Transformação Foldy-Wouthuytsen exata para campo de Dirac interagindo com uma onda gravitacional

Abstract

At the beginning of this thesis, we present a brief review of the basic elements of General Relativity, including necessary information about weak gravitational waves. The Klein-Gordon and Dirac fields will be formulated in an external gravitational field. In the original part of the work, we consider a particle described by Dirac equation in presence of a constant magnetic field, in a region where there are also gravitational waves. In order to extract some physical information from the Hamiltonian, it is necessary to make a Foldy-Wouthuysen transformation on it. The standard Foldy-Wouthuysen transformation is not exact, it represents an expansion in power series in external fields. In the present thesis, we introduce a method for performing an exact transformation Foldy-Wouthuysen for the given case. The formalism is general in a sense it enables one to treat many versions of exact Foldy-Wouthuysen transformation, studied before, as particular cases. The corresponding calculations may be used as a strong verification of the general result of exact Foldy-Wouthuysen transformation. The non relativistic limit shows perfect correspondence between the result of the exact Foldy-Wouthuysen transformation and Pauli equation, including the (specially derived) case with gravitational waves. Finally, using the Hamiltonian derived within the Foldy-Wouthuysen method, we write the non relativistic equations of motion for a particle with spin 1/2.