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Prog. Theor. Phys. Vol. 58 No. 2 (1977) pp. 560-574

[ Full Text PDF : FREE ACCESS (1036K) ]

On a Quantized Scalar Field in Some Bianchi-Type I Universe

Hidekazu Nariai

Research Institute for Theoretical Physics, Hiroshima University, Takehara, Hiroshima 725

(Received March 4, 1977)

Abstract:

To elucidate the relation between the Parker-Fulling momentum-space approach and DeWitt's configuration-space approach to a cosmological gravitational field interacting with quantized matter fields, an attempt is made to study a quantized scalar field in the Bianchi-type I universe whose geodesic bi-scalar and the associated propagators (except for Hadamard's elementary solution) were dealt with in a previous paper. On the basis of the former approach in which we can set up a time-independent set of annihilation and creation operators and the associated vacuum state, an elementary solution is defined by the vacuum expectation value of field operators and a time-dependent vacuum state at any time is also introduced by a suitable Bogoliubov transformation. Some limit of the latter vacuum states at two separate epochs leads to DeWitt's vacuum states |in, vac> and |out, vac> connected causally, in terms of which his elementary solution can be defined. The difference appears in the respective regular parts of both elementary solutions. Contrary to ours, DeWitt's regular part includes an information at the limiting two epochs. Its implication is also touched upon in reference to the requirement that the finite part extractable from the vacuum expectation value of the energy-momentum tensor should be a local tensor.


URL : http://ptp.ipap.jp/link?PTP/58/560/
DOI : 10.1143/PTP.58.560

[ Full Text PDF : FREE ACCESS (1036K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 58 No. 3 (1977) pp. 842-849 :
    On a Quantized Scalar Field in Some Bianchi-Type I Universe. II
    Hidekazu Nariai
  2. Progress of Theoretical Physics Vol. 59 No. 1 (1978) pp. 296-298 :
    On the Creation of Scalar Particles in an Isotropic Universe
    Hidekazu Nariai and Akira Tomimatsu
  3. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1522-1531 :
    Propagators for a Quantized Scalar Field in Some Isotropic Universe
    Hidekazu Nariai and Takehiro Azuma
  4. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1532-1542 :
    On the Creation of Scalar Particles in Some Anisotropic Universe
    Hidekazu Nariai
  5. Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 324-326 :
    Canonical Approach to the Creation of Scalar Particles in the Chitre-Hartle Model-Universe
    Hidekazu Nariai
  6. Progress of Theoretical Physics Vol. 64 No. 4 (1980) pp. 1280-1293 :
    On the Definition of a Positive Frequency Part for a Quantized Scalar Field in Several Robertson-Walker Universes
    Hidekazu Nariai and Takehiro Azuma

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