On the properties of Alfvén waves in relativistic magnetohydrodynamics

Simple Alfvén waves and Alfven shocks are considered in the framework of relativistic magnetohydrodynamics. It is found that the tangential components of vector fields trace ellipses instead of the circles of Newtonian MHD. Their properties are studied in the general wave frame, Hoffmann-Teller wave frame, and the general laboratory frame.     

“Projective relativity” and magnetohydrodynamics

The geometrical structure of the Castelnuovo space-time and the Fantappié group are analyzed with the Inönj-Wigner method of contraction of a group with respect to the various subgroups. If we utilize the two vectorsposition andvelocity, we can study the structure of the magnetohydrodynamics tensor. It follows that from projective magnetohydrodynamics we can deduce as limiting cases four theories (two by two duals in the sense of the classical projective geometry).     

On the “nonclassical many-valuedness” of the universe

Two problems connected with Dirac quantization of relativistic cosmological models are considered. The difficulties with this approach have been the lack of physical interpretation of the spinor wave functions and the difficulty in extracting the spinor square root with a variable mass term in the classical Hamiltonian. It is suggested here that the spinor wave functions may be connected with the temporal irreversibility of physical processes in the universe. The analytical difficulty of extracting the spinor square root suggests a modification of the classical theory, in analogy with the theory of the Dirac electron in an electromagnetic field.     

On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac?s theory of constraints

The Hamiltonian structures of the incompressible ideal fluid, including entropy advection, and magnetohydrodynamics are investigated by making use of Dirac?s theory of constrained Hamiltonian systems. A Dirac bracket for these systems is constructed by assuming a primary constraint of constant density. The resulting bracket is seen to naturally project onto solenoidal velocity fields.     

On the “Equivalence” of the Maxwell and Dirac Equations

It is shown that Maxwell's equation cannot be put into a spinor form that is equivalent to Dirac's equation. First of all, the spinor in the representation of the electromagnetic field bivector depends on only three independent complex components whereas the Dirac spinor depends on four. Second, Dirac's equation implies a complex structure specific to spin 1/2 particles that has no counterpart in Maxwell's equation. This complex structure makes fermions essentially different from bosons and therefore insures that there is no physically meaningful way to transform Maxwell's and Dirac's equations into each other.     

On the concept of “nonlocalization” associated with the gravitational field

The concept of nonlocalization associated with the gravitational field, which is carried by the internal variable () annexed to each point, is considered in connection with the geometrical theory of gauge fields. Two concrete examples of nonlocalization are proposed by taking as a vector and a spinor, respectively.     

On the Energy of a “Two-Dimensional” Two-Electron Atom

With the use of the known solution of the Schrödinger equation for an electron in the nucleus field in the polar coordinates, the energy of a “two-dimensional” two-electron atom in the ground state, as well as its single ionization energy, has been calculated both in perturbation theory and with an almost century-old method of variation of the parameter Z in a trial wavefunction of the ground state. Since such two-dimensional atoms, e.g., helium atoms, can in principle be implemented in experiments by “freezing” of one degree of freedom in the phase of Bose–Einstein condensate, the conclusions made in this work can be tested. Fundamental features of the calculation of the energy of “one-dimensional” two-electron atoms and the formation of their Bose–Einstein condensate have also been discussed. The results obtained in this work coincide in a number of particular cases with the results obtained in a previous work, where some results were absent.     

On the Energy of a “One-Dimensional” Two-Electron Atom

Based on the perturbation theory and variational method long known for a “three-dimensional” atom, the ground and first excited state energies are calculated for a “one-dimensional” two-electron atom in the “one-dimensional ortho-helium” configuration, which can be obtained experimentally in principle, as has been already done for a Na Bose condensate, or produced in a super strong magnetic field B ? (2α)²B₀ (B₀ = m²c³/e? ≈ 4.41 × 10¹³ G). The “screening constant” σ for this atom in the ground and excited states was about 0.20 and 0.17, 0.18, respectively, depending on the relative parity PP' of the electronic states, which is somewhat smaller than in “two-dimensional” and “three-dimensional” variants (in these cases, this constant in the ground state is almost the same and about 0.3). The frequencies of the main spectral lines of a “onedimensional” He atom representing a doublet split over the relative parity PP' are found. The presence of the close lines of this doublet in the emission spectrum of magnetars at frequencies ω_{1, 2} ≈ {1.15; 1.17}α²(c/λC) (α = e²/?c, λ_C =?/mc) corresponding to the “one-dimensional ortho-helium” would suggest the existence of a superstrong magnetic field in such astrophysical objects.     

On the theory of “true” three particle scattering

The Hulthen, Kohn and Schwinger-type variational principles for the phase of true three particle scattering is formulated using the method of the hyperspherical basis. The optical theorem for such processes is proved.     

On the “covariantized light-cone” string field theory II

We present a full non-linear BRS transformation which corresponds to one of the generators of the OSp(1, 1|2) or OSp(26, 2|2) algebra using the covariantly extended joining-splitting type interaction vertex functions in open string field theory.     

Comment on “On the analytical solution of the optical Bloch equations”

In a recent paper [P.J. Colmenares and J.L. Paz, Opt. Commun. 284 (2011) 5171], analytical solutions of the optical Bloch equations are presented. This paper follows the same procedures as presented in the paper by the authors [H.R. Noh and W. Jhe, Opt. Commun. 283 (2010) 2353] but concludes that their results are substantially different from the results of the authors. We find that the discrepancy results from the wrong initial conditions employed by those authors for one of the Bloch vector components (w), whose initial value must be 1 not 0. We also find that if proper initial conditions are used, there are no discrepancies between the two results.     

Reply to the comment on “On the Barut-Vigier model of the hydrogen atom”

It is shown that the main conclusion of Dragić and Marić [Phys. Lett. A 229 (1997) 130] about the ground state of the hydrogen atom in the Barut-Vigier potential is based on the wrong use of the radial wave function which cannot be normalized.     

On the Sharp Constant in the “Magnetic” 1D Embedding Theorem

The problem of finding the sharp (exact) constant in the “magnetic” embedding theorem is considered.     

On stability of the elliptical “orbits” of diamagnetic positronium

The stability of the elliptical orbits of diamagnetic positronium is studied and it is found to depend only on the eccentricity ε and the combination of parameters λ = B²r_0c³ (where B is the magnetic field strength and r_0c the conserved guiding center). For small and large values of λ the orbits remain stable while at approximately λ = 1 unstable behavior appears when the eccentricity becomes larger than ε = 0.25.     

On the charge transfer in the “single-sheet graphene-intercalated metal layer-SiC substrate” system

The proposed scheme for the consideration of charge transfer in the three-layer Gr/Me/SiC system (where Gr is a single-sheet graphene, Me is an intercalated metal layer, and SiC is a substrate) contains three stages. At the first stage, a metal monolayer adsorbed on silicon carbide is considered and the charge of adatoms in this monolayer is calculated. At the second stage, the shift of the Dirac point of free-standing single-layer graphene in an electrostatic field induced by charged adatoms of the monolayer is estimated. At the third stage, a weak interaction between Me/SiC and free-standing graphene is included, which allows electrons to tunnel but does not significantly distort the density of states of free-standing graphene. Estimations are performed for n- and p-type 6H-SiC(0001) substrates and Cu, Ag, and Au layers. The charge state of the graphene sheet and the shift of the Dirac point with respect to the Fermi level of the system are calculated. A comparison with the available experimental and theoretical results shows that the proposed scheme works quite satisfactorily.     

On the theory of electronic states of the “epitaxial graphene-quantum-well film” system

The problem of an epitaxial graphene formed on a thin metal film in an external magnetic field has been considered. It has been shown that the problem can be solved using the Green’s function method within the Kadanoff-Baym formalism. Analytical expressions for the transferred charge as a function of the magnetic field and the thickness of the film have been obtained.     

On the “near to minimal” canonical realizations of the lie algebraC n

It is proved that canonical realizations of the Lie algebraC _n in the quotient division ringD _2(2n–2) of the Weyl algebraW _2(22–2) in 2n – 2 quantum canonical pairs are, in a definite sense, related to the standard minimal one inD _2n D _2(2n–2). Further, in any realization ofC _n inW _2(2n-1) all Casimir operators are realized by multiples of identity element.     

Aharonov–Bohm effects in magnetohydrodynamics

It is shown that an Aharonov–Bohm (AB) effect exists in magnetohydrodynamics (MHD). This effect is best described in terms of the MHD variational variables (Kats, 2004; Yahalom and Lynden-Bell, 2008; Yahalom, 2010) [1], [10], [12]. If a MHD flow has a non-trivial topology some of the functions appearing in the MHD Lagrangian are non-single-valued. These functions have properties similar to the phases in the AB celebrated effect (Aharonov and Bohm, 1959; van Oudenaarden et al., 1998) [2], [3]. While the manifestation of the quantum AB effect is in interference fringe patterns (Tonomura et al., 1982) [4], the manifestation of the MHD Aharonov–Bohm effects are through new dynamical conservation laws.     

On the zero fluctuation of the “microscopic free energy” and its potential use

The fluctuations of the microscopic free energy calculated with the ensemble probability are shown to be zero. We suggest that this result be used for estimating approximate free energies calculated on the basis of the minimum free energy principle. As an example the estimation is performed with respect to a certain computer simulation of the square Ising lattice. The zero fluctuations also can be used to obtain relations among fluctuations with the accurate ensemble probability distribution.