Theoretical Physics

This book proposes a new formulation of the main concepts of Theoretical Physics. Rather thanoffering an interpretation based on exotic physical assumptions (additional dimension, newparticle, cosmological phenomenon,…) or a brand new abstract mathematical formalism, itproceeds to a systematic review of the main concepts of Physics, as Physicists have alwaysunderstood them: space, time, material body, force fields, momentum, energy… and proposethe right mathematical objects to deal with them, chosen among well-grounded mathematicaltheories. Proceeding this way, the reader will have a comprehensive, consistent and rigorousunderstanding of the main topics of the Physics of the XXI° century, together with many tools todo practical computations.After a short introduction about the meaning of Theories in Physics, a new interpretation ofthe main axioms of Quantum Mechanics is proposed. It is proven that these axioms comeactually from the way mathematical models are expressed, and this leads to theorems whichvalidate most of the usual computations and provide safe and clear conditions for their use, asit is shown in the rest of the book.Relativity is introduced through the construct of the Geometry of General Relativity, from 5propositions and the use of tetrads and fiber bundles, which provide tools to deal with practicalproblems, such as deformable solids. A review of the concept of motion leads to associate aframe to all material bodies, whatever their scale, and to the representation of motion inClifford Algebras. Momenta, translational and rotational, are then represented by spinors,which provide a clear explanation for the spin and the existence of anti-particles.The force fields are introduced through connections, in the framework of gauge theories,which is here extended to the gravitational field. It shows that this field has actually a rotationaland a transversal component, which are masked under the usual treatment by the metric andthe Levy-Civita connection. A thorough attention is given to the topic of the propagation offields with interesting results, notably to explore gravitation.The general theory of lagrangians in the application of the Principle of Least Action isreviewed, and two general models, incorporating all particles and fields are explored, and usedfor the introduction of the concepts of currents and energy-momentum tensor. Preciseguidelines are given to find solutions for the equations representing a system in the mostgeneral case.The topic of the last chapter is discontinuous processes. The phenomenon of collision isstudied, and we show that bosons can be understood as discontinuities in the fields.