Quantization and contact structure on manifolds with projective structure

We consider complex manifolds with a class of holomorphic coordinate functions satisfying the condition that each transition function is given by the standard action on of some element in . We show that such a manifold has a natural contact structure. Given any contact manifold, one can associate with it a symplectic manifold. It is shown that the symplectic manifolds arising from complex manifolds with special coordinate functions of the above type admit a canonical quantization.     

Spherically symmetric conformally flat distributions of charged dust and zero-mass scalar fields

The problem of charged dust distribution in the presence of zero-mass scalar field for a spherically symmetric conformally flat metric has been investigated. Exact solutions are obtained in the comoving coordinate system for the static model as well as for the nonstatic model. It has been shown that in the nonstatic model the electromagnetic field and dust distribution cannot survive when the scalar field is taken to be a function of timet only. Physical interpretation of the solutions has been investigated.     

Spatial distortions of the orientational structure of a ferronematic in the presence of external fields

Spatial distortions of the director field and magnetization of a ferronematic (suspension of magnetic nanoparticles in a nematic liquid crystal) that are induced by simultaneous action of electric and magnetic fields are studied with allowance for the flexoelectric polarization of the liquid-crystalline matrix. Soft coupling of liquid crystal and magnetic particles and layer boundaries is considered. The dependence of the phase lag of the transmitted light on the external magnetic field is analyzed.     

Covariant construction of the symmetric energy-momentum tensor of vector and spinor fields in an orthogonal frame of reference

A covariant method is devised to construct the symmetric energy-momentum tensor for vector fields in an orthogonal frame of reference. The method is then used to construct the symmetric energy-momentum tensor for spinor fields. Kazan’ University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1997.     

Spreading resistance of a flat circular contact

Equations are derived for the spreading resistance of a flat contact on the surface of a conducting half-space and on an infinite semiconducting film. The values of the factor Q, which depends on the ratio of the contact radius to the layer thickness, are tabulated. Under certain conditions the spreading resistance can be calculated from simple equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 100–105, September, 1970.     

Experiments on the viscosity of some symmetric top molecules in the presence of magnetic and electric fields

In order to obtain information on the scalar structure of non-equilibrium polarizations a comparison between the magnetic and the electric field effect on the viscosity of some symmetric top molecules has been carried out. It is shown that the polarization produced in viscous flow is more complicated than assumed so far.     

The connection between the energy-momentum tensor and the tensor field in presence of a mass gap

The conditions under which a tensor field can be regarded as an energy-momentum tensor are discussed. The problem connected with dilatational and conformal symmetries are exhibited.     

Theory of MRI in the presence of zero to low magnetic fields and tensor imaging field gradients

Today, all commonly practiced magnetic resonance imaging (MRI) reconstruction methods assume that the magnetic field created by the gradient coils is everywhere truncated by a dominant static uniform magnetic field. However, with the advent of SQUID detected MRI at microtesla fields, the opposite limit attracts attention, i.e., image formation in the unperturbed tensor field of the gradient coils. Here, we show by numerical simulations that, in principle, it is possible to reconstruct the image of an object in the absence of a uniform static field, working with the same gradient field setup as used in conventional MRI. Our calculations show that this approach could increase the image resolution limit attainable at low fields with a minimal incorporation of additional hardware and pulse sequences.     

Static spherically symmetric solutions in general projective relativity

Static spherically symmetric solutions have been obtained for general projective relativity withn=0 andn0 both in isotropic and curvature coordinates. In curvature coordinates, only a restricted exact solution is possible. However, an approximate solution can always be obtained following a method similar to Vanden Bergh. In these spacetimes there is no horizon, but only a naked singularity atr=0. Thus there are no black holes. It is shown that there is no solution in static, spherically symmetric, conformally flat spacetime.     

Fictitious Yang-Mills fields in a plane symmetric universe

It is shown that if we apply the Ansatz recently proposed by Oh and Teh to find a static Yang-Mills field in a plane symmetric universe, we get simply the vacuum Taub solution or the maxwellian Patnaik solution. In addition, we have shown that there are no plane wave solutions.     

Geometry in a manifold with projective structure

Parallel transport of line elements, surface elements etc. along geodesics and more general curves in a projectively connected manifold is investigated analytically and in terms of geometrical constructions. Projective curvature is characterized geometrically by a projective analogue of the geodesic deviation equation and by a geometrical construction. The results are interpreted physically as statements about free fall world lines in space-time.This paper is dedicated to our friend John Archibald Wheeler, geometer and physicist, who celebrated his sixtieth birthday on July 9, 1971.This work was supported in part by the National Science Foundation (Grant No. GP-34639X). One of the authors (A.S.) did much of this work while visiting the Université Libre de Bruxelles (summer, 1968), Cambridge University (summer, 1970), and the Nordic Institute for Theoretical Atomic Physics (1970-71); he wishes to thank these institutions and Drs. I. Prigogine, D. Sciama, and C. Møller for their kind hospitality.     

Energy-momentum tensor of fields in the standard cosmology

With the use of the equations of motion of massless fields moving in a curved Friedmann-Robertson-Walker universe, we show, in some simple cases, that the energy-momentum tensor of a maximally 3-space symmetric distribution of the fields (i.e., an incoherent averaging over a complete set of modes of the field propagating in a Robertson-Walker background) has the standard perfect fluid form. As far as we know such an explicit demonstration, as well as the establishment of the compatibility of the equations of motion of the gravitational field with such an incoherently averaged source in the standard cosmology, has not previously been presented in the literature. Our results are found to hold for any value of the spatial curvature of the universe.     

Spherically symmetric configurations of General Relativity in presence of scalar fields: separation of circular orbits

We show that the test body stable circular orbits around the spherically symmetric black hole (BH) configuration can form disjoint structures in presence of a minimally coupled nonlinear scalar field. General conditions for the disjoint structures to exist are formulated. To present examples we construct a two-parametric family of exact solutions to Einstein equations with scalar fields for appropriate self-interaction potentials. For different values of the family parameters the solutions describe either BH or naked singularity (NS). We found numerically regions of the parameters when there exist two disjoint regions of stable circular orbits; such nonconnected structures indeed can exist in case of both BH and NS solutions.     

Classical pion fields in the presence of a source

A classical pion field that is similar to a disoriented chiral condensate is considered in the presence of an external source. The field is similar to the condensate in that the isotopic orientation of the field in the whole space is determined by a single vector. Within the nonlinear sigma model, classical solutions are considered both in the chiral limit, where the pions are massless, and in the case of a finite pion mass. In either case, the classical filed is similar to the Coulomb field of a charged particle; however, the nonlinear pion interaction results in the existence of several solutions. In the massless case and in the case where the source is sufficiently small, there are a great number of classical solutions characterized by finite discrete energies. In the more realistic case of heavy ions, there are no stable solutions of this type; however, long-lived quasistationary states, which slowly decay, emitting very soft pions, can be formed. The structure and the energies of these solutions are studied numerically.     

Axisymmetric vacuum fields in general projective relativity

A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.     

Ghost neutrino fields in flat space-time

The Weyl neutrino equation is integrated in flat space-time assuming that the energy-momentum tensor of the neutrino field vanishes. It is shown that the flux vector of the neutrino field is tangent to a twist-free and shear-free congruence of null geodesics, which is a special Robinson congruence and constitutes a geometrical representation of a null twistor. It is also shown that, conversely, given such a congruence, a ghost neutrino field can be constructed.     

On the projectivity of conformally flat spaces created by a hydrodynamical energy-momentum tensor

It is shown that under the condition _ju _k = _k u_j imposed on the mapping function the geodesics in conformai gravitational fields are the same. The following fact is also established: all conformally flat spaces satisfying this condition correspond to the gravitational fields of an ideal fluid.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 16–19, 1972.     

Static spherically symmetric fields in the scalar-tetradic theoryA

The scalar-tetradic TheoryA has been recently formulated. In this paper it is proved that, for a suitable tetrad field and any given value of the coupling constantW of the theory, there is a unique static spherically symmetric solution of the field equations describing the outer field of a standard perfect fluid sphere (such as the sun); the explicit form of this solution in terms of the radial isotropic coordinater appears to be different in the three cases: (1)W <0 orW > 2, (2) 0 <W < 2, and (3)W =2. On account of the Birkhoff theorem the quoted solution appears to have considerable physical interest.