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Prog. Theor. Phys. Vol. 16 No. 3 (1956) pp. 157-176

[ Full Text PDF : FREE ACCESS (1618K) ]

On the Quantum Field Theory of the Interaction between the Graviton and the Matter Field

Toshiei Kimura

Research Institute for Theoretical Physics, Hiroshima University, Takehara-machi, Hiroshima-ken

(Received April 30, 1956)

Abstract:

In order to quantize the gravitational field so as to be consistent with the general relativistic treatment, we investigate what physical effects the quantizable and unquantizable parts of gravitational field have, when the matter fields exist. To construct the Hamiltonian, we show that the interaction Hamiltonian in the interaction representation can be obtained by the method extended from that of Yang-Feldman. The role of the non-linear part of gravitational field for such a problem is also discussed. Only the potential, obtained by eliminating the longitudinal and scalar parts of gravitational field with the aid of the supplementary condition, has an effect upon the macroscopical phenomena and gives the equation of two-body problem in general relativity found by Einstein, Infeld and Hoffmann. On the other hand, while the pure transverse graviton does not contribute to the macroscopical phenomena, it gives, in the region of high energy, the large damping effect upon the interaction between the elementary particles.


URL : http://ptp.ipap.jp/link?PTP/16/157/
DOI : 10.1143/PTP.16.157

[ Full Text PDF : FREE ACCESS (1618K) ] Citation:

References:

  1. A. Einstein, L. Infeld and B. Hoffmann, Ann. Math. 39 (1938), 65, Eq. (17 ·2).
    Cf. also B. Bertotti, Nuovo Cim. 12 (1954), 226.
  2. De Donder, La gravifique Einsteininne. (Paris: Ganthiers-Villars) 1921.
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 16 No. 6 (1956) pp. 555-568 :
    On the Quantum Field Theory of the Interaction between the Graviton and the Matter Field, II
    Toshiei Kimura
  2. Progress of Theoretical Physics Vol. 19 No. 1 (1958) pp. 112-124 :
    On the Decay Interactions of Strange Particles
    Yoshihiko Miyachi
  3. Progress of Theoretical Physics Vol. 20 No. 4 (1958) pp. 476-486 :
    Perturbational Calculations of Propagators of the Elementary Particles interacting with Gravitational Field
    Yoshio Miyatake
  4. Progress of Theoretical Physics Vol. 20 No. 5 (1958) pp. 703-714 :
    On the Tests of Gravitational Theories in Terms of an Artificial Satellite
    Hidekazu Nariai and Yoshio Ueno
  5. Progress of Theoretical Physics Vol. 26 No. 2 (1961) pp. 157-172 :
    Fixation of Physical Space-Time Coordinates and Equation of Motion of Two-Body Problem
    Toshiei Kimura
  6. Progress of Theoretical Physics Vol. 31 No. 2 (1964) pp. 311-321 :
    On the Commutation Relation for the Canonical Energy Density
    Toshiei Kimura
  7. Progress of Theoretical Physics Vol. 36 No. 2 (1966) pp. 394-409 :
    Note on the Gravitational Interaction
    Toshiei Kimura
  8. Progress of Theoretical Physics Vol. 38 No. 1 (1967) pp. 261-281 :
    A Theory of Anomalous Gravitational Interaction. II
    Toshiei Kimura and Kei Senba
  9. Progress of Theoretical Physics Vol. 47 No. 5 (1972) pp. 1743-1757 :
    Gauge Transformation and Gravitational Potentials
    Kichiro Hiida and Hiroshi Okamura

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