The Lorentz Group

Abstract

In this project we aim to understand the structure and some properties of the Lorentz group, a mathematical object arising from the theory of special relativity which is said to express some of the main symmetries in the laws of Physics. The first section of the project is concerned about providing physical intuition about the concepts involved in the definition of the Lorentz group. The main goal of the project is to prove an isomorphism between the restricted Lorentz group and the projective linear group PSL 2 (C). Once achieved this result, we use it to build a scheme that will let us study the conjugacy classes of the restricted Lorentz group.