arXiv subjects
Publications and source records attributed to Boris V. Gisin.
Assuming that universe is the object of point rotation at a frequency, the relationship is established between this frequency and the cosmological constant. Using the transformation for point-like rotating coordinate systems, an unusual exact solution of the Einstein equation is found.
The idea of determining the magnetic resonance condition in a rotating frame of reference is being studied. In this frame, the rotating magnetic field should be at rest. The 3D transformation that determines the transition to the frame is found. The Dirac equation in a rotating electromagnetic field after such a transition is obtained. The magnetic resonance condition is determined by the stationarity of solutions. The connection between g-factor in the anomalous magnetic moment and a constant in 3D transformation is established.
General relativity is the theory with unclear energy momentum tensor. An approach is considered, allowing to construct the energy momentum tensor for relativity with nonsymmetric metric. A consequence of the approach is confirmed in the nuclear physics.
The Dirac equation is invariant under rotations with a constant frequency and invariable cylindrical radius. 3D transformation for rotating frames is found with help of this invariance. Exact localized solutions of the Dirac equation in the field of a traveling circularly polarized electromagnetic wave and constant magnetic field exist and possess unusual properties. Temporal changes of spin pertaining to the solutions are studied.
The problem of Dirac's equation in a rotating electromagnetic field can be reduced to the stationary by using a transformation for point rotating reference frames. The general form of the non-Galilean transformation is deduced in the paper. For the non-Galilean transformation time is different in the rotating and resting frame. This transformation contains a constant, with the dimension of time. The constant is assumed to be fundamental. The transformation forms the necessary condition for the existence of periodic, bounded and square integrable solutions in both the rotating and resting frame. Variety of such solutions exists. Among the solutions massless states are identified. They describe localized neutrinos with invariable spin. The states in the resting frame are not stationary but they have a good chance to be stable.
The Dirac equation, in the field of a traveling circularly polarized electromagnetic wave and a constant magnetic field, has singular solutions, corresponding the expansion of energy in vicinity of some singular point. These solutions described relativistic fermions. States relating to these solutions are not stationary. The temporal change of average energy, momentum and spin for single and mixed states is studied in the paper. A distinctive feature of the states is the disappearance of the longitudinal component of the average spin. Another feature is the equivalence of the condition of fermion minimal energy and the classical condition of the magnetic resonance. Finding such solutions assumes the use of a transformation for rotating and co-moving frames of references. Comparison studies of solutions obtained with the Galilean and non-Galilean transformation shown that some parameters of the non-Galilean transformation may be measured in high-energy physics.
Dirac's equation in the field of a circularly polarized electromagnetic wave and constant magnetic field has exact localized non-stationary solutions. The solutions corresponds relativistic fermions only. Among them singular solutions with energy eigenvalues close to each other are found. The solutions are most practicable and can be separated by means of the phase matching between the momentum of the electromagnetic wave and spinor. Characteristic parameters of the singular states are defined.
In the paper a new class of exact localized solutions of Dirac's equation in the field of a circularly polarized electromagnetic wave and a constant magnetic field is presented. These solutions possess unusual properties and are applicable only to relativistic fermions. The problem of the magnetic resonance is considered in the framework of the classical theory of fields. It is shown that interpretation of the magnetic resonance for relativistic fermions must be changed. Numerical examples of parameters of the electromagnetic wave, constant magnetic field and the localization length scale for real measurements are presented.
Recently the general linear transformation for point rotation coordinate frames was considered. A distinguishing feature of the frame, in contrast to the Cartesian one, is the existence of the rotation axis at every point. The frame coordinates are an angle and time, the frequency of rotation is a parameter. The concept of the frame originated from the optical indicatrix (index ellipsoid). Rotation of the optical indicatrix arises in three-fold electrooptical crystals under the action of the rotating electric field applied perpendicular to the optical axis \cite% {pat}. Such a rotation is possible as in the Pockels as Kerr crystals and also in the isotropic Kerr medium. The rotation is used in single-sideband modulators. The single-sideband modulation has very interesting features from the theoretical viewpoint. In applications it may be used for the frequency modulation and frequency shifting. In contrast to usual modulation such a shifting is "100 persent transformation" of the initial into output frequency. However at present the modulation practically is not in use. It is connected with the high controlling voltage of bulk modulators; creating waveguide single-sideband modulators calls for considerable technological efforts.
We consider the transformation for the point rotation frames with the angle, spatial coordinate along the axis of rotation and time as variables. The problem arises when light, propagating through 3-fold electrooptical crystal, is modulated by the circularly polarized electromagnetic wave traveling along the optical axis of the crystal. With help of the transformation we show that such a wave cannot produce an extra optical frequency shift discussed earlier. In contrast to that the modulation by the rotating spatially invariable electric field produces the shift. The formal change to this case may be carried out by reducing the velocity of the traveling wave to zero. Some properties of the three-dimensional transformation are discussed.
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the reverse frequency. Using symmetry of the direct and reverse transformation as well as symmetry of the frame coordinates we show that two different type of the transformation are possible. The first type is a generalization of the Lorentz transformation. This case can not be checked in optical measurements. In contrast to that the second unusual type allows us to observe consequences of the transformation in an optical experiment even though the characteristic constant inherent in the transformation is less than "nuclear time" of the order of 10^{-23} sec. We describe the experiment.
Starting from the Maxwell's equations and without resort to the paraxial approximation, we derive equations describing stationary (1+1)-dimensional beams propagating at an arbitrary direction in an optical crystal with cubic symmetry and purely quadratic nonlinearity. The equations are derived separately for beams with the TE and TM polarizations. In both cases, they contain and cubic nonlinear terms, the latter ones generated via the cascading mechanism. The final TE equations and soliton solutions to them are quite similar to those in previously known models with mixed quadratic-cubic nonlinearities. On the contrary to this, the TM model is very different from previously known ones. It consists of four first-order equations for transverse and longitudinal components of the electric field at the fundamental and second harmonics. Fundamental-soliton solutions of the TM model are also drastically different from the usual "quadratic" solitons, in terms of the parity of their components. In particular, the transverse and longitudinal components of the electric field at the fundamental harmonic in the fundamental TM solitons are described, respectively, by odd and single-humped even functions of the transverse coordinate. Amplitudes of the longitudinal and transverse fields become comparable for very narrow solitons, whose width is commensurate to the carrier wavelength.
Very narrow spatial bright solitons in (1+1)D and (2+1)D versions of cubic-quintic and full saturable models are studied, starting from the full system of the Maxwell's equations, rather than from the paraxial (NLS) approximation. For the solitons with both TE and TM polarizations, it is shown that there always exists a finite minimum width, and they cease to exist at a critical value of the propagation constant, at which their width diverges. Full similarity of the results obtained for both nonlinearities suggests that the same general conclusions apply to narrow solitons in any non-Kerr model.