Spinor and electromagnetic fields in space with torsion

A combined system of Einstein-Cartan, Ivanenko-Heisenberg, and Maxwell equations is reduced to a combined system of Einstein, Dirac, and Maxwell equations in Riemann space. A solution in which metric singularities are absent is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 31–35, November, 1978.     

Some zero rest mass test fields in general relativity

Zero rest mass test fields of pure algebraic type are defined and studied via the newly developed GHP formalism. The field equations are written explicitly and an immediate generalisation of Robinson's theorem is obtained. The form for the general zero rest mass test field of pure type is determined in terms of the tetrad components of the background Weyl spinor and an additional gauge dependent function which can be thought of as representing a test neutrino field.     

Spinor fields in Bianchi type-I universe

A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.     

Spinor fields in non-abelian Klein-Kaluza theories

We introduce a dimensional reduction procedure for a spinor field and a generalization of the minimal coupling scheme. We get an electric dipole moment of fermions of value 10^–31 cm and PC breaking for a gauge groupG with odd parameters. Reflection in higher (additional) dimensions are proposed as a conjugation of color charges connected with Yang-Mills fields. Our approach cancels Planck's mass terms in the Dirac equation.     

Flexomagnetoelectric effect in nonuniform external fields in isotropic centrosymmetric nonlinear media with spatial dispersion

The flexomagnetoelectric effects in isotropic centrosymmetric nonlinear media with spatial dispersion in nonuniform external fields are theoretically analyzed. General theoretical concepts are applied to the case of a capacitor with metallic plates in the form of two infinite cylinders with confocal elliptic generatrices that is filled with a nonlinear dielectric. The developed theory is generalized to the case of an isotropic centrosymmetric collinear antiferromagnet in a disordered phase.     

Spinor fields at spacelike infinity

The concept of a spinor structure at spacelike infinity is introduced for space-times which are asymptotically flat. It is shown how zero-rest-mass fields on space-time acquire smooth limits on this structure and that these limits satisfy certain differential equations characterized by the helicity and regularity of the field. The geometry of the limits of twistor fields is also discussed, and it seems possible that one can define the momentum and angular momentum of an asymptotically flat space-time in terms of a twistor space at spacelike infinity.     

Spinor slow-light and dirac particles with variable mass

We consider the interaction of two weak probe fields of light with an atomic ensemble coherently driven by two pairs of standing wave laser fields in a tripod-type linkage scheme. The system is shown to exhibit a Dirac-like spectrum for light-matter quasiparticles with multiple dark states, termed spinor slow-light polaritons. They posses an "effective speed of light" given by the group velocity of slow light, and can be made massive by inducing a small two-photon detuning. Control of the two-photon detuning can be used to locally vary the mass including a sign flip. Particularly, this allows the implementation of the random-mass Dirac model for which localized zero-energy (midgap) states exist with unusual long-range correlations.     

Spinor fields and symmetries of the spacetime

We show that in the background of a stationary and axisymmetric black hole, there is a particular spinor field whose “conserved current” interpolates between the null Killing vector on the horizon and the time Killing vector at the spatial infinity. The spinor field only needs to satisfy a very general and simple constraint.     

Uniqueness of Gibbs fields with unbounded random interactions on unbounded degree graphs

Letters in Mathematical Physics - Gibbs fields with continuous spins are studied, the underlying graphs of which can be of unbounded vertex degree and the spin–spin pair interaction...     

Critical character of gravitational-wave modulation of electric and magnetic fields in isotropic media

The exactly integrable model of the evolution of electric and magnetic fields in an isotropic dielectric medium under the action of gravitational radiation is analyzed. It is shown that as a result of the action of the gravitational radiation field, the dynamic characteristics of an electromagnetic field as a function of the dielectric constant lose continuity in a neighborhood of the value n=1.V. I. Ul'yanov Lenin Kazan' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 28–33, September, 1993.     

Spinor fields in the nonsymmetric,non-Abelian Kaluza-Klein theory

Spinor fields are considered in the framework of the nonsymmetric Kaluza-Klein theory and the nonsymmetric Jordan-Thiry theory (in non-Abelian case). Dipole moments for fermions of value 10^–31 and pseudomass-like terms are found.     

The uniqueness regime of Gibbs fields with unbounded disorder

We consider lattice spin systems with short-range but random and unbounded interactions. We give an elementary proof of uniqueness of Gibbs measures at high temperature or strong magnetic fields, and of the exponential decay of the corresponding quenched correlation functions. The analysis is based on the study of disagreement percolation (as initiated by van den Berg and Maes).Partially supported by EC grant CHRX-CT93-0411.     

Spinor fields on 2 + 1 topologically nontrivial spacetime

Zeta-function regularization is used to evaluate the vacuum energy for a spinor field defined on a space-time of the formR ×H ²/,H ² being the Lobatchevsky plane and a strictly hyperbolic discrete subgroup ofPSL(2,R). The necessary analytic continuation is performed making use of the Selberg trace formula.     

Acoustic-elastodynamic interaction in isotropic fractal media

This research explores the acoustic-elastodynamic interaction in isotropic fractal media. The analysis discusses the direct coupling of two constitutive models under dynamic loading: a continuous solid and an isotropic fractal medium. We consider two situations where in the first, the fractal medium is enclosed within a thin spherical shell (interior problem), while in the second, the fractal medium extends infinitely outside the shell (exterior problem). The two problems are simulated analytically, and the exact solution for the shell displacement is expressed in closed form in the Laplace domain. The formulation of the radiation condition for infinite fractal media is essential to derive the exterior problem’s solution. This study represents a meaningful idealization of real-application problems involving the interaction of multi-constitutive media, e.g. the human brain, whereby fractal features affect the response of this body under various excitations.     

Theory of fermion field with zero mass

A theory is constructed for a free fermion field with spin 1/2 and zero mass, on the basis of the equation (d+a₅-b)(x) = 0, wherea ² = b² = 1. The theory is invariant against continuous Lorentz transformation. It is also invariant against combined Landau reflection, time reversal, and the Schwinger strong space-time inversion, but is not invariant against space reflection or change transformation. An important role is played in this theory by the appearance of projectors. The latter arise as a result of the presence of a zero divisor in the mass term of the equation. They enter in the normalization conditions for the solutions of the equation, and hence in all the conserved operators and their eigenfunctions. Results of the analogous researches by Tokuoka [20] and Gupta [21] are also discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 7–12, December, 1970.In conclusion, the author is grateful to Professor S. V. Izmailov for his attention and interest in discussions of the work.     

Generating sensor signals in isotropic noise fields

Researchers in the signal processing community often require sensor signals that result from a spherically or cylindrically isotropic noise field for simulation purposes. Although it has been shown that these signals can be generated using a number of uncorrelated noise sources that are uniformly spaced on a sphere or cylinder, this method is seldom used in practice. In this paper algorithms that generate sensor signals of an arbitrary one- and three-dimensional array that result from a spherically or cylindrically isotropic noise field are developed. Furthermore, the influence of the number of noise sources on the accuracy of the generated sensor signals is investigated.     

Lateral transport in quasiperiodically ordered layered media with isotropic randomness

Abstract

We investigate the lateral wave transport in quasiperiodically ordered layer media with isotropic randomness. As an example, we consider the case of the Fibonacci sequence and study the ergodic properties in such systems. From the results of the channel occupation number of nine generations, we find that the wave transport in such systems falls between the transport of anisotropic hopping systems and that of randomly layered media and can be associated with a fractal dimension that can be tuned according to the strength of the layer coupling. The origin of this fractal dimensionality is attributed to the interplay between the quasiperiodic ordering in the layer direction and the presence of isotropic randomness in the system.     

Lateral transport in quasiperiodically ordered layered media with isotropic randomness

We investigate the lateral wave transport in quasiperiodically ordered layer media with isotropic randomness. As an example, we consider the case of the Fibonacci sequence and study the ergodic properties in such systems. From the results of the channel occupation number of nine generations, we find that the wave transport in such systems falls between the transport of anisotropic hopping systems and that of randomly layered media and can be associated with a fractal dimension that can be tuned according to the strength of the layer coupling. The origin of this fractal dimensionality is attributed to the interplay between the quasiperiodic ordering in the layer direction and the presence of isotropic randomness in the system.