Obtenção da equação de Pauli com a presença de um campo gravitacional fraco

Abstract

Since Einstein developed the theory of General Relativity, much effort has been spent trying to unify this theory with Quantum Mechanics. An important step in this direction is the formulation of a semi-classical theory, starting from the equations of motion for matter fields in the external metric background. In particular, it is interesting to explore the gravitational corrections to the Schr¨odinger equation. The first low-energy relativistic generalization of the equation for the electron is called the Pauli equation, as it was developed by Wolfgang Pauli in 1927, before the fully relativistic Dirac equation, for which the Pauli equation works as a non-relativistic limit in the presence of an electromagnetic field. In the presence of gravity, we have to go in the opposite direction because it’s well known how to formulate the Dirac equation. In this work developed in collaboration with Guilherme Yoshi Oyadomari, we show how to perform the derivation of the Pauli equation in the presence of a electromagnetic and weak gravitational fields, in order to keep a general metric background, respecting the linearity of the metric perturbation.The results can be applied to the relativistic gravity test in atomic physics and can also be useful to describe the motion of 1/2 spin particles in the external field of a gravitational wave and non-relativistic limit of the Schwazrschild metric. These two forms of metrics will be specified at the end of this dissertation, as a way of test and application for the results obtained.