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Quantum Theory of Gravitation: General Formulation and Linearized Theory

Arnowitt, R. and Deser, S. (1959) Quantum Theory of Gravitation: General Formulation and Linearized Theory. Physical Review, 113 (2). pp. 745-750. ISSN 0031-899X. doi:10.1103/PhysRev.113.745.

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The problem of quantizing general relativity using the Schwinger action principle is considered. The advantages of this technique are discussed and the general formulation of the action principle using the Palatini Lagrangian is given. The difficulty in quantizing general relativity is due to the constraint equations. Two types of constraints are distinguished: algebraic constraint equations and differential constraint equations. The former may be dealt with trivially in this formalism. The latter arise due to the presence of function-type ("gauge") group invariances. In order to eliminate these variables one must make use of the group transformations themselves. Thus in general relativity the transformation from the full set of variables to the independent canonical ones is a coordinate transformation. The linearized theory is treated in detail from this viewpoint and the full theory is briefly discussed.

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Deser, S.0000-0001-9285-9434
Additional Information:© 1959 American Physical Society. (Received September 11, 1958) The writing of this paper was done while both authors enjoyed the hospitality of the working conference on general relativity and elementary particles in Switzerland, summer of 1958, sponsored by Wright Air Development Command, United States Air Force. Supported in part by a National Science Foundation research grant. We should like to thank Professor O. Klein for stimulating conversations.
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Official Citation:Quantum Theory of Gravitation: General Formulation and Linearized Theory R. Arnowitt and S. Deser Phys. Rev. 113, 745
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72875
Deposited By: George Porter
Deposited On:16 Dec 2016 16:36
Last Modified:11 Nov 2021 05:08

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