Relativistic quantum mass distributions on velocity space

Suresh Kumar.S

Eliade Stefanescu

In this chapter, we consider the wave function of a particle as a wavepacket describing the density amplitude in the coordinate space, and its inverse Fourier transform, as a wave function in the momentum space. We obtain the momentum from the mass Lagrangian in the time-dependent phase of the wave function, and the particle dynamics from the group velocities of these wave-packets in the two conjugate spaces of the coordinates and of the momentum. From the equality of the mass in the relativistic Lagrangian, which describes the matter dynamics, with the total mass as an integral of the density, we obtain the matter quantization.

Hiroshi Enatsu

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.

Arno Böhm, Hani Kaldass, Sujeewa Wickramasekara

A state vector description for relativistic resonances is derived from the first order pole of the $j$-th partial $S$-matrix at the invariant square mass value $\sm_R=(m-iΓ/2)^2$ in the second sheet of the Riemann energy surface. To associate a ket, called Gamow vector, to the pole, we use the generalized eigenvectors of the four-velocity operators in place of the customary momentum eigenkets of Wigner, and we replace the conventional Hilbert space assumptions for the in- and out-scattering states with the new hypothesis that in- and out-states are described by two different Hardy spaces with complementary analyticity properties. The Gamow vectors have the following properties: - They are simultaneous generalized eigenvectors of the four velocity operators with real eigenvalues and of the self-adjoint invariant mass operator $M=(P_μP^μ)^{1/2}$ with complex eigenvalue $\sqrt{\sm_R}$. - They have a Breit-Wigner distribution in the invariant square mass variable $\sm$ and lead to an exactly exponential law for the decay rates and probabilities.