Preface

Some time ago, after a long career, I asked myself what quantum mechanics is. Starting an investigation with the basic laws of Plank-Einstein and de Broglie, I came to the conclusion that a quantum system is completely described only by two dynamic equations in the two conjugate spaces of the coordinates and momentum, and more than that, with the Lagrangian instead of the Hamiltonian as it is considered in the Schrödinger equation. With the Lagrangian in the time-dependent phase of the wave packet describing a quantum particle in the coordinate space for a certain energy, we obtain this phase as a function of the coordinate velocity, which leads to the equality of the wave/group velocities with this velocity. More than that, when the relativistic Lagrangian, as a function of the coordinate velocities, is considered, this equality remains. On this basis, the two wavefunctions in the two conjugate spaces can be considered as amplitudes of matter distributions. We obtain the mass quantization rule as the equality of the mass of a particle and as the integral of its density, with the mass as a dynamic characteristic in the time-dependent phases of its wavefunctions. In this way, quantum mechanics and general relativity became a single theory. In this framework, we obtain a cosmological model describing the main characteristics of our universe, such as the Big Bang, inflation, redshift, dark matter, and dark energy, which is in full agreement with the theory of relativity. These subjects have been approached in the third volume of this book.

In this book, we reconsider this new quantum-relativistic theory in the more general case of the field-dressed particles. For such a field, we obtain the Lorentz force and the Maxwell equations in general relativity. We obtain quantum dynamic equations and wavefunctions for a field-dressed particle-antiparticle system, entirely describing the relativistic effects. We use Dirac’s formalisms for quantum mechanics and for general relativity. We revise the Fermi golden rule with applications to quantum electrodynamics. In this theoretical framework, we consider the quark dynamics under the action of the four forces acting in nature and obtain a grand unified theory. In this way, we avoid the huge ontological and cosmological difficulties raised by the Schrödinger-Heisenberg description, which, however, remains a brilliant approximate description and formalism, perfect for the steady states and, for one hundred years, has been leading to the spectacular results of our civilization and today is used in very important application fields.