Quantum gravity : A comprehensible first approach

Abstract

The aim of the present work is to reconstruct, in a comprehensive and self-contained way, the path that scientists followed a century ago in order to build a self-consistent quantum theory of gravity, and show the inevitable failure that is encountered at the end when using our currently accepted theories of nature. We Will therefore start from scratch using the methods of quantum field theory and the observed properties of the gravitational field. A Lagrangian, the Fierz-Pauli Lagrangian, Will be derived from these concepts and analized The geodesic equation is obtained, and from it, the relation between our new field and Einstein's geometrical quantity {Gamma]. Conservation of mass-energy Will reveal the need to include an infinite number of self-interaction terms, which Will lead to the Hilbert Lagrangian. After proving that our gravitational theory is a gauge field theory, a simple dimensional analysis of the coupling constant Will show its non-renormalizable character. From then on, some of the roads research has taken Will be mentioned.