Duality in Yang’s theory of gravity

The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a vacuum degeneracy. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.     

On Ohm’s law in the thin current sheets of the Earth’s magnetosphere

The analytical and numerical dependences of the total transverse current on an electric field, the normal component of a magnetic field and the ion and electron temperatures are obtained using analytical approximation of numerical results provided by a self-consistent model of the magnetospheric thin sheet. The dependence of current on the parameters ?, T _i , b _n is shown to be nonlinear. The relative contributions of different plasma components into the total current are estimated.     

A critical fluid in the Earth’s gravity field

This work proposes a mechanism for the physical processes underlying the wide practical application of the unique properties of a substance in a critical state—critical fluid (CF)—in contemporary technologies. According to the fluctuation theory of phase transitions (FTPT), this mechanism may be due to the fluctuation and structural characteristics of a critical fluid, which determine its equilibrium and kinetic properties. Among such characteristics are the system correlation radius Rs, the number of order parameter fluctuations N _f ~ R _s ^-3 per mole of critical fluid, and the fluctuation component of the thermodynamic potential F*_f = N _f k T _c/(P _c V _c) = C ₀ R _s ^-3 . These structural characteristics are studied with the use of experimental gravity effect data, such as the altitude and temperature dependencies of the scattered light intensity I(z, t) in a heterogeneous substance (n-pentane) near the critical vaporization temperature. Using these results and the literature data on the formation of Al₂O₃ nanoparticles with the use of SC-H₂O, the propagation velocity of substance molecules v _f ≈ 106 cm/s is estimated for the origination and decay of order parameter fluctuations. It has been concluded that just such high propagation velocities of substance molecules most likely cause the unique properties of a critical fluid during their practical application in a number of engineering processes.     

Republication of: On the formal analogy between the basic electromagnetic equations and Einstein’s gravity equations in first approximation

This is an English translation of a paper by Hans Thirring, first published in German in 1918, which contains the first and correct presentation of the basic equations of gravitomagnetism in linear order. The paper has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Herbert Pfister, and Thirring’s brief biography compiled by Andrzej Krasinski from internet sources     

Opening the Pandora’s box of quantum spinor fields

Lounesto’s classification of spinors is a comprehensive and exhaustive algorithm that, based on the bilinears covariants, discloses the possibility of a large variety of spinors, comprising regular and singular spinors and their unexpected applications in physics and including the cases of Dirac, Weyl, and Majorana as very particular spinor fields. In this paper we pose the problem of an analogous classification in the framework of second quantization. We first discuss in general the nature of the problem. Then we start the analysis of two basic bilinear covariants, the scalar and pseudoscalar, in the second quantized setup, with expressions applicable to the quantum field theory extended to all types of spinors. One can see that an ampler set of possibilities opens up with respect to the classical case. A quantum reconstruction algorithm is also proposed. The Feynman propagator is extended for spinors in all classes.     

The role of cosmic rays in the Earth’s atmospheric processes

In this paper, we have provided an overview of cosmic ray effects on terrestrial processes such as electrical properties, global electric circuit, lightning, cloud formation, cloud coverage, atmospheric temperature, space weather phenomena, climate, etc. It is suggested that cosmic rays control short-term and long-term variations in climate. There are many basic phenomena which need further study and require new and long-term data set. Some of these have been pointed out.     

On the Classical Limit in Bohm’s Theory

The standard means of seeking the classical limit in Bohmian mechanics is through the imposition of vanishing quantum force and quantum potential for pure states. We argue that this approach fails, and that the Bohmian classical limit can be realized only by combining narrow wave packets, mixed states, and environmental decoherence.     

On the Geodesic Nature of Wegner’s Flow

Wegner’s method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some physical examples.     

On Zurek’s Derivation of the Born Rule

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or envariance [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.     

On the CHSH Form of Bell’s Inequalities

A common mistake present in the derivation of the usually known as the CHSH form of Bell’s inequalities is pointed out. References and comments to the correct approach are given. This error does not alter the final result and only affects the logical consistency of the derivation, but since it seems to be a widespread misconception regarding the roll and interpretation of the of use of hidden variables in Bell’s theorem it is considered to be of general interest.     

On the Road Map of Vogel’s Plane

We define “population” of Vogel’s plane as points for which universal character of adjoint representation is regular in the finite plane of its argument. It is shown that they are given exactly by all solutions of seven Diophantine equations of third order on three variables. We find all their solutions: classical series of simple Lie algebras (including an “odd symplectic” one), \({D_{2,1,\lambda}}\) superalgebra, the line of sl(2) algebras, and a number of isolated solutions, including exceptional simple Lie algebras. One of these Diophantine equations, namely \({knm=4k+4n+2m+12,}\) contains all simple Lie algebras, except so\({(2N+1).}\) Among isolated solutions are, besides exceptional simple Lie algebras, so called \({\mathfrak{e}_{7\frac{1}{2}}}\) algebra and also two other similar unidentified objects with positive dimensions. In addition, there are 47 isolated solutions in “unphysical semiplane” with negative dimensions. Isolated solutions mainly belong to the few lines in Vogel plane, including some rows of Freudenthal magic square. Universal dimension formulae have an integer values on all these solutions at least for first three symmetric powers of adjoint representation.     

On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system.     

Quantum–classical correspondence and the role of the dipole function in molecular dissociation

We consider the quantum and classical dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses. The field–molecule interaction is given by the product of the time-dependent electric field and the molecule permanent dipole. We investigate the influence of the dipole function in molecular dissociation. We show that the dissociation can be suppressed at certain external field frequencies for a nonlinear and finite-range dipole function. The correspondence between quantum and classical results is established by relating classical Fourier amplitudes to discrete–continuum quantum matrix elements.     

Densities of electron’s continuum in gravitational and electromagnetic fields

Relativistic dynamics of distributed mass and charge densities of the extended classical particle is considered for arbitrary gravitational and electromagnetic fields. Both geodesic and field gravitational equations can be derived by variation of the same Lagrange density in the classical action of a nonlocal particle distributed over its radial field. Vector geodesic relations for material space densities are contraction consequences of tensor gravitational equations for continuous sources and their fields. Classical four-flows of elementary material space depend on local electromagnetic fourpotentials for charged densities, as in quantum theory. Besides the Lorentz force, these potentials result in two more accelerating factors vanishing under equilibrium internal stresses within the continuous particle.     

Asymptotic quasinormal modes of scalar field in a gravity’s rainbow

In the framework of the gravity's rainbow, the asymptotic quasinormal modes of the modified Schwarzschild black holes undergoing a scalar perturbation are investigated. By using the monodromy method, we analytically calculated the asymptotic quasinormal frequencies, which depend on not only the mass parameter of the black hole, but also the particle's energy of the perturbation field. Meanwhile, the real parts of the asymptotic quasinormal modes can be expressed as T_H\ln 3, which is consistent with Hod's conjecture. In addition, for the quantum corrected black hole, the area spacing is independent of the particle's energy, even though the area itself depends on the particle's energy. And that, by relating the area spectrum to loop quantum gravity, the Barbero-Immirzi parameter is given and it remains the same as from the usual black hole.     

On the fictitious nonlinearity of the surface impedance of the Earth’s crust

The observations of Alfvén oscillations of the magnetosphere are used to study the Earth’s crust and upper mantle by the magnetotelluric sounding method. The sounding procedure involves the measurement of the horizontal components of the electromagnetic field at a given point on the ground, the calculation of the surface impedance, and the determination of the conductivity of rocks from these data. It has been shown that the anharmonicity of the oscillations of the magnetosphere in combination with the nonlocality of the boundary condition on the ground gives rise to the amplitude dependence of the impedance calculated using the classical magnetotelluric sounding method. This apparent nonlinearity of the impedance can be manifested in the sounding of the Earth’s interior with intense electromagnetic pulsations, which appear when the Earth’s magnetosphere is embedded in the highspeed solar wind flow.