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Bacry, Henri; Lévy-Leblond, Jean-Marc

Possible kinematics. (English) Zbl 0162.58606

J. Math. Phys. 9, 1605-1614 (1968).
Summary: The kinematical groups are classified; they include, besides space-time translations and spatial rotations, “inertial transformations” connecting different inertial frames of reference. When parity and time-reversal are required to be automorphisms of the groups, and when a weak hypothesis on causality is made, the only possible groups are found to consist of the de Sitter groups and their rotation-invariant contractions. The scheme of the contractions connecting these groups enables one to discuss their physical meaning. Beside the de Sitter, Poincaré, and Galilei groups, two types of groups are found to present some interest. The “static group” applies to the static models, with infinitely massive particles. The other type, halfway between the de Sitter and the Galilei groups, contains two nonrelativistic cosmological groups describing a nonrelativistic curved space-time.
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Cited in 3 Reviews
Cited in 181 Documents

MSC:

81R05 Finite-dimensional groups and algebras motivated by physics and their representations
83C99 General relativity

Keywords:

classification of kinematical groups; space-time translations; spatial rotations, inertial transformations; inertial frames of reference; de Sitter groups; rotation-invariant contractions; static group; nonrelativistic cosmological groups; nonrelativistic curved space-time
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Full Text: DOI

References:

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