A precessão de Thomas: a correção na energia de interação spin-órbita e o efeito Zeeman anômalo

Abstract

The research’s primordial objective is to analyze the spin-orbit interaction energy and the anomalous Zeeman effect of an electron in motion in the presence of an external electromagnetic field. For this purpose, an analysis of the electron’s rest frame was conducted utilizing the main concepts of Special Relativity, such as the Lorentz transformation between inertial frames, and of Quantum Mechanics, such as the concept of spin angular momentum. Afterwards, based on Group Theory, it is noted that groups SO(3) and SU(2) have the same algebra and that they are related to the rotation group. The matrices representing the generators of such groups are used to construct the angular momentum operators for spin 1/2, as well as to describe the non-commutative boost and rotation generators of the Lorentz group, whose successive transformations alter the kinematics of the problem depending on the order in which they were applied. One of the examples of such application is the Thomas precession, a phenomenon that explains, from the results obtained for the gyromagnetic ratio of the electron through the Perturbation Theory, the anomalous Zeeman effect related to displacement in two possible energy levels due to electron spin and the correction known as the Thomas factor 1/2 in the spin-orbit interaction term.