Quantum Particle Distributions of Matter

Eliade N. Stefanescu

In this paper, a quantum particle is described by a time-space distribution of matter according to the general theory of relativity, which is essentially based on the invariance of the time-space interval. If we consider a time-space interval for two successive points of the trajectory of a punctual quantum particle, as such a particle is conceived in the conventional quantum mechanics, any interaction with a field is described by a variation of this interval. It is remarkable that the velocity induced by such an interaction, for a rest particle is equal to the light velocity, which means that the mass of any punctual particle is null. This is perfectly understandable from the physical point of view, since a particle described only by position coordinates is a punctual one, i.e. with a null volume, and, consequently, a null mass. Unlike the present understanding of a quantum particle, as a punctual entity randomly occupying different positions given by its wave function, and with a mass given by coupling with a Higgs boson, we conceive a quantum particle as a distribution of matter, quantized by the equality of the mass given by the space integral of the wave function, with the mass given by the matter dynamics according to the general theory of relativity. In this framework, we previously described the spinor propagation under the interaction with an electromagnetic field, the particle spin, the graviton spin, the black hole dynamics, the matter dynamics of our universe, as a hypersurface defined by the time-space parameters in the total universe, with the Big Bang, inflation, redshift, and the crushing up of the quantum particles at the Big Bang and at the Schwarzschild boundary. Here, we describe essential quantum phenomenon of the particle scattering.

G. Kaniadakis, P. Quarati

Eliade N. Stefanescu

In this paper, the quantum dynamics was obtained in the framework of the general theory of relativity, where a quantum particle is described by a distribution of matter, with amplitude functions of the matter density, in the two conjugate spaces of the spatial coordinates and of the momentum, called wave functions. For a free particle, these wave functions are conjugate wave packets in the coordinate and momentum spaces, with time-dependent phases proportional to the relativistic Lagrangian, as the wave velocities in the coordinate space are equal to the distribution velocity described by the wave packet in this space. From the wave velocities of the particle wave functions, Lorentz’s force and the Maxwell equations were obtained. From the wave/group equation in the momentum space describing the Lorentz force, the expressions of the electric and magnetic fields as functions of the electric potential conjugated to time and of the vector potential conjugated to the coordinates in the particle-field Lagrangian were obtained. With these expressions, the electric and magnetic fields that satisfy the Faraday-Maxwell law of electromagnetic induction and the two Gauss-Maxwell laws of these fields were obtained. The Ampère-Maxwell law is obtained only by taking into account the physical consistency of the matter-field interaction of the equality of the propagation field velocity with the maximum relativistic velocity c. For a quantum particle in the electromagnetic field, dynamic equations in the coordinate and momentum spaces and the particle and antiparticle wave functions were obtained. It was shown that the electromagnetic potentials as functions of the coordinates describing the matter distribution of the quantum particle do not alter this distribution – under the action of an electromagnetic a quantum particle moves as a whole. The scattering or tunneling rate in an electromagnetic field, for the two possible cases, with the spin conservation, or inversion, were obtained. This description of a quantum particle as a distribution of matter with a density amplitude/wavefunction of the form of a wave packet, with the time-dependent phase proportional to the relativistic Lagrangian as a function of the metric tensor including also the gravitational field, enables the application of this theory in quantum gravity and quantum field theory in agreement with general relativity.

S. B. Khasare, S. B. Khasare

G. Kaniadakis, P. Quarati

Eliade N. Stefanescu

We calculate the scattering rate of a quantum particle, based on Fermi’s golden rule for a quantum particle as a distribution of matter, where the density of states is a function of the particle Lagrangian, not of the Hamiltonian, as in the conventional theory based on the Schrödinger equation. Thus, the density of states does not refer to the energies as in the conventional form, but to the Lagrangian functions, which, besides the energies, include the momentum-velocity products, that are also constants of motion for the initial and the final states. We obtain the relativistic dependence on the momentum, and the two scattering rates for the two possible cases, with the spin conservation, or the spin inversion.