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Prog. Theor. Phys. Vol. 66 No. 2 (1981) pp. 672-684

[ Full Text PDF : FREE ACCESS (531K) ]

Covariant Schrödinger Equation via Path Integrals

Takashi Miura

Department of Physics, Faculty of Engineering, Kanagawa University, Yokohama 221

(Received September 18, 1980)

Abstract:

Propagation equations of infinitesimal time differences in path integral representations are investigated in a manifestly covariant way in the curved space-time. Covariant Schrödinger equations via these path integrals are studied by using a formula which expresses explicitly the relation between normal coordinates and general covariant ones within the required approximation.
The Dirac equation is investigated by using the devices that we developed in our previous paper and the ambiguity in defining the normalization factor is removed.
Path integrals in phase space are discussed by applying such factor orderings as the geodesic distance approximation to the metric fields and the hermitian one to the gauge fields, which reduces the Hamiltonian formulations to the Lagrangian ones. The Kaluza-Klein theory is studied in the framework of path integrals as an example of the above investigations.


URL : http://ptp.ipap.jp/link?PTP/66/672/
DOI : 10.1143/PTP.66.672

[ Full Text PDF : FREE ACCESS (531K) ] Citation:

References:

  1. T. Miura, Prog. Theor. Phys. 61 (1979), 1521[PTP].
  2. B. DeWitt, Rev. Mod. Phys. 29 (1957), 377[APS].
  3. C. DeWitt-Morette, Feynman Path Integral, Lecture Notes Phys. 106 (1979), 227.
  4. K. Cheng, J. Math. Phys. 13 (1972), 1723[CrossRef].
  5. J. Dowker, Functional Integration and Its Applications (Clarendon, 1975), p. 34.
  6. C. Hsue, J. Math. Phys. 16 (1975), 2326[CrossRef].
  7. J. Hartle and S. Hawking, Phys. Rev. D 13 (1976), 2188 [APS](Appendix).
  8. R. Feynman, Rev. Mod. Phys. 20 (1948), 367[APS].
  9. J. Dowker and I. Mayes, Nucl. Phys. B 29 (1971), 259[CrossRef]; J. Math. Phys. 14 (1973), 434[CrossRef].
  10. M. Marinov, Phys. Rep. 60 (1980), 1, [CrossRef]and references given therein.
  11. L. Cohen, J. Math. Phys. 11 (1970), 3296[CrossRef]; ibid. 17 (1976), 597[CrossRef].
  12. O. Klein, Z. Phys. 37 (1926), 895.
  13. W. Pauli, The Theory of Relativity (Pergamon, 1958).
  14. L. Schulman, Functional Integration and Its Applications (Clarendon, 1975), p. 144.
  15. E. Schrödinger, Sitzber. Preuss. Akad. Wiss. 7 (1932), 105.
  16. B. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, 1965).
  17. C. Morette, Phys. Rev. 81 (1951), 848[APS].
  18. Von Westenholz, Differential Forms in Mathematical Physics (North-Holland, 1978).
  19. M. Kac, Trans. Am. Math. Soc. 65 (1979).
  20. D. Chitre and J. Hartle, Phys. Rev. D 16 (1977), 251[APS].
  21. R. Hermann, Interdisci. math. x 436 (Math sci press, 1976).
  22. A. Inomata and M. Trinkala, Phys. Rev. D 18 (1978), 1861[APS].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 571-575 :
    WKB Approximations for Relativistic Particles
    Takashi Miura

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