Can a Circulating Light Beam Produce a Time Machine

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC’s) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC’s occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett’s solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.     

The electrostatics of Einstein’s unified field theory

When sources are added at their right-hand sides, and g_(ik) is a priori assumed to be the metric, the equations of Einstein’s Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_(ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_(ik), however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély’s physically correct metric is adopted.     

Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory

No Heading We show that the Dirac-von Neumann formalism for quantum mechanics can be obtained as an approximation of classical statistical field theory. This approximation is based on the Taylor expansion (up to terms of the second order) of classical physical variables – maps f : Ω → R, where Ω is the infinite-dimensional Hilbert space. The space of classical statistical states consists of Gaussian measures ρ on Ω having zero mean value and dispersion σ²(ρ) ≈ h. This viewpoint to the conventional quantum formalism gives the possibility to create generalized quantum formalisms based on expansions of classical physical variables in the Taylor series up to terms of nth order and considering statistical states ρ having dispersion σ²(ρ) = hⁿ (for n = 2 we obtain the conventional quantum formalism).     

Cotunneling through a quantum dot coupled to ferromagnetic leads with noncollinear magnetizations

Spin-dependent electronic transport through a quantum dot has been analyzed theoretically in the cotunneling regime by means of the second-order perturbation theory. The system is described by the impurity Anderson Hamiltonian with arbitrary Coulomb correlation parameter U. It is assumed that the dot level is intrinsically spin-split due to an effective molecular field exerted by a magnetic substrate. The dot is coupled to two ferromagnetic leads whose magnetic moments are noncollinear. The angular dependence of electric current, tunnel magnetoresistance, and differential conductance are presented and discussed. The evolution of a cotunneling gap with the angle between magnetic moments and with the splitting of the dot level is also demonstrated.     

Hierarchy of the Selberg Zeta Functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Mathematics Subject Classifications (2000). Primary 11M36, Secondary 33B15     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

On the asymptotic character of electromagnetic waves in a Friedmann–Robertson–Walker universe

Asymptotic properties of electromagnetic waves are studied within the context of Friedmann–Robertson–Walker (FRW) cosmology. Electromagnetic fields are considered as small perturbations on the background spacetime and Maxwells equations are solved for all three cases of flat, closed and open FRW universes. The asymptotic character of these solutions is investigated and their relevance to the problem of cosmological tails of electromagnetic waves is discussed.     

Quantum Groups and Double Quiver Algebras

For a finite dimensional semisimple Lie algebra and a root q of unity in a field k, we associate to these data a double quiver . It is shown that a restricted version of the quantized enveloping algebras is a quotient of the double quiver algebra .*The author is partially supported by the National Science Foundation of China (Grant. 10271014) and Natural Science Foundation of Beijing City (grant. 1042001)