Elementos de teoria clássica de campos e uma aplicação de métodos de computação simbólica.

Abstract

This work presents complementary elements of the degree formation for the work in elementary particle field theory and high energy physics. We discussed

aspects of classical (Newtonian) mechanics in the Lagrangian and Hamiltonian formulation with

as an objective the understanding of its generalization for systems with infinite Gaus of freedom, in other words, field theories. This work has as main theme a review on

classical field theories with special emphasis on the theory of general relativity. This theory and a theory of gravitation and its development marks the entry of advanced methods of differential geometry of Physics and has as its fundamental element the use of symmetries. In that work we seek to emphasize the elements necessary for the mathematical understanding of General Relativity, reviewing aspects of differential geometry and showing how methods of

symbolic computation can be used to obtain fast results physically uprisings. The physical example worked on in this work and the Friedman-Robetson-Walker metric,

key element in modern cosmology.