Abstract
In Section 1 we analyse the structure of the infinite-dimensional Hamiltonian system described by the Klein-Gordon equation (free real scalar field) in stationary space-times with closed space sections; we give an existence and uniqueness theorem for the Lichnerowicz distribution kernelG 1 together with its proper Fourier expansion, and we construct the Hilbert spaces of frequency-part solutions defined by means ofG 1.
In Section 2 an analysis, a theorem and a construction similar to the above are formulated for thefree real field spin 1, massm>0, in one kind of static space-times.
In this letter, only results are given. For detailed proofs and further results, see reference [9], [10] and [11].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bogolioubov-Chirkov,Introduction à la théorie quantique de champs, Dunod, Paris, 1960.
Chernoff-Marsden, ‘Properties of Infinite Dimensional Hamiltonian Systems’,Lectures Notes in Mathematics, No. 425, Springer-Verlag.
ChevalierM.,J. Math. Pures et Appl. 53, 223 (1974).
Combet, E., Sém. Phys. Math., Collège de France, 1965.
Combet, E.,C.R. Acad. Sci. Paris, t. 262, série A, 1077–1080.
LichnerowiczA.,Théories Relativistes de la Gravitation et de l'Electromagnétisme, Masson, Paris, 1965.
Lichnerowicz, A.,Bull. Soc. Math. de France 92 (1964).
Lichnerowicz, A., inRelativity Groups and Topology, Gordon & Breach, 1963.
Moreno, C., ‘Free Scalar Quantum Field in Stationary Space-times’, to appear inJ. Math. Phys.
Moreno, C., ‘Free Vector Quantum Field in Static Space-times’, to appear inCommun. Math. Phys.
Moreno, C., ‘Sur les noyaux de la théorie quantique des champs sur un espace-temps courbe’, Thèse, Paris, 1974.
Rideau, G., ‘Sur une définition intrinsèque de la distribution Δ(1)’,C.R. Acad. Sci. Paris, t. 268, 2719–2721.
Seeley, T.,Am. Math. Soc. Proc. Symp. Pure. Math. 10, 288–307.
Segal, I.,Sém. Phys. Math. Collège de France, 1964–65.
TrautmanA., inGravitation: An Introduction to Current Research, Wiley, N.Y., 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Moreno, C. On quantization of free fields in stationary space-times. Lett Math Phys 1, 407–416 (1977). https://doi.org/10.1007/BF01793955
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01793955