Abstract
From the unitary representations of the Lorentz transformations two four-vector operators,u μ andU μ, are constructed that satisfy the equationsu μ u μ = −1 andU μ U μ=+1 as operator relations, thus behaving like a timelike and a spacelike velocity, respectively. With the help of one of the Casimir operators (K) of the Lorentz group they are represented by difference operators. Eigenvalues and eigenfunctions for the componentsu 4 andU 4 are derived for spin 0 and 1. In contrast to the case of spin 1/2, in which they could be worked out only in approximation, the solutions for the integral spin values can be given in closed form. At the end, a possible use in particle physics of theK-representation is exhibited by the discussion of a linearized infinite-component wave equation.
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