The wave equation of the electron, recently improved, allows physics to obtain all the quantum numbers and other results explaining the hydrogen spectrum. The Pauli exclusion principle then gives the description of electron clouds used in chemistry. The relativistic wave equation is associated with a Lagrangian density, thus also with an energy-momentum tensorial density. The wave of an electron cloud adds these energy-momentum densities, while photons in light are precisely those differences between such energy-momentum densities.

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.

The standard model of quantum physics has been built up over the last eighty years, thanks to discoveries in high-energy physics and enriched by various physicists’ daring ideas. They have made numerous hypotheses, tested them, and retained those which best fit experimental results.

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.

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.

The improved Dirac equation is completely solved in the case of the hydrogen atom. A method of separation of variables in spherical coordinates is used. The angular functions are the same as with the linear Dirac equation: they account for the spin 1/2 of the electron. The existence of a probability density governs the radial equations. This gives all the quantum numbers required by spectroscopy, the true number of energy levels and the true levels obtained by Sommerfeld’s formula.

An increased Dirac’s wave aimed at unified interactions. We study a wave spreading the quantic wave of the electron (Dirac spinor), which components represent all elementary particles, electron, neutrino, quarks with 3 colors, and their antiparticles , interacting for the first generation. The wave equation is an extension of the electron Dirac equation with a mass term. It is relativistic invariant under a widened group and invariant under the gauge model of the standard model (exactly). This equation reports a large part of the standard model by using less free parameters. We also reduce the conceptual gap between quantum fields theory and general relativity.

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.

The scientific community controls the possible errors by a rigorous process using referees.Consequently the only possible errors are very few, they come from what anyone considers obviously true.Three of these errors are pointed here: the main one is the belief that any quantum state follows a Schrödinger equation.This induces two secondary errors: the impossibility of magnetic charges and the identification between the Lorentz group and ( ) 2, SL  .

Describing a wave with spin 1/2, the Dirac equation is form invariant under \({SL(2,\mathbb{C})}\), subgroup of \({Cl_3^*=GL(2,\mathbb{C})}\) which is the true group of form invariance of the Dirac equation. Firstly we use the Cl 3 algebra to read all features of the Dirac equation for a wave with spin 1/2. We extend this to electromagnetic laws. Next we get the gauge group of electro-weak interactions, first in the leptonic case, electron+neutrino, next in the quark case. The complete wave for all objects of the first generation uses the Clifford algebra Cl 1,5. The gauge group is then enlarged into a \({U(1)\times SU(2)\times SU(3)}\) Lie group. We consolidate both the standard model and the use of Clifford algebras, true mathematical frame of quantum physics.

We continue the study of the Standard Model of Quantum Physics in the Clifford algebra of space. We get simplified mass terms for the fermion part of the wave. We insert the simplified equations in the frame of General Relativity. We construct the electromagnetic field of the photon, alone boson without proper mass. We explain how the Pauli principle comes from the equivalence principle of General Relativity. We transpose in the frame of the algebra of space the second quantification of the electromagnetic field. We discuss the changes introduced here.

For the unification of gravitation with electromagnetism, weak and strong interactions, we use a unique and very simple framework, the Clifford algebra of space . We enlarge our previous wave equation to the general case, including all leptons, quarks and antiparticles of the first generation. The wave equation is a generalization of the Dirac equation with a compulsory non-linear mass term. This equation is form invariant under the group of the invertible elements in the space algebra. The form invariance is fully compatible with the gauge invariance of the standard model. The wave equations of the different particles come by Lagrange equations from a Lagrangian density and this Lagrangian density is the sum of the real parts of the wave equations. Both form invariance and gauge invariance are exact symmetries, not only partial or broken symmetries. Inertia is already present in the part of the gauge group and the inertial chiral potential vector simplifies weak interactions. Relativistic quantum physics is then a naturally yet unified theory, including all interactions.

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.

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.

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.

The resolution of our wave equation for electron + neutrino is made in the case of the H atom. From two non-classical potentials, we get chiral solutions with the same set of quantum numbers and the same energy levels as those coming from the Dirac equation for the lone electron. These chiral solutions are available for each electronic state in any atom. We discuss the implications of these new potentials.