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Extended Relativistic Invariance, Quantization of the Kinetic Momentum

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Journal of Modern Physics 2020年第9期11卷 1263-1278页

作者： claude daviau Jacques Bertrand Le Moulin de la Lande Pouill&eacute -les-Coteaux France 15 Avenue Danielle Casanova Saint-Gratien France

The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons with the value. It is a consequence of the extended relativistic invariance of the wave of fundamental particles with spin 1/2. This logical link is due to properties of the quantum waves of fermions, which are functions of space-time with value into the and End(Cl3) Lie groups. Space-time is a manifold forming the auto-adjoint part of . The Lagrangian densities are the real parts of the waves. The equivalence between the invariant form and the Dirac form of the wave equation takes the form of Lagrange's equations. The momentum-energy tensor linked by Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under of the kinetic momentum tensor gives eight vectors. One of these vectors has a time component with value . Resulting aspects of the standard model of quantum physics and of the relativistic theory of gravitation are discussed.

关键词： Geometry Invariance Group Dirac Equation Electromagnetism Weak Interactions Strong Interactions Clifford Algebras Gravitation Quantization

Including Space-Time in the Extended Group Cl₃* of Relativistic Form-Invariance

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Journal of Modern Physics 2022年第8期13卷 1147-1156页

作者： claude daviau Jacques Bertrand Pouillé-les-Coteaux France Saint-Gratien France

The inclusion of space-time in the extended group of relativistic form-invariance, Cl3*, is specified as the inclusion of the whole space-time manifold in this multiplicative Lie group. First physical results presented here are: the geometric origin of the time arrow, a better understanding of the non-simultaneity in optics and a mainly geometric origin for the universe expansion, and its recent acceleration.

关键词： Space-Time Manifold Invariance Group Standard Model Acceleration of Expansion

Christoffel Symbols and Chiral Properties of the Space-Time Geometry for the Atomic Electron States

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Journal of Modern Physics 2021年第4期12卷 483-512页

作者： claude daviau Jacques Bertrand Fondation Louis de Broglie Paris France

Quantum electron states, in the case of an improved Dirac equation, are linked to the Christoffel symbols of the connection of space-time geometry. Each solution of the wave equation, in the case of the hydrogen atom induces a connection which is completely calculated. This allows us to discover the global and chiral properties of the space-time connection, with spin 2.

关键词： Quantum Mechanics Clifford Algebra Differential Geometry Dirac Equation Hydrogen Atom Chirality

Relativistic Gauge Invariant Wave Equation of the Electron-Neutrino

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Journal of Modern Physics 2014年第11期5卷 1001-1022页

作者： claude daviau Jacques Bertrand 15 Avenue Danielle Casanova Saint-Gratien France Le Moulin de la Lande Pouillé-les-Coteaux France

With the right and the left waves of an electron, plus the left wave of its neutrino, we write the tensorial densities coming from all associations of these three spinors. We recover the wave equation of the electro-weak theory. A new non linear mass term comes out. The wave equation is form invariant, then relativistic invariant, and it is gauge invariant under the U(1)×SU(2), Lie group of electro-weak interactions. The invariant form of the wave equation has the Lagrangian density as real scalar part. One of the real equations equivalent to the invariant form is the law of conservation of the total current.

关键词： Invariance Group Dirac Equation Weak Interactions Gauge Invariance Electron Neutrino Clifford Algebras Magnetic Monopole

Soliton Wave for the Magnetic Electron

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Journal of Modern Physics 2023年第11期14卷 1426-1436页

作者： claude daviau Jacques Bertrand Fondation Louis de Broglie Paris France

A century ago, de Broglie discovered the wave associated to the motion of the electron. We present here the soliton solutions of a nonlinear relativistic wave equation. Two such solitons exist, corresponding to the two possible states of a particle with spin j = 1/2. The mystery of wave-particle dualism is solved: the electron is both a particle, a point which is a singularity, and a wave extended throughout the whole space.

关键词： Quantum Mechanics Nonlinear Wave Equation Relativity Wave-Particle Dualism

Electro-Weak Gauge, Weinberg-Salam Angle

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Journal of Modern Physics 2015年第14期6卷 2080-2092页

作者： claude daviau Jacques Bertrand Le Moulin de la Lande 44150 Pouillé-les-Coteaux France 15 Avenue Danielle Casanova 95210 Saint-Gratien France

The main aim of this paper is to explain why the Weinberg-Salam angle in the electro-weak gauge group satisfies . We study the gauge potentials of the electro-weak gauge group from our wave equation for electron + neutrino. These potentials are space-time vectors whose components are amongst the tensor densities without derivative built from the three chiral spinors of the wave. The ?gauge invariance allows us to identify the four potential space-time vectors of the electro-weak gauge to four of the nine possible vectors. One and only one of the nine derived bivector fields is the massless electromagnetic field. Putting back the four potentials linked to the spinor wave into the wave equation we get simplified equations. From the properties of the second-order wave equation we obtain the Weinberg-Salam angle. We discuss the implications of the simplified equations, obtained without second quantification, on mass, charge and gauge invariance. Chiral gauge, electric gauge and weak gauge are simply linked.

关键词： Invariance Group Dirac Equation Chirality Electron Neutrino Electro-Weak Gauge Gauge Bosons Photon Weinberg-Salam Angle

Three Clifford Algebras for Four Kinds of Interactions

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Journal of Modern Physics 2016年第9期7卷 936-951页

作者： claude daviau Jacques Bertrand Le Moulin de la Lande Pouillé-les-Coteaux France 15 Avenue Danielle Casanova Saint-Gratien France

Three Clifford algebras are sufficient to describe all interactions of modern physics: The Clifford algebra of the usual space is enough to describe all aspects of electromagnetism, including the quantum wave of the electron. The Clifford algebra of space-time is enough for electro-weak interactions. To get the gauge group of the standard model, with electro-weak and strong interactions, a third algebra is sufficient, with only two more dimensions of space. The Clifford algebra of space allows us to include also gravitation. We discuss the advantages of our approach.

关键词： Geometry Invariance Group Dirac Equation Electromagnetism Weak Interactions Strong Interactions Clifford Algebras Gravitation

Geometry of the Standard Model of Quantum Physics

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Journal of Applied Mathematics and Physics 2015年第1期3卷 46-61页

作者： claude daviau Jacques Bertrand Le Moulin de la Lande Pouillé-les-coteaux France 15 Avenue Danielle Casanova Saint-Gratien France

General relativity links gravitation to the structure of our space-time. Nowadays physics knows four types of interactions: Gravitation, electromagnetism, weak interactions, strong interactions. The theory of everything (ToE) is the unification of these four domains. We study several necessary cornerstones for such a theory: geometry and mathematics, adapted manifolds on the real domain, Clifford algebras over tangent spaces of these manifolds, the real Lagrangian density in connection with the standard model of quantum physics. The geometry of the standard model of quantum physics uses three Clifford algebras. The algebra ?of the 3-dimensional physical space is sufficient to describe the wave of the electron. The algebra of space-time is sufficient to describe the wave of the pair electron-neutrino. A greater space-time with two additional dimensions of space generates the algebra . It is sufficient to get the wave equation for all fermions, electron, its neutrino and quarks u and d of the first generation, and the wave equations for the two other generations. Values of these waves allow defining, in each point of space-time, geometric transformations from one intrinsic manifold of space-time into the usual manifold. The Lagrangian density is the scalar part of the wave equation.

关键词： Geometry of the Standard Model of Quantum Physics

A Wave Equation including Leptons and Quarks for the Standard Model of Quantum Physics in Clifford Algebra

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Journal of Modern Physics 2014年第18期5卷 2149-2173页

作者： claude daviau Jacques Bertrand Le Moulin de la Lande Pouillé-les-Coteaux France

A wave equation with mass term is studied for all fermionic particles and antiparticles of the first generation: electron and its neutrino, positron and antineutrino, quarks u and d with three states of color and antiquarks and . This wave equation is form invariant under the group generalizing the relativistic invariance. It is gauge invariant under the U(1)×SU(2)×SU(3) group of the standard model of quantum physics. The wave is a function of space and time with value in the Clifford algebra Cl1,5. Then many features of the standard model, charge conjugation, color, left waves, and Lagrangian formalism, are obtained in the frame of the first quantization.

关键词： Invariance Group Dirac Equation Electromagnetism Weak Interactions Strong Interactions Clifford Algebras