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Prog. Theor. Phys. Vol. 60 No. 3 (1978) pp. 739-746

[ Full Text PDF : FREE ACCESS (518K) ]

On a Quantized Scalar Field in an Isotropic Closed Universe

Hidekazu Nariai

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

(Received March 27, 1978; Revised May 11, 1978)

Abstract:

As a preliminary step to our future work on the back reacion of a quantized field in an isotropic closed universe through its vacuum fluctuation, a massive scalar field is canonically quantized by taking full account of its coupling with the background universe and of the latter's topological (spherical or elliptic) nature. In terms of a vacuum state corresponding to our time-independent set of annihilation and creation operators, the most general formulae (without regularization) for the energy density and pressure are derived from two components of the stress-energy tensor. If the universe becomes static in particular, the formulae are reduced to a generalized version of Streeruwitz's ones in the Einstein universe. General formulae for various propagators of the quantized scalar field are also presented for future usefulness.


URL : http://ptp.ipap.jp/link?PTP/60/739/
DOI : 10.1143/PTP.60.739

[ Full Text PDF : FREE ACCESS (518K) ] Citation:

References:

  1. H. Nariai and T. Kimura, Prog. Theor. Phys. 29 (1963), 296[PTP]; ibid. 29 (1963), 915[PTP]; ibid. 31 (1964), 1138[PTP].
  2. L. Parker, Nature 261 (1976), 20[CrossRef].
    D. M. Chitre and J. B. Hartle, Phys. Rev. D 16 (1977), 251[APS].
    H. Nariai and A. Tomimatsu, Prog. Theor. Phys. 59 (1978), 296[PTP].
    H. Nariai and T. Azuma, Prog. Theor. Phys. 59 (1978), 1522[PTP].
  3. B. S. DeWitt, Phys. Rep. C 19 (1975), 295[CrossRef].
    L. Parker, in Asymptotic Property of Space-Time, edited by F. P. Esposito and L. Witten (Plenum Press, New York, 1977), p. 107.
    In these papers, many original papers are cited.
  4. R. Utiyama and B. S. DeWitt, J. Math. Phys. 3 (1962), 608[CrossRef].
  5. H. Nariai, Prog. Theor. Phys. 46 (1971), 433[PTP].
    H. Nariai and K. Tomita, Prog. Theor. Phys. 46 (1971), 776[PTP].
    See, also T. V. Ruzmaikina and A. A. Ruzmaikin, Sov. Phys. -JETP 30 (1970), 372.
  6. B. N. Breizman, V. Ts. Gurovich and V. P. Sokorov, Sov. Phys. -JETP 32 (1971), 155.
  7. E. Streeruwitz, Phys. Lett. B 55 (1975), 93[CrossRef]; ibid. 67 (1977), 210[CrossRef].
  8. H. Nariai, Prog. Theor. Phys. 40 (1968), 657[PTP].
  9. S. L. Adler, J. Lieberman and Y. J. Ng, Ann. of Phys. 106 (1977), 279[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 60 No. 6 (1978) pp. 1728-1738 :
    Propagators for a Quantized Scalar Field in a Static Closed Universe
    Hidekazu Nariai and Takahiro Azuma
  2. Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 832-834 :
    On the Creation of Particles in a Robertson-Walker Universe
    Hidekazu Nariai
  3. Progress of Theoretical Physics Vol. 62 No. 4 (1979) pp. 1169-1170 :
    A Metric Representation of Belavin's Yang-Mills Pseudoparticle Solution and Its Relation to Some Isotropic Universe
    Hidekazu Nariai and Takahiro Azuma
  4. Progress of Theoretical Physics Vol. 68 No. 4 (1982) pp. 1147-1156 :
    On the Creation of Scalar Particles in an Early Stage of the Friedmann Closed-Universe
    Hideki Ishihara and Hidekazu Nariai
  5. Progress of Theoretical Physics Supplement No.70 (1981) pp. 301-321 :
    Initial Behavior of a Quantized Scalar Field and the Associated Pair-Creation in Several Isotropic Closed and Open Universes
    Hidekazu Nariai

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