HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 7 (1952) > Number 5
| Next Article >

Prog. Theor. Phys. Vol. 7 No. 5 (1952) pp. 449-468

[ Full Text PDF : FREE ACCESS (1379K) ]

Operator Calculus in Quantized Field Theory

Kazuo Yamazaki

Department of Physics, Kyoto University

(Received April 7, 1952)

Abstract:

Following the suggestion of Feynman, we analyze the operators corresponding to the electron-positron field by means of the operator calculus. Thus we can deduce operationally Feynman's theory from the second quantized theory. With the aid of the external spinors, which are considered as the analogues of the Schwinger's prescribed source, we obtain formally a closed form of the S-matrix. Using this result we can derive the diffusion equation for the Dirac field very simply. The relations to the Schwinger's new theory of Green function are also discussed. Finally the formula for multiple boson or fermion pair-production are presented as illustrations for applications.


URL : http://ptp.ipap.jp/link?PTP/7/449/
DOI : 10.1143/PTP.7.449

[ Full Text PDF : FREE ACCESS (1379K) ] Citation:

References:

  1. J. Schwinger, Proc. Nat. Acad. Sci. 37 (1951), 452; ibid. 37 (1951), 455.
  2. R. P. Feynman, Phys. Rev. 84 (1951), 108[APS].
  3. I. Fujiwara, Prog. Theor. Phys. 7 (1952), 433[PTP].
  4. M. Neuman, Phys. Rev. 83 (1951), 1258[APS]; ibid. 85 (1952), 129[APS].
  5. N. Fukuda and S. Tomonaga, Lecture at REKS in Nagoya on February 1951.
  6. Y. Nambu, Lecture at REKS in Kyoto on December 1951.
  7. Y. Katayama, Prog. Theor. Phys. 7 (1952), 205, [PTP]
    and also independently S. Hori, Prog. Theor. Phys. 7 (1952), 578[PTP].
  8. R. J. Glauber, Phys. Rev. 84 (1951), 395[APS].
  9. J. Schwinger, Phys. Rev. 74 (1948), 1439[APS]; ibid. 75 (1949), 651[APS].
  10. R. Courant and D. Hilbert, Methoden der Mathematishen Physik, second edition, Vol I. Chapter III.
  11. R. P. Feynman, Phys. Rev. 76 (1949), 749[APS].
  12. R. P. Feynman, Phys. Rev. 80 (1950), 440[APS].
  13. D. Ito, H. Tanaka, Y. Watanabe, M. Yamazaki, Prog. Theor. Phys. 7 (1952), 128[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 7 No. 5 (1952) pp. 601-602 :
    Convergence Problem in Quantum Electrodynamics
    Y. Katayama and K. Yamazaki
  2. Progress of Theoretical Physics Vol. 12 No. 6 (1954) pp. 723-746 :
    On the Meaning of the Solution of the One-Body Dirac Equation
    Smio Tani and Kazuo Yamazaki
  3. Progress of Theoretical Physics Vol. 24 No. 5 (1960) pp. 1109-1117 :
    On Radiative Corrections due to Soft Photons
    Toshiyuki Murota
  4. Progress of Theoretical Physics Vol. 44 No. 3 (1970) pp. 590-598 :
    Vacuum Expectation Values of Some Exponential Operators
    R. J. Blomer
  5. Progress of Theoretical Physics Vol. 49 No. 6 (1973) pp. 2125-2132 :
    Super-Quantization. I
    Susumu Okubo

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.