Theoretical and Condensed Matter Physics

Biography

Biography: Eliade Stefanescu

Abstract

Generally, the theory of relativity and quantum mechanics are conceived as two different theories, the first for the classical particles, and the second referring to the smallest conceivable particles, called quantum particles, which satisfy the wave equation of Schrödinger. However, when we tried to understand a quantum particle as a packet of waves as solutions of a Schrödinger equation, we came to a serious inconsistency: the group velocities of the wave packets in the two conjugated spaces, of the coordinates and of the momenta, were not in agreement with the Hamilton equations. For this agreement, instead of the Hamiltonian in the time-dependent phase of a particle wave function, one has to consider the Lagrangian. More than that, we find that, with the relativistic Lagrangian, a particle spectrum takes the physical form of a bound one, for spectrum cut-off velocity c (Figure 1). In this framework, we defined a relativistic quantum principle, asserting that any quantum particle is described by waves with scalar time dependent phases, invariant to any change of coordinates. Based on this principle, we obtain the relativistic kinematics and dynamics of a quantum particle. Describing the particle dynamics in an electromagnetic field by terms of the time dependent phase, with a vector potential conjugated to the coordinate variations, and a scalar potential conjugated to the time variation, we reobtain the Lorentz force and the Maxwell equations. These equations describe field waves propagating with the “light velocity”, which, for the physical consistency, is considered the same as the cutoff velocity c. In this framework, a Schrödinger wave function is only a slowly varying amplitude of a particle wave function with a rapid oscillation given by the particle rest mass. We reobtain the proper rotation of a quantum particle called spin, and demonstrate the spin-statistics relation. We generalize a particle wave packet for a curvilinear system of coordinates and consider the gravitational field as a deformation of these coordinates. In this framework, a quantum particle is considered as a continuous distribution of matter according the theory of the general relativity.