In this paper, the versions of quantum electrodynamics (QED) with spinors in fermion equations are briefly examined. In the new variants of the theory, the concept of vacuum polarization is ...unnecessary. The new content of fermion vacuum (without the Dirac sea) in the examined versions of QED leads to new physical consequences, part of which can be tested experimentally in the future.
The existence of the ergosphere of the Kerr metric does not manifest itself in quantum equations for particles of different spins.To justify the Penrose process with energy extraction from the ...ergosphere, it is necessary to substantiate and prove its existence within the framework of the consistent quantum theory.
When using a second-order Schrödinger-type equation with the effective potential of the Schwarzschild field, the existence of a stationary state of half-spin particles with energy
E
= 0 is proved. ...For each of the values of quantum numbers
j
,
l
, the physically meaningful energy
E
= 0 (the binding energy is
) is implemented at the value of the gravitational coupling constant
. The particles with
E
= 0 are, with the overwhelming probability, at some distance from the event horizon within the range from zero to several fractions of the Compton wavelength of a fermion depending on value of the gravitational coupling constants and the values of
j
,
l
. In this paper, similar solutions of the second-order equation are announced for bound states of fermions in the Reissner–Nordström, Kerr, Kerr–Newman fields. Atomic-type systems (the point sources of the Schwarzschild gravitational field) with fermions in bound states are proposed as particles of dark matter.
We obtain relativistic self-adjoint second-order equations for fermions in Schwarzschild, Reissner–Nordström, Kerr, and Kerr–Newman gravitational and electromagnetic fields. Second-order equations ...with effective potentials and spinor wave functions extend opportunities for obtaining regular solutions of quantum mechanics equations for spin-1/2 particles.
We have studied self-conjugate second-order equations with spinor wavefunctions for fermions moving in an external Coulomb field. For stationary states, the equations are characterized by separated ...states with positive and negative energies, which render probabilistic interpretation possible. For the Coulomb field of attraction, the energy spectrum of the second-order equation coincides with the spectrum of the Dirac equation, while the probability densities of states are slightly different. For a Coulomb field of repulsion, there exists an impermeable potential barrier with radius depending on the classical electron radius and on the electron energy. The existence of the impermeable barrier does not contradict the results of experiment for determining the inner electron structure and does not affect (in the lowest order of perturbation theory) the Coulomb electron scattering cross section. The existence of the impermeable barrier can lead to positron confinement in supercritical nuclei with
Z
≥ 170 in case of realization of spontaneous emission of vacuum electron–positron pairs.
The existence of degenerate stationary bound states with square-integrable radial wavefunctions was proven when second-order equations are used with the effective potential of the Reissner–Nordström ...(RN) field with two event horizons for charged and uncharged fermions. The fermions in such states are localized near event horizons within the ranges from zero to several fractions of Compton wavelength of fermions versus the values of gravitational and electromagnetic coupling constants and the values of angular and orbital momenta
j
,
l
. In case of extreme RN fields, the absence of stationary bound states of fermions with the energies of
E
<
mc
2
is shown for solutions of the second-order equation for any value of gravitational and electromagnetic coupling constants. The existence of a discrete energy spectrum is shown for the naked RN singularity, due to the solution of the second-order equation at definite values of physical parameters. The discrete spectrum exists for both charged and uncharged fermions. The naked RN singularity in quantum mechanics with the second-order equation for half-spin particles poses no threat to cosmic censorship, since it is covered with an infinitely large potential barrier. Electrically neutral systems of atomic type (RN collapsars with the definite number of fermions in degenerate bound states) are proposed to consider as particles of dark matter.
Analysis of quantum mechanical motion of charged half-spin particles in the repulsive Coulomb field results in that an impenetrable potential barrier not explored earlier was found. For a particle at ...rest with a reduced mass m, the barrier radius is equal to half classical radius: the barrier radius decreases with increase in the particle energy. For the stable and quasi-stable nuclei with Z > 118, presence of an impenetrable barrier as β+-decay leads to the existence of "traps" for positrons in the neighbourhood of nuclei and as Zcr ≃ 170 (with emission of electron-positron pairs by vacuum) leads to the existence of a quasi-constant source of annihilation quanta.
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