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THEORETICAL PHYSICS 2nd Edition
In this Second Edition the presentation of some important topics has been improved, and new results added. Geometry : the definition of matter fieldss has been improved. Symmetries have been added. Kinematics : the model of atoms has been added. Fields : an introduction to the Einstein's Theory of gravitation has been added. The section on the phenomenon of propagation has been rewritten. It is shown that fields propagate on Killing curves. As a consequence a general specification of the metric can be given. Continuous Models : it is proven that non relativist particles follow geodesics. Explicit solutions for the Fields and metric are provided. This book proposes a review and, on important points, a new formulation of the main concepts of Theoretical Physics. Rather than offering an interpretation based on exotic physical assumptions or a brand new abstract mathematical formalism, it proceeds to a systematic review of the main concepts of Physics, as Physicists have always understood them : space, time, material body, force fields, momentum, energy. . . and proposes the right mathematical objects to deal with them, chosen among well grounded mathematical theories. Proceeding this way, the reader will have a comprehensive, consistent and rigorous understanding of the main topics of the Physics of the XXI Century, together with many tools to do practical computations. After a short introduction about the meaning of Theories in Physics, a new interpretation of the main axioms of Quantum Mechanics is proposed. It is proven that these axioms come actually from the way mathematical models are expressed, and this leads to theorems which validate most of the usual computations and provide safe and clear conditions for their use, as it is shown in the rest of the book. Relativity is introduced through the construct of the Geometry of General Relativity, from 5 propositions and the use of tetrads and fiber bundles, which provide tools to deal with practical problems, such as deformable solids. A review of the concept of motion leads to associate a frame to all material bodies, whatever their scale, and to the representation of motion in Clifford 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 rotational and a transversal component, which are masked under the usual treatment by the metric and the Levy-Civita connection. A thorough attention is given to the topic of the propagation of fields with new and important results. The general theory of lagrangians in the application of the Principle of Least Action is reviewed, and two general models, incorporating all particles and fields are explored, and used for the introduction of the concepts of currents and energy-momentum tensor. Precise guidelines are given to fnd solutions for the equations representing a system in the most general case. The topic of the last chapter is discontinuous processes. The phenomenon of collision is studied, and we show that bosons can be understood as discontinuities in the fields. The book is available in printed Edition, through Amazon or retailers.