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Elementary Systems of (1 + 1) Kinematical Groups: Contraction and Quantization
Author(s) -
Arratia Oscar,
Olmo Mariano A. Del
Publication year - 1997
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190450202
Subject(s) - contraction (grammar) , quantization (signal processing) , mathematics , pure mathematics , algebra over a field , poincaré group , mathematical physics , group (periodic table) , physics , quantum mechanics , algorithm , medicine
We present the (algebra) group contraction chain SU (1, 1) → P (1, 1) → G (1, 1), where P (1, 1) and G (1, 1) are the Poincaré and the Galilei groups, respectively, in (1 + 1) dimensions. We have paid attention to the contraction of the pseudo‐extended Poincaré group to the central extended Galilei group. Objects like group laws, coadjoint orbits and representations of the contracted groups have been obtained in terms of their noncontracted counterparts. As an application we study the Moyal quantization of classical systems, having those groups as symmetry groups, by means of the contraction of the so called Stratonovich‐Weyl kernels which provide such quantization.