Composition of Lorentz Transformations in Terms of Their Generators

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.