thereof.)
  25. T. Takabayasi, Prog. Theor. Phys. 66 (1981), 736[PTP].
  26. T. Takabayasi, Prog. Theor. Phys. 66 (1981), 1466[PTP].
  27. W. G. Dixon, Nuovo Cim. 38 (1965), 1616.
  28. V. Bargmann, L. Michel and V. L. Telegdi, Phys. Rev. Lett. 2 (1959), 435[APS].
  29. Cf. P. A. M. Dirac, Lectures on Quantum Mechanics (New York, 1964).

Citing Article(s) :

  1. Progress of Theoretical Physics Supplement No.105 (1991) pp. 270-286 :
    25. Nonlocal Theories and Related Topics
    Takehiko Takabayasi

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.