Wightman Formulation for the Quantization of the Gravitational Field

M. Flato; J. Simon

doi:10.1103/PhysRevD.5.332

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Wightman Formulation for the Quantization of the Gravitational Field

M. Flato^* and J. Simon^†

Department of Theoretical Physics, Royal Institute of Technology, 10044 Stockholm, Sweden.

^*Nordita Guest-Professor at the Royal Institute of Technology.
^†A.F.R. research fellow at the Royal Institute of Technology.

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Phys. Rev. D 5, 332 – Published 15 January, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.332

Abstract

A generalization of Wightman field theory is formulated which makes the theory also applicable to the gravitational field. Strongly geodesically complete manifolds are found to be the most suitable for description of curved space-time in our approach. After the formulation of generalized axioms, the schemes of proofs of the fundamental theorems of the theory (Bargmann-Hall-Wightman theorem, $θ$ theorem, main reconstruction theorem, etc.) are given. The paper ends with hints on the possible ways of constructing the theory of asymptotic states for the quantized gravitational field.

References (15)

P. G. Bergmann, Helv. Phys. Acta Suppl. 4, 79 (1956)
P. A. M. Dirac, Proc. Roy. Soc. (London) A246, 326 (1958)
B. S. DeWitt and C. DeWitt, Phys. Rev. Letters 4, 317 (1960)
R. P. Feynman, Acta Phys. Polon. 24, 697 (1963)
A. Lichnérowicz, Publications IHES, No. 10 (1961)
B. S. DeWitt, Phys. Rev. 162, 1195 (1967)
B. S. DeWitt, Ph. D. thesis (unpublished)
S. Mandelstam, Phys. Rev. 175, 1604 (1968)
V. N. Popov and L. D. Faddeev, Phys. Letters 25B, 29 (1967)
M. Flato, J. Simon, and D. Sternheimer, Ann. Phys. (N.Y.) 61, 78 (1970)
M. Flato and J. Simon, Physica Scripta 3, 53 (1971)
A. Lichnérowicz, Théories Relativistes de la Gravitation et de l'Electromagnétisme (Masson, Paris, 1955)
G. de Rham, Variétés différentiables (Hermann, Paris, 1955)
R. Jost, The General Theory of Quantized Fields (Am. Math. Soc., Providence, R. I., 1965)
I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1

[c1] P. G. Bergmann, Helv. Phys. Acta Suppl. 4, 79 (1956)

[c2] P. A. M. Dirac, Proc. Roy. Soc. (London) A246, 326 (1958)

[c3] B. S. DeWitt and C. DeWitt, Phys. Rev. Letters 4, 317 (1960)

[c4] R. P. Feynman, Acta Phys. Polon. 24, 697 (1963)

[c5] A. Lichnérowicz, Publications IHES, No. 10 (1961)

[c6] B. S. DeWitt, Phys. Rev. 162, 1195 (1967)

[c7] B. S. DeWitt, Ph. D. thesis (unpublished)

[c8] S. Mandelstam, Phys. Rev. 175, 1604 (1968)

[c9] V. N. Popov and L. D. Faddeev, Phys. Letters 25B, 29 (1967)

[c10] M. Flato, J. Simon, and D. Sternheimer, Ann. Phys. (N.Y.) 61, 78 (1970)

[c11] M. Flato and J. Simon, Physica Scripta 3, 53 (1971)

[c12] A. Lichnérowicz, Théories Relativistes de la Gravitation et de l'Electromagnétisme (Masson, Paris, 1955)

[c13] G. de Rham, Variétés différentiables (Hermann, Paris, 1955)

[c14] R. Jost, The General Theory of Quantized Fields (Am. Math. Soc., Providence, R. I., 1965)

[c15] I. M. Gelfand and G. E. Shilov, Generalized Functions (Academic, New York, 1964), Vol. 1

Physical Review D

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Wightman Formulation for the Quantization of the Gravitational Field

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