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A parametrization of the general Lorentz group
N. I. Ostrosablin Lavrentyev Institute of Hydrodynamics SB RAS, pr. Akad. Lavrentyeva 15, Novosibirsk 630090, Russia
Abstract:
We obtain the two new variants of an explicit parametrization for the general Lorentz group. Formulas are given for the direct and inverse four-dimensional Lorentz transformations. These formulas use the orthogonal three- or four-dimensional matrices.
We find the infinitesimal operators of the proper Lorentz group and the multiplication formulas (commutators) of the infinitesimal operators. The orthogonal three- and four-dimensional matrices are parameterized by lower triangular matrices containing three or six independent parameters.
Keywords:
Lorentz transformation, relativity theory, wave equation,
Lorentz group, orthogonal matrix, infinitesimal operator.
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Received: 12.03.2020 Revised: 12.03.2020 Accepted: 10.09.2020
Citation:
N. I. Ostrosablin, “A parametrization of the general Lorentz group”, Sib. Zh. Ind. Mat., 23:4 (2020), 114–125; J. Appl. Industr. Math., 14:4 (2020), 743–753
Linking options:
https://www.mathnet.ru/eng/sjim1113 https://www.mathnet.ru/eng/sjim/v23/i4/p114
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Abstract page: | 227 | Full-text PDF : | 132 | References: | 37 | First page: | 2 |
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