Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation |
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| Authors: | C Duval H P Künzle |
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| Institution: | (1) Centre de Physique Théorique, C.N.R.S. Luminy, Case 907, 13288 Marseille, France;(2) Faculté des Sciences de Luminy et Centre de Physique Théorique, C.N.R.S., 70 Route Léon Lachamp, Case 907, F. 13288 Marseille Cedex 9;(3) Institut für Astrophysik, Max-Planck-Institut für Physik und Astrophysik, D. 8046 Garching bei München, Germany;(4) Present address: Department of Mathematics, University of Alberta, T6G 2G1 Edmonton, Canada |
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| Abstract: | The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schrödinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory.Partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A8059. |
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