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On the Hamiltonian treatment of a quantum scalar field in a Bianchi I universe

II: The explicit construction of the Hamiltonian

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Lettere al Nuovo Cimento (1971-1985)

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References

  1. E. Pessa:Lett Nuovo Cimento,15, 291 (1976).

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  2. Defined in I by formula (8) and similar for a; seeJ. D. Bjorken andS. D. Drell:Relativistic Quantum Fields (New York, N. Y., 1965), p. 27.

  3. A similar situation arises in the Bose gas theory; see,e.g.,L. Landau andE. Lifshitz Physique statistique (Moscou 1967), p. 286;A. A. Abrikosov, L. P. Gor’kov andI. Ye. Dzyaloshinskii:Quantum Field Theoretical Methods in Statistical Physics Chap. I (Oxford, 1965).

  4. N. Bogoliubov:Journ. Phys. (U.S.S.R.),9, 23 (1947);Sov. Phys., JETP,7, 51 (1958);Nuovo Cimento,7, 794 (1958); the use of Bogoliubov transformations in our problem has been introduced byL. Parker:Phys. Rev.,183, 1057 (1969); later calculations making use of the Bogoliubov transformations are those ofYa. B. Zel’dovich andA. A. Starobinskij;Scv. Phys. JETP,34, 1159 (1972);B. L. Hu, S. A. Fulling andL. Parker:Phys. Rev. D,8, 2377 (1973);M. Castagnino, A Verbeure andR. A. Weder:Nuovo Cimento,26 B, 396 (1975); see also for a mathematical characterizationF. A. Berezin:The Method of Second Quantization (New York, N. Y., 1966);A. Van Daele andA. Verbeure Comm. Math. Phys.,20, 268 (1971).

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  5. See,e.g.,S. Gasiorowicz:Elementary Particle Physics (New York, N. Y., 1966), p. 15.

  6. The first which has spoken, about «quasi-particles» in Riemann spaces wasL. Parker:Phys. Rev.,183, 1057 (1969).

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  7. L. Landau andE. Lifshitz:Physique statistique (Moscou, 1967), p. 289.

  8. We are speaking only of the situation in which metric and field interact one with another; the case of a fixed «background» metric is very well known; seee.g.,B. S. De Witt:Dynamical theory of groups and fields, inB. S. De Witt andC. De Witt, Editors:Relativity, Groups and Topology (London, 1964), p. 587;A. Lichnerowicz:Propagateurs, commutateurs et anticommutateurs en relativité générale, inB. S. De Witt andC. De Witt, Editors:Relativity, Groups and Topology (London, 1974), p. 823;D. Ivanenko:Gravitation and the unified picture of matter, inAtti del Convegno sulla Relatività Generale (Firenze, 1965), p. 205.

  9. E. Pessa: paper to be submitted for publication.

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  1. E. Pessa

    Present address: Istituto Tecnico Industriale Statale, Rieti

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  1. Istituto di Fisica dell’Università, Roma

    E. Pessa

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Pessa, E. On the Hamiltonian treatment of a quantum scalar field in a Bianchi I universe. Lett. Nuovo Cimento 15, 295–299 (1976). https://doi.org/10.1007/BF02725165

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