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The equations of motion of a particle in the gravitational field of a black hole are considered in a formulation that uses generalized coordinates, velocities, and accelerations and is convenient for finding the integrals of motion. The equations are rewritten in terms of the physical velocities and accelerations measured in the Schwarzschild frame by a stationary observer using proper local length and time standards. The attractive force due to the field and the centripetal acceleration of a particle is proportional to the particle kinetic energy , consistently with the fact that the particle kinetic energy and the photon energy in the field increase by the same factor compared with their values without a field. The attraction exerted on particles and photons by a gravitational field source is proportional to their kinetic energies. The particle trajectory in the ultrarelativistic limit coincides with the photon trajectory.

Duality of four-dimensional electrodynamics and two-dimensional field theory leads to a finite value $$ {e}_0=\pm \sqrt{\hbar c} $$ of the point-like bare charge with the fine structure constant a 0 = 1/4π. On the other hand, the calculated (by several authors) energy shifts E B = a B ћc/2r and E L = a L ћc/a of zero-point electromagnetic vacuum fluctuations by neutral conducting shells of a sphere of radius r and a cube of edge a are defined by the dimensionless parameters αB and αL, which differ from each other by less than 0.8% and even more weakly differ from the fine structure constant α times 4π, since a L

This review is an extended version of a report delivered at a session of the Department of Physical Sciences, the Department of Energetics, Mechanical Engineering, Mechanics, and Control Processes, and the Coordination Council on Technical Sciences of the RAS devoted to the 60th anniversary of the first hydrogen bomb test. The significant physical ideas suggested by A D Sakharov and V L Ginzburg underlying our first hydrogen bomb, RDS-6s, and numerous concrete problems and difficulties that had to be solved and overcome in designing thermonuclear weapons are presented. The understanding of the country's leaders and the Atomic Project managers of the exceptional role of fundamental science in the appearance and implementation of our scientists' concrete ideas and suggestions is emphasized.

We dicuss the holographic duality consisting in the functional coincidence of the spectra of the mean number of photons (or scalar quanta) emitted by a point-like electric (scalar) charge in -space with the spectra of the mean number of pairs of scalar (spinor) quanta emitted by a point mirror in -space. Being functions of two variables and functionals of the common trajectory of the charge and the mirror, the spectra differ only by the factor (in Heaviside units). The requirement =1 leads to unique values of the point-like charge and its fine structure constant, , , all their properties being as stated by Gell-Mann and Low for a finite bare charge. This requirement follows from the holographic bare charge quantization principle we propose here, according to which the charge and mirror radiations respectively located in four-dimensional space and on its internal two-dimensional surface must have identically coincident spectra. The duality is due to the integral connection of the causal Green's functions for - and -spaces and to connections of the current and charge densities in -space with the scalar products of scalar and spinor massless fields in -space. We discuss the closeness of the values of the point-like bare charge , the `charges' and characterizing the shifts of the energy of zero-point electromagnetic oscillations in the vacuum by neutral ideally conducting surfaces of a sphere of radius and a cube of side 2, and the electron charge times . The approximate equality means that is the fine structure constant.

A D Sakharov was an amazingly gifted person for whom, with his combined talents as a physicist and inventor, "physical laws and the relation among phenomena were directly visualized and tangible in all their inherent simplicity" (I E Tamm). The author of the key ideas involved in the hydrogen weapons and fusion reactor programs, and well aware of his scientific and public status, Sakharov was, nevertheless, a modest and highly decent man, always trustful of people in discussing their or his problems. Although his greatest satisfaction lay in successfully solving fundamental problems in physics and cosmology, fate and duty made him turn to matters of universal human significance, particularly human rights, to the gruelling struggle to which he devoted many years of his life.

Gravitational radiation (GR) from compact relativistic systems with a known energy–momentum tensor (EMT) and GR from two masses elliptically orbiting their common center of inertia are considered. In the ultrarelativistic limit, the GR spectrum of a charge rotating in a uniform magnetic field, a Coulomb field, a magnetic moment field, and a combination of the last two fields differs by a factor 4πGm2Γ2/e2 (Γ being of the order of the charge Lorentz factor) from its electromagnetic radiation (EMR) spectrum. This factor is independent of the radiation frequency but does depend on the wave vector direction and the way the field behaves outside of the orbit. For a plane wave external field, the proportionality between the gravitational and electromagnetic radiation spectra is exact, whatever the velocity of the charge. Qualitative estimates of Γ are given for a charge moving ultrarelativistically in an arbitrary field, showing that it is of the order of the ratio of the nonlocal and local source contributions to the GR. The localization of external forces near the orbit violates the proportionality of the spectra and reduces GR by about the Lorentz factor squared. The GR spectrum of a rotating relativistic string with masses at the ends is given, and it is shown that the contributions by the masses and string are of the same order of magnitude. In the nonrelativistic limit, the harmonics of GR spectra behave universally for all the rotating systems considered. A trajectory method is developed for calculating the GR spectrum. In this method, the spatial (and hence polarization) components of the conserved EMT are calculated in the long wavelength approximation from the time component of the EMTs of the constituent masses of the system. Using this method, the GR spectrum of two masses moving in elliptic orbits about their common center of inertia is calculated, as are the relativistic corrections to it.

The asymmetry of the relativistic addition law for noncollinear velocities under the velocity permutation leads to two modified triangles on a Euclidean plane depicting the addition of unpermuted and permuted velocities and the appearance of a nonzero angle ω between two resulting velocities. A particle spin rotates through the same angle ω under a Lorentz boost with a velocity noncollinear to the particle velocity. Three mutually connected three-parameter representations of the angle ω, obtained by the author earlier, express the three-parameter symmetry of the sides and angles of two Euclidean triangles identical to the sine and cosine theorems for the sides and angles of a single geodesic triangle on the surface of a pseudosphere. Namely, all three representations of the angle ω, after a transformation of one of them, coincide with the representations of the area of a pseudospherical triangle expressed in terms of any two of its sides and the angle between them. The angle ω is also symmetrically expressed in terms of three angles or three sides of a geodesic triangle, and therefore it is an invariant of the group of triangle motions over the pseudo-sphere surface, the group that includes the Lorentz group. Although the pseudospheres in Euclidean and pseudo-Euclidean spaces are locally isometric, only the latter is isometric to the entire Lobachevsky plane and forms a homogeneous isotropic curved 4-velocity space in the flat Minkowski space. In this connection, relativistic physical processes that may be related to the pseudosphere in Euclidean space are especially interesting.

An account is given of the Wigner concept of particle spin and velocity rotations and of the variation of the angle between them under Lorentz transformations with noncollinear velocities. It is shown that Moller's description of spin rotation can be reduced to the Wigner rotation, and Moller's formula for the angle of spin rotation in the curvilinear motion of a particle is corrected. The permutation asymmetry of the relativistic velocity addition law distinguishes the Wigner sequence of Lorentzian boosts by its applicability to the description of spin and velocity rotations in curvilinear motion.

The symmetry between the creation of pairs of massless bosons or fermions by accelerated mirror in 1+1 space and the emission of single photons or scalar quanta by electric or scalar charge in 3+1 space is deepened in this paper. The relation of Bogoliubov coefficients, describing the processes generated by the mirror, with Fourier's components of current or charge density leads to the coicidence of the spin of any disturbances bilinear in scalar or spinor field with the spin of quanta emitted by the electric or scalar charge. The mass and invariant momentum transfer of these disturbances are essential for the relation of Bogoliubov coefficients with invariant singular solutions and Green's functions of wave equations both for 1+1 and 3+1 spaces and especially for the integral relation (20) between these solutions. Namely the last relation leads to the coincidence of the self-action changes and vacuum-vacuum amplitudes for the accelerated mirror in two-dimentional space-time and charge in four-dimentional space-time. Thus, both invariants of the Lorentz group, spin and mass, perform intrinsic role in established symmetry.

Calculated by the author previously [8], the anomalous magnetic moment (AMM) of the electron in an intense constant electric field changes nonmonotonically as the field increases, passing through a minimum and tending to the doubled Schwinger value for very strong fields. In the present paper, it is supposed that the AMM is related by the Lande factor to the angular momentum of a virtual electron accompanied by a virtual photon. This factor changes its effective value because of the influence of the external field on the motion of the virtual electron and its self-action. With increase of the electric field strength, the virtual electron can successively occupy the excited states l = 1, j = 1/2 and l = 1, j = 3/2 in addition to the original state with the orbital angular momentum l = 0 and the total angular momentum j = 1/2. The first of these excited states decreases the AMM and the second increases and doubles it if only this state is occupied for a very strong field. The latter condition is equivalent to the alignment of the spin and the orbital angular momentum of the electron along the field, while the total angular momentum of the entire system of the virtual electron and the virtual photon remains equal to 1/2.

It is shown that right and left combinations of the positive-and negative-frequency hyperbolically symmetric solutions of the Klein-Fock-Gordon equation possess an everywhere timelike current density vector with a definite Lorentz-invariant sign of the charge density, and similar combinations of solutions to the Dirac equation possess the energy-momentum tensor with everywhere real eigenvalues and a definite Lorentz-invariant sign of the energy density. These right and left modes, just as their ±-frequency components, are eigenfunctions of the Lorentz boost generator with the eigenvalue к. The sign of the charge (energy) density coincides with the sign of к for the right scalar (spinor) modes and is opposite to it for the left modes. It is then reasonable to assume that the particles (antiparticles) are precisely described by the right modes with к>0(к 0).

We show that the singular behavior of Rindler solutions near horizon testifies to the currents of particles from a region arbitrarily close to the horizon. Besides, the Rindler solutions in right Rindler sector of Minkowski space can be represented as a superposition of only positive-or only negative-frequency plane waves; these states require infinite energy for their creation and possess infinite charge in a finite space interval, containing the horizon. The positive-or negative-frequency representations of Rindler solutions analytically continued to the whole Minkowski space make up a complete set of states in this space, which have, however, the aforementioned singularities. These positive (negative)-frequency states are characterized by positive (negative) total charge, the charge of the same sign in right (left) Rindler sector and by quantum number κ. But in other Lorentz invariant sectors they do not possess positive (negative)-definite charge density and have negative (positive) charge in left (right) Rindler sector. Therefore these states describe both the particle (antiparticle) and pairs, the mean number of which is given by Planck function of κ. These peculiarities make the Rindler set of solutions nonequivalent to the plane wave set and the inference on the existence of thermal currents for a Rindler observer moving in empty Minkowski space is unfounded.

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 1+1 space and satisfies a single condition on it. The symmetry is embodied in the Bogolyubov matrix coefficients α and β that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of α and β and are related to each other by the transformation (12). The coefficient β ω′ω * plays the role of the source amplitude of a pair of oppositely directed particles with frequencies ω and ω′ of which one is in the left half-space and the other is in the right half-space because one of them has undergone reflection. Such an interpretation makes β ω′ω * observable and explains why, as shown by Eq. (1) and found earlier by Nikishov and Ritus [Zh. Eksp. Teor. Fiz. 108, 1121 (1995); transl. JETP 81, 615 (1995)] and by Ritus [Zh. Eksp. Teor. Fiz. 110, 526 (1996); transl. JETP 83, 282 (1996)], the emission spectra of a mirror in 1+1 space coincide with those of charges in 3+1 space. The reason is that the angular momentum of the pair emitted by the mirror coincides with the angular momentum of the single particle emitted by the charge.

On the basis of the theory of nonlinear QED processes occurring in collisions of high-energy electrons and γ-quanta with a strong laser pulse [1], the feasibility of their experimental investigation is discussed. The use of existing ⋍100 GeV electron beam accelerators and terawatt lasers of ultrashort pulses enables one to attain optimal values for the parameters and to have fields ⋍Fo=m2c3/ħe act on the electron. The choice and organization of laser system, synchronization of accelerator and laser operation, distributions of created γ-quanta and e+e−-pairs in different variables and parameters, their dependence on polarization of laser target and incident particles, background problems, and other questions connected with carrying out the experiments are discussed.

The concept of Stokes line width is introduced for the asymptotic expansions of functions near an essential singularity. Explicit expressions are found for functions (switching functions) that “switch on” the exponentially small terms for the Dawson integral, Airy function, and the gamma function. A different, more natural representation of a function, not associated with expansion in an asymptotic series, in the form of dominant and recessive terms is obtained by a special division of the contour integral which represents the function into contributions of higher and lower saddle points. This division leads to a narrower, natural Stokes line width and a switching function of an argument that depends on the topology of the lines of steepest descent from the saddle point.

The action changes (and thus the vacuum conservation amplitudes) in the proper-time representation are found for an accelerated mirror interacting with scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to within the multiplier e^2 with the action changes of electric and scalar charges accelerated in 3+1 space. This coincidence is attributed to the fact that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0 as do the photons and scalar quanta emitted by charges. It is shown that the propagation of virtual pairs in 1+1 space can be described by the causal Green's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This is because the pairs can have any positive mass and their propagation function is represented by an integral of the causal propagation function of a massive particle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In this integral the lower limit \mu is chosen small, but nonzero, to eliminate the infrared divergence. It is shown that the real and imaginary parts of the action change are related by dispersion relations, in which a mass parameter serves as the dispersion variable. They are a consequence of the same relations for \Delta_f(z,\mu). Therefore, the appearance of the real part of the action change is a direct consequence of the causality, according to which real part of \Delta_f(z,\mu) is nonzero only for timelike and zero intervals., Comment: 23 pages, Latex, revtex

This paper discusses the symmetry of the wave field that lies to the right and left of a two-sided accelerated mirror in 111 space and satisfies a single condition on it. The symmetry is accumulated in the Bogolyubov matrix coefficients a and b that connect the two complete sets of solutions of the wave equations. The amplitudes of the quantum processes in the right and left half-spaces are expressed in terms of a and b and are related to each other by transformation ~12!. Coefficient bv8v * plays the role of the source amplitude of a pair of particles that are directed to opposite sides with frequencies v and v8 but that are in either the left or the right half-space as a consequence of the reflection of one of them. Such an interpretation makes bv8v * observable and explains the fact, given by Eq. ~1! and found earlier by Nikishov and Ritus @JETP 81, 615 ~1995!# and by Ritus @JETP 83, 282 ~1996!#, that the emission spectra of a mirror in 111 space coincide with those of charges in 311 space by the fact that the moment of the pair emitted by the mirror coincide with the moment of the single particle emitted by the charge.