Statistical systems with phantom scalar interaction in gravitation theory. I. Microscopic dynamics

Abstract

Based on one the authors' approach to a macroscopic description of the scalar interaction, we develop a macroscopic model of a relativistic plasma with a phantom scalar interaction of elementary particles. In this model, as opposed to previous models, the restriction of nonnegativity of the particles' effective mass is removed.

Nonminimal macroscopic models of a scalar field based on microscopic dynamics: Extension of the theory to negative masses

“…As it was shown in [10], the negativeness of the particle's effective mass function does not lead to any contradictions at the level of microscopic dynamics since the observable momentum of particle (as well as the 3-dimensional velocity v α = u α /u 4 ) conserves its orientation as opposed to the unobservable kinematic 4-velocity of a particle u i :…”

“…Not specifying this function for now, let us note the next important circumstance: For equations of motion (6) to allow the linear integral of motion Ψ = (ξ, P ) = Const, according to (8) it is enough and sufficient that [H, Ψ] = 0. This, in turn, is possible if and only if [10]:…”

“…Thus for a free massive scalar field we obtain wave equations in form of standard Klein-Gordon equations with the only difference being bosons rest mass changed to the effective mass [10]:…”

“…In the recent Author's works [5,6,7] 1 the macroscopic theory of the statistical systems has been improved significantly in part of formalism development and also it has been extended to the case of fantom scalar fields 2 . In [10,12] a question about possibility to include negative effective particle masses in the theory has been raised. The negative answer to this question has been given in [12] since negative values have been obtained for particle number density in the statistical theory at given assumption.…”

Qualitative and numerical analysis of the cosmological model based on the phantom scalar field with self-interaction. II. Comparative analysis of models of classical and phantom fields

“…In particular, certain features of phantom fields like peculiarities of inter-particle interaction, were revealed in these works. Since 2014 [10], [11], [11], [12], [13], [14] these researches were enriched to expand the theory of scalar and in particular, phantom fields, to the range of negative masses of particles, degenerated Fermi-system, conformally invariant interactions and suchlike. In 2015, the constructed mathematical models of scalar fields were applied to investigation of the cosmological evolution of systems of interacting particles and scalar fields of both classical and phantom types [15], [16], [17].…”