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Journal of Mathematical Physics / Volume 27 / Issue 1

J. Math. Phys. 27, 7 (1986); http://dx.doi.org/10.1063/1.527391 (7 pages)

Hamiltonian particle mechanics on curved space‐times—A no‐interaction theorem

Stephan De Bièvre

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627

(Received 3 April 1985; accepted 23 August 1985)

Hamiltonian particle mechanics is formulated on a space‐time (M,g). The restrictions imposed by the isometry group G of g on the possible dynamics are analyzed; a no‐interaction theorem is obtained on a large class of homogeneous space‐times. The results are in particular applied to the de Sitter space‐time: here it is proven that a G‐invariant dynamics can describe geodesic particle motion only.

KEYWORDS and PACS

Keywords

SPACE−TIME, DE SITTER GROUP, DYNAMICS, PARTICLE INTERACTIONS, PHASE SPACE, CANONICAL TRANSFORMATIONS, PARTICLE KINEMATICS, HAMILTONIANS, GEODESICS, RELATIVITY THEORY, GRAVITATION, MINKOWSKI SPACE

PACS

  • 45.05.+x

    General theory of classical mechanics of discrete systems

  • 02.20.Qs

    General properties, structure, and representation of Lie groups

  • 04.20.Cv

    Fundamental problems and general formalism

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.527391

PUBLICATION DATA

ISSN

0022-2488 (print)  
1089-7658 (online)


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