New SubRelativistic quantum mechanics of quantum particles as distributions of matter with applications in quantum electrodynamics, a unified theory of the four forces acting in nature, and cosmology

Unlike the traditional quantum mechanics describing some wavefunctions with no material support, as probability amplitudes of punctual particles, we conceive a quantum theory describing wave packets as matter density amplitudes in the two conjugate spaces of the coordinates and momentum, of particles quantized by the propagation characteristics according to general relativity. This theory is essentially based on the remarkable fact that in the coordinate space the wave/group velocities are equal to the coordinate velocities, in the nonrelativistic case according to the Hamilton equations, and in the relativistic case, according to general relativity, while the wave/group velocities in the momentum space describe possible forces acting on these distributions of matter. For a collision of two quantum particles, with a volume of the collision region equal to the volume of the photon mediating this collision, we obtain the transition rates depending on the initial two momenta and the final two momenta of these particles for the two possible processes, with spin conservation, and spin inversion. Besides the relativistic Lagrangian, describing the mass quantization and the inertial-gravitational dynamics of a quantum particle, we consider additional Lagrangian terms for the one-dimensional electromagnetic space depending on the four-dimensional electromagnetic potential, for the two-dimensional flavor space of the weak interactions depending on the four-dimensional potentials of the three Pauli operators which can be defined in this space, and for the three-dimensional color space of the strong interactions, depending on the four-dimensional potentials of the eight Gell-Mann operators which can be defined in this space – a unified theory of all forces acting in nature is obtained. For the three quarks of a nucleon, we consider a steady state, a propagation operator equals to 1, a null coordinate-momentum product, leading to a system of equations for the three coordinate vectors of these quarks. We calculate the velocity of a particle in a black hole, and its matter dynamics. Thus, essential characteristics, such as Big Bang, Inflation, redshift, the low large-scale density, the quasi-inertial behavior of the distant bodies, the dark matter and the dark energy, are explained according to general relativity.