Algebras de Clifford, transformações de Lorentz e o movimento de particulas carregadas




The main result presented in this thesis is a finite form (the MASTER equation) for the series of exponentials of infinitesimal generators of the Lorentz group. Explicitly, the exponential of a generator appears written by means of the first powers of the generators, in the SL(2,C) and SO(1,3) representations of the Lorentz group, multiplied by elementary functions of two real variables, these latter related to the generators. The master equation also permits us to sum the famous Campbell-Baker-Hausdorff series for the Lorentz group. This result is a powerful tool for relativistic kinematics and dynamics, since the finite form of exponential solves the motion equation of a charged particle under the action of a constant (in spacetime) electromagnetic field (the Lorentz force). That result is possible because the electromagnetic field is expressed by the same mathematical object that the generators of the Lorentz group. We believe that this method to solve the motion s equation of a charged particle can be generalized to include variable electromagnetic fields as we discuss in our conclusions


lie grupos de algebra abstrata

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