Zero rest mass soliton solutions

Abstract

In this paper, extended Klein-Gordon field systems will be introduced. Theoretically, it will be shown that for a special example of these systems, it is possible to have a single zero rest mass soliton solution, which is forced to move at the speed of light provided it is considered a non-deformed rigid object. This special soliton solution has the minimum energy among the other solutions, i.e. any arbitrary deformation in its internal structure leads to an increase in the total energy. * physmohammadi@pgu.ac.ir † gheisari@pgu.ac.ir 1 arXiv:1901.10910v5 [physics.class-ph]

Introducing a relativistic nonlinear field system with a single stable non-topological soliton solution in 1+1 dimensions

“…The last section is devoted to summary and conclusions. It should be note that, this work is in line with [64,65], but with more detail and accuracy.…”

“…We have borrowed this expectation from the quantum field theory at which any standard (nonlinear) Klein-Gordon (-like) system is used just to describe a special type of the known particles. It should be noted that, for the known CNKG systems [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62], in general, there are infinite solitary wave solutions with different rest frequencies ω o , but this new system (which we call it extended CNKG system [64][65][66]) has just a single solitary wave solution with a specific rest frequency ω s for which the general dynamical equations are reduced to the same standard CNKG versions, as we expected. In other words, the simple CNKG system is a special case of the general extended CNKG system which is obtained just for the single solitary wave solution.…”

“…However, in this paper we use another rigorous criterion for the stability (i.e. the energetically stability criterion [63][64][65]). The rest energy of an energetically stable solitary wave solution is at the minimum among the other (close) solutions.…”

Faster-Than-Light Solitons in 1 + 1 Dimensions

“…In line with [67][68][69][70], here we are going to introduce an extended KG system in 1 + 1 dimensions, which leads to a single zero-energy soliton solution at FTL speeds. For this goal, three scalar fields ϕ, θ and ψ are used to introduce a proper Lagrangian density.…”

“…In this paper, the special Lagrangian density which is used to obtain a zero-energy FTL soliton solution is an extended KG Lagrangian density (see Refs. [67][68][69][70][71]). Briefly, for a set of scalar fields φ i (i = 1, 2, • • • , N ) the extended KG systems have Lagrangian densities which are not linear in the kinetic scalar terms S ij = S ji = ∂ µ φ i ∂ µ φ j .…”