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Prog. Theor. Phys. Vol. 31 No. 6 (1964) pp. 1138-1152

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Quantum Theory of Fields in an Expanding Space. I

Hidekazu Nariai and Toshiei Kimura

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

(Received November 4, 1963)

Abstract:

In order to deal with the quantum theory of fields in an expanding space relying on a well-defined quantum picture, a device is proposed to join the metric for the expanding space with those for flat space-time and a new time variable is introduced in a suitable manner. In this paper the quantization of the electromagnetic field is mainly discussed in the whole region defined by the joined metrics. If the physical component of vector potential is quantized, there appears some peculiar feature, which serves to destroy the macroscopic causality based on a particle image, in the four-dimensional commutation function according to the manner of joining two adjacent metrics. The appearance of such a peculiar feature has an intimate connection with that of an abnormal transformation function like the one in van Hove's model. On the other hand, the quantization of original vector potential does not lead to such difficulties. It is concluded that the quantization of the electromagnetic field should be carried out in terms of the original vector potential, but not its physical component.


URL : http://ptp.ipap.jp/link?PTP/31/1138/
DOI : 10.1143/PTP.31.1138

[ Full Text PDF : FREE ACCESS (763K) ] Citation:

References:

  1. H. Nariai and T. Kimura, Prog. Theor. Phys. 29 (1963), 296 [PTP][Errata; 29 (1963), 915[PTP]], (referred to as [G]).
  2. M. Fierz, Helv. Phys. Acta 23 (1950), 731.
  3. Y. Takahashi and H. Umezawa, Nuovo Cim. 6 (1957), 1324.
  4. T. Imamura, Phys. Rev. 118 (1960), 1430[APS].
  5. L. van Hove, Physica 18 (1952), 145[CrossRef].
  6. R. Haag, Kgl. Danske Videnskab. Selskab. Mat.-fys. Medd. 29 (1955), No. 12.
  7. J. von Neumann, Composition Math. 6 (1938), 1.
  8. For instance, S. Kamefuchi and H. Umezawa, Nuovo Cim. 31 (1964), 428.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 33 No. 3 (1965) pp. 510-523 :
    An Attempt to Derive the Gravitational Potential
    Toshiei Kimura
  2. Progress of Theoretical Physics Vol. 40 No. 1 (1968) pp. 49-59 :
    On the Green's Function in an Expanding Universe and Its Role in the Problem of Mach's Principle
    Hidekazu Nariai
  3. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 657-667 :
    The Behavior of a Massless Scalar Field in a Closed Universe
    Hidekazu Nariai
  4. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1116-1132 :
    Propagators for a Scalar Field in a Homogeneous Expanding Universe. I
    Hidekazu Nariai and Kenji Tanabe
  5. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 67-81 :
    Propagators for a Scalar Field in Some Bianchi-Type I Universe
    Hidekazu Nariai
  6. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 560-574 :
    On a Quantized Scalar Field in Some Bianchi-Type I Universe
    Hidekazu Nariai
  7. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1532-1542 :
    On the Creation of Scalar Particles in Some Anisotropic Universe
    Hidekazu Nariai
  8. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 739-746 :
    On a Quantized Scalar Field in an Isotropic Closed Universe
    Hidekazu Nariai

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