Composition of Lorentz Transformations in Terms of Their Generators

Details Composition of Lorentz Transformations in Terms of Their Generators Composition of Lorentz Transformations in Terms of Their Generators

2001-06-15

arxiv.org/abs/gr-qc/0106052v1

Gen.Rel.Grav. 34 (2002) 1345-1356

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, no figures

Scientific paper

Two-forms in Minkowski space-time may be considered as generators of Lorentz transformations. Here, the covariant and general expression for the composition law (Baker-Campbell-Hausdorff formula) of two Lorentz transformations in terms of their generators is obtained. Every subalgebra of the Lorentz algebra of such generators, up to one, may be generated by a sole pair of generators. When the subalgebra is known, the above BCH formula for the two two-forms simplifies. Its simplified expressions for all such subalgebras are also given.

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