Advanced Studies in Physics Centre of the Romanian Academy, Romania
Title: Electromagnetic field, spin and gravitation, as characteristics of a charged quantum particle wave function
Biography: Eliade Stefanescu
Our starting point is a wave packet of a quantum particle, which, for the agreement of the group velocities in the coordinate and momentum spaces with the Hamilton equations, instead of the Hamiltonian in the time dependent phase, includes the Lagrangian. We consider the interaction of such a particle with an external field, with potentials conjugated to time (the scalar potential), and to the spatial coordinates (the vector potential), and a quantum relativistic principle, asserting that the time-dependent phase of a quantum particle is an invariant for an arbitrary change of coordinates. For this field, we obtain the Lorentz equation of the particle-field interaction, the Faraday-Maxwell equation and the Gauss-Maxwell equations for the field components of the two potentials, and the Ampère-Maxwell equation for an electromagnetic field. For a nonrelativistic case, we obtain a Schrödinger equation with a Hamiltonian including the rest mass. With this equation, we obtain the spin as a characteristic of the particle wave function. From the group velocity of a particle wave packet, we obtain an acceleration, proportional to the Christoffel symbols, which take non-zero values only in the curved space of a gravitational field.