Singularity-free model of electrically charged fermionic particles and gauged Q -balls

Abstract

We propose a model of an electrically charged fermion as a regular localized solution of electromagnetic and spinor fields interacting with a physical vacuum, which is phenomenologically described as a logarithmic superfluid. We analytically study the asymptotic behavior of the solution, while obtaining its form by numerical methods. The solution has physically plausible properties, such as finite size, self-energy, total charge and mass. In the case of spherical symmetry, its electric field obeys the Coulomb asymptotics at large distances from its core. It is shown that the observable rest mass of the fermion arises as a result of interaction of the fields with the physical vacuum. The spinor and scalar field components of the solution decay exponentially outside the core; therefore they can be regarded as internal degrees of freedom which can only be probed at sufficiently large scales of energy and momentum. Apart from conventional Fermi particles, our model can find applications in a theory of exotic localized objects, such as U (1) gauged Q-balls with half-integer spin.

Scattering of the double sine-Gordon kinks

“…[78]- [88]. Besides that, we have to mention various configurations of the type of Q-balls [89]- [96]. Topologically non-trivial field configurations could also lead to a variety of phenomena in the early Universe [97,98].…”

Solution of the logarithmic Schrödinger equation with a Coulomb potential

“…A version of SVT favors a logarithmic Schrödinger equation over a Gross-Pitaevski equation [9,15]. In particular, the logarithmic model can account for the upside-down Mexican hat shape of the Higgs potential and its solution is claimed to be even more stable and energetically favorable than the model with a quartic (Higgslike) potential [9,16,17]. Although the Higgs boson reported at 125 Gev has been confirmed, the Higgs potential has not been firmly established.…”

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ φ 4 model

“…It is also of interest to mention the so-called Q-balls and similar configurations [18][19][20][21][22][23], which are charged and protected against decaying into the elementary excitations supported by the respective model. Also, it is worth mentioning other possibilities, such as the study of solitons in fibers [24], bubble collisions in cosmology [25], and localized excitations in nonlinear systems [26].…”