Dynamics of Matter in a Unitary Relativistic Quantum Framework - Eliade Stefanescu (Current Research Progress in Physical Science Vol. 7, 2025)
The matter dynamics as a positively defined density \(ρ(x^i,t)=M|Ψ(x^i,t)|^2\) was described and showed that, according to the general theory of relativity, such a distribution can be conceived only as a fragment of matter with a finite mass M equal to a mass M0, as a characteristic of the matter dynamics, M=M0 – the matter quantization. The group velocities of the Fourier conjugate representations in the coordinate and momentum spaces describe the dynamics of a quantum particle in agreement with the Hamiltonian equations, unlike the Schrodinger representation which is in disagreement with these equations. Under the action of an external (nongravitational) field, the acceleration of the quantum matter has two components: 1) A component perpendicular to the velocity, given by the relativistic mechanical component of the time-dependent phase, and 2) A component given by the additional field terms of this phase. A free quantum particle is described by a non-dispersing wave function\(Ψ(x^i,t)\) , contrary to the solution of the Schrödinger equation. A coherent electromagnetic field, in resonance with a system of active quantum particles in a Fabry-Perot cavity, has a wave vector approximately proportional to the metric elements, as the resonance frequency is approximately constant – a gravitational wave can be detected by the transmission characteristics of an active Fabry-Perot cavity. In a constant gravitational field, a quantum particle undertakes a velocity and an acceleration, which, at the boundary of a black hole are null – absorption and evaporation processes at the boundary of a black hole arise only by gravitational perturbations. Important perturbations, significantly deforming the gravitational spherical symmetry of a black hole, are produced by strong nuclear and electromagnetic forces leading to the big matter concentrations of the celestial bodies. Generally, a quantum particle is described by a time-space volume, called a graviton, with a spin of 2, and a distribution of a specific matter in this volume, with a half-integer spin for Fermions and an integer spin for Bosons. A graviton Lagrangian is obtained as a curvature integral on a graviton volume, and a Hamiltonian tensor is obtained for the gravitational coordinates and velocities.