On Verification of the Non-Generational Conjectural-Derivation of First Class Constraints: HP Monopole’s Field Case

In an earlier work we proposed a non-generational conjectural-derivation of all first class constraints (involving, only, variables compatible with canonical Poisson brackets) for “realistic” gauge (singular) field theories; and we verified the conjecture in cases of electromagnetic field, Yang-Mills fields interacting with scalar and spinor fields, and the gravitational field. Here, we will further verify our conjecture for the case of ’t Hooft-Polyakov (HP) monopole’s field (i.e. in the Higgs vacuum); and show that we will reproduce the results of Qandalji (Int. J. Theor. Phys. 45:1158, 2006), which were reached at using Dirac’s standard multi-generational algorithm.     

Gravity induced particle production in earth’s gravitational field in TeV region

We discuss the production of particles via interaction with the earth’s gravitational field. Explicit calculations are done for high energy scalars passing through earth’s gravitational field. We show for example, that the width for the scalar processφ→3φ can become comparable with a typical weak decay width at an energy scale of a few TeV. (Similar conclusions can be drawn about particles that ultimately couple to some scalar field.) We speculate that similar processes may be responsible for many of the anomalies in the 10–10⁴ TeV experimental data.     

Accelerating electromagnetic magic field from the C-metric

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the “magic field” of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr–Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the “accelerating magic field” represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born’s solution for two uniformly accelerated monopole charges.     

Valid for Much of “Realistic” Fields: A Non-Generational Conjecture for Deriving All First-Class Constraints at Once

We propose a single-step non-generational conjecture for derivation of all first class constraints, (involving, only, variables compatible with canonical Poisson brackets), of a realistic gauge (singular) field theory. We verify our conjecture for the free electromagnetic field, the Yang-Mills fields in interaction with spinor and scalar fields, and we also verify our conjecture in the case of gravitational field. We show that the first class constraints, which were reached at using the standard Dirac’s multi-generational algorithm, will be reproduced using the proposed conjecture. We make no claim that this conjecture is valid for all “mathematically” plausible Lagrangians; but, nevertheless, the examples we consider here show that this conjecture is valid for a “wide” range or much of realistic fields of Physical interest that are known to exist and be manifested in nature.     

Thomson scattering induced by gravitational waves

We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically, as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization.     

Astrophysically significant solutions of the Einstein and Einstein-Maxwell equations from the Laplace’s seed

The stationary solutions given by Amenedo and Manko generated from known solutions of Laplace’s equation as seed have been generalised to include the electromagnetic field. Further, the exterior solution of an axially symmetric rotating body with higher multipole moments and a solution corresponding to a Kerr object embedded in a gravitational field are given. We also give a method for constructing stationary vacuum solutions from static magnetovac solutions and vice versa and discuss a specific application of this method.     

Algebraic classification of a stationary electromagnetic field as a Kaluza space

Petrov’s approach to classification of four-dimensional space—time without a gravitational field with a cylindrical fifth coordinate is extended to five dimensions. An algebraic classification is presented for a stationary electromagnetic field without sources. This field is treated as part of the geometry of a Kaluza space. Examples of such a classification are given. This work was performed for the Russian Federal Scientific and Technical Program "Astronomy." Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 119–123, January, 1997.     

Spinor Relativity

Spinor relativity is a unified field theory, which derives gravitational and electromagnetic fields as well as a spinor field from the geometry of an eight-dimensional complex and ‘chiral’ manifold. The structure of the theory is analogous to that of general relativity: it is based on a metric with invariance group GL(ℂ²), which combines the Lorentz group with electromagnetic U(1), and the dynamics is determined by an action, which is an integral of a curvature scalar and does not contain coupling constants. The theory is related to physics on spacetime by the assumption of a symmetry-breaking ground state such that a four-dimensional submanifold with classical properties arises. In the vicinity of the ground state, the scale of which is of Planck order, the equation system of spinor relativity reduces to the usual Einstein and Maxwell equations describing gravitational and electromagnetic fields coupled to a Dirac spinor field, which satisfies a non-linear equation; an additional equation relates the electromagnetic field to the polarization of the ground state condensate.     

One-dimensional finite motion of a particle in the field of a weak gravitational wave

The Hamiltonian formalism of classical mechanics can be used effectively to describe the motion of a particle (including a massless one) along a segment of material that is in a nonsteady gravitational field. The problem of applying this formalism to the detection of gravitational waves using a Michelson or Fabry—Perot interferometer is considered. The existence of a phase shift of an electromagnetic wave due to the interaction of the electromagnetic and gravitational fields is noted. Moscow State Aviation Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 13–17, August, 1997.     

The meaning of general covariance of einstein’s theory of gravity

The fundamental symmetry of Einstein’s theory of gravity is Lorentz-invariance which leads to a well defined energy-momentum tensor. This is also true for Maxwell’s theory of electromagnetism which has an additional symmetry due to its spin one, restmass zero character. Similarly, the spin two, restmass zero character of the gravitational field leads to an additional gauge symmetry that happens to be isomorphic to the concept of general covariance. The gauge-covariant energy-momentum tensor for gravitational interactions vanishes identically.     

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.     

Antimatter gravity studies with interferometry

There has never been a direct measurement of the gravitational force on antimatter. This paper describes a possible measurement of this force by measuring the phase shift of neutral antimatter in a transmission-grating interferometer caused by the Earth’s gravitational field. This experiment avoids the severe problem of shielding stray electromagnetic fields necessary for making a gravity measurement with charged particles, and also avoids the need to trap neutral particles. The neutral antimatter for this experiment could be either antihydrogen, positronium, or antineutrons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equilibrium of a high-current channel in the general theory of relativity

The condition for equilibrium of a high-current channel taking account of both electromagnetic and gravitational interactions of the charges with an arbitrary drift-to-light velocity ratio is derived from the equations of Einstein’s general theory of relativity. The relative motion appearing between the electron and ion subsystems as a result of the current flow gives rise to an additional gravitational attraction between these subsystems. This is a relativistic effect that cannot be obtained in the Newtonian approximation. Zh. éksp. Teor. Fiz. 112, 385–399 (August 1997)     

Bianchi-I Space-time with Variable Gravitational and?Cosmological “Constants”

We consider Einstein’s field equations with variable gravitational and cosmological “constants” for a spatially homogeneous and anisotropic Bianchi-I space-time. A law of variation for the Hubble parameter, which is related to the average scale factor and yields a constant value of the deceleration parameter, is assumed to solve the field equations. The gravitational constant is allowed to follow a power-law form. We find that a time-increasing gravitational constant is suitable for describing the present evolution of universe. The solutions reveal the dynamics of a universe, which expands forever. The physical interpretation of the solutions is discussed in detail.     

Problem of bremsstrahlung in: The case of gravitational interaction

A study is made of scalar bremsstrahlung associated with the gravitational and electromagnetic scattering of point particles. It is shown that the interaction between the gravitational field and the scalar field leads to a significant change in the spectral and angular distribution of the radiated energy when there is gravitational interaction of the radiating particles as compared with the case of electromagnetic interaction. The information that the low-frequency approximation can give for this problem is also discussed.Translated from Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 40–47, May, 1980.     

On the gravitodynamics of moving bodies

In the present work we propose a generalization of Newton’s gravitational theory from the original works of Heaviside and Sciama, that takes into account both approaches, and accomplishes the same result in a simpler way than the standard cosmological approach. The established formulation describes the local gravitational field related to the observables and effectively implements the Mach’s principle in a quantitative form that retakes Dirac’s large number hypothesis. As a consequence of the equivalence principle and the application of this formulation to the observable universe, we obtain, as an immediate result, a value of Ω = 2. We construct a dynamic model for a galaxy without dark matter, which fits well with recent observational data, in terms of a variable effective inertial mass that reflects the present dynamic state of the universe and that replicates from first principles, the phenomenology proposed in MOND. The remarkable aspect of these results is the connection of the effect dubbed dark matter with the dark energy field, which makes it possible for us to interpret it as longitudinal gravitational waves.     

On the cosmological constant problem and brane-world geometry

The cosmological constant problem is examined within the context of the covariant brane-world gravity, based on Nash’s embedding theorem for Riemannian geometries. We show that the vacuum structure of the brane-world is more complex than General Relativity’s because it involves extrinsic elements, in specific, the extrinsic curvature. In other words, the shape (or local curvature) of an object becomes a relative concept, instead of the “absolute shape” of General Relativity. We point out that the immediate consequence is that the cosmological constant and the energy density of the vacuum quantum fluctuations have different physical meanings: while the vacuum energy density remains confined to the four-dimensional brane-world, the cosmological constant is a property of the bulk’s gravitational field that leads to the conclusion that these quantities cannot be compared, as it is usually done in General Relativity. Instead, the vacuum energy density contributes to the extrinsic curvature, which in turn generates Nash’s perturbation of the gravitational field. On the other hand, the cosmological constant problem ceases to be in the brane-world geometry, reappearing only in the limit where the extrinsic curvature vanishes.     

The low-energy compton scattering and polarizability of spin-0 Hadrons in a Gaugeinvariant approach

In this work, the amplitude of the interaction of an electromagnetic field with π-mesons has been determined in the context of a relativistic gauge-invariant approach by solving electrodynamic equations with the use of the covariant Green’s function method. Based on this approach, the effective Lagrangian of the two-photon interaction with spin-0 hadrons taking into account the electric and magnetic polarizabilities has been obtained.     

On “Gauge Renormalization” in Classical Electrodynamics

In this paper we pay attention to the inconsistency in the derivation of the symmetric electromagnetic energy–momentum tensor for a system of charged particles from its canonical form, when the homogeneous Maxwell’s equations are applied to the symmetrizing gauge transformation, while the non-homogeneous Maxwell’s equations are used to obtain the motional equation. Applying the appropriate non-homogeneous Maxwell’s equations to both operations, we obtained an additional symmetric term in the tensor, named as “compensating term”. Analyzing the structure of this “compensating term”, we suggested a method of “gauge renormalization”, which allows transforming the divergent terms of classical electrodynamics (infinite self-force, self-energy and self-momentum) to converging integrals. The motional equation obtained for a non-radiating charged particle does not contain its self-force, and the mass parameter includes the sum of mechanical and electromagnetic masses. The motional equation for a radiating particle also contains the sum of mechanical and electromagnetic masses, and does not yield any “runaway solutions”. It has been shown that the energy flux in a free electromagnetic field is guided by the Poynting vector, whereas the energy flux in a bound EM field is described by the generalized Umov’s vector, defined in the paper. The problem of electromagnetic momentum is also examined.     

Gravitational field of a tachyon in a de Sitter universe

An exact solution of Einstein’s equations is interpreted as describing the gravitational field of a tachyon in a de Sitter universe. Switching off the cosmological constant yields the gravitational field of a tachyon in flat spacetime background.