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Prog. Theor. Phys. Vol. 59 No. 5 (1978) pp. 1522-1531

Propagators for a Quantized Scalar Field in Some Isotropic Universe

Hidekazu Nariai and Takehiro Azuma

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

(Received December 16, 1977)

Abstract:

To make clearer the relation examined in a previous paper between Chitre and Hartle's path-integral quantization procedure and our canonical one for a massive scalar field in a special isotropic universe, various propagators such as the 4-dimensional commutation function, the elementary solution and the associated Feynman propagator are explicitly determined. Owing to the determination, there arises a new changing procedure superior to the previous one from the isotropic expanding universe to the Minkowski space-time. Thus it is shown without any ambiguity that both the path-integral quantization procedure and our canonical one leading to the same pair-creation of particles as Chitre and Hartle's cannot recover the usual theory for a free field in the limit when the cosmic expansion disappears. (Notice, however, that our quantization procedure permits another case which can recover the Minkowski theory for a free field in the above limit , while it gives rise to no pair-creation.) Propagators for a massless scalar field are also dealt with in connection with the problem of conformal anomaly arising in the vacuum expectation value of the stress-energy tensor for our quantized scalar field, which is common to any quantized field in a curved space-time.

URL : http://ptp.ipap.jp/link?PTP/59/1522/
DOI : 10.1143/PTP.59.1522

[ Full Text PDF : FREE ACCESS (730K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. H. Nariai and A. Tomimatsu, Prog. Theor. Phys. 59 (1978), 296[PTP].
2. H. Nariai, Prog. Theor. Phys. 58 (1977), 560[PTP]; ibid. 58 (1977) 842[PTP].
3. D. M. Chitre and J. B. Hartle, Phys. Rev. D 16 (1977), 251[APS].
4. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale Univ. Press, New Haven, 1923).
   B. S. DeWitt and R. W. Brehme, Ann. of Phys. 9 (1960), 220[CrossRef].
5. B. S. DeWitt, Phys. Rep. 19 (1975), 295[CrossRef].
   L. Parker, in Asymptotic Structure of Space-Time edited by F. P. Esposito and L. Witten (Plenum Press, New York, 1977), p. 107.
   S. M. Christensen, Phys. Rev. D 14 (1976), 2490[APS].
   S. L. Adler, J. Lieberman and Y. J. Ng, Ann. of Phys. 106 (1977), 279[CrossRef].
   L. S. Brown, Phys. Rev. D 15 (1977), 1469[APS].
   S. M. Christensen and S. A. Fulling, Phys. Rev. D 15 (1977), 2088[APS].
6. H. Nariai, Nuovo Cim. B 35 (1976), 259; Prog. Theor. Phys. 57 (1977), 67[PTP].
7. L. Parker, Phys. Rev. D 7 (1973), 976[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1532-1542 :

   On the Creation of Scalar Particles in Some Anisotropic Universe

   Hidekazu Nariai

2. Progress of Theoretical Physics Vol. 60 No. 2 (1978) pp. 414-426 :

   Particle Creations in the Pseudoparticle Gravitational Fields

   Akira Tomimatsu

3. Progress of Theoretical Physics Vol. 60 No. 3 (1978) pp. 739-746 :

   On a Quantized Scalar Field in an Isotropic Closed Universe

   Hidekazu Nariai

4. 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

5. Progress of Theoretical Physics Vol. 66 No. 3 (1981) pp. 892-902 :

   The Renormalized Energy-Momentum Tensor in a Robertson-Walker Universe

   Takahiro Azuma

6. Progress of Theoretical Physics Vol. 66 No. 6 (1981) pp. 2003-2010 :

   High-Energy Behaviour of the Particle Spectrum Created by a Linearly Expanding Universe

   Mario Castagnino

7. Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 693-696 :

   Cosmological Particle Creation

   Ch. Charach

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