Finite form of proper orthochronous Lorentz transformations and its dynamic interpretation

In this paper using the Pauli Algebra we obtain the finite form of a generic proper orthochronous Lorentz transformations - denoded L sup(↑) sub(+), or in other words, we give to the exponential of a generic generator of SL (2,C) - the universal covering group of sup(↑) sub(+), the proper orthochronous Lorentz group - a closed form, which represents a generalization of the well known exponential form for pure boosts and pure rotations. We show also that there exists a dynamical interpretation of the transformations of when applied to the relativistic four vector velocity namely, that these transformations yield the integral solution of the equation of motion of a charged particle under the action of electric and magnetic fields in many configurations. (author)