Self-Localized Quasi-Particle Excitation in Quantum Electrodynamics and Its Physical Interpretation

The self-localized quasi-particle excitation of the electron-positron field (EPF) is found for the first time in the framework of a standard form of the quantum electrodynamics. This state is interpreted as the ''physical'' electron (positron) and it allows one to solve the following problems: i) to express the ''primary'' charge e0 and the mass m0 of the ''bare'' electron in terms of the observed values of e and m of the ''physical'' electron without any infinite parameters and by essentially nonperturbative way; ii) to consider μ-meson as another self-localized EPF state and to estimate the ratio mμ/m; iii) to prove that the self-localized state is Lorentz-invariant and its energy spectrum corresponds to the relativistic free particle with the observed mass m; iv) to show that the expansion in a power of the observed charge e << 1 corresponds to the strong coupling expansion in a power of the ''primary'' charge e₀⁻¹ ~ e when the interaction between the ''physical'' electron and the transverse electromagnetic field is considered by means of the perturbation theory and all terms of this series are free from the ultraviolet divergence

Parametric beam instability in a crystal

Analysis of the optimal conditions for realization of X-ray free electron laser is considered for the case when an electron beam radiates in a crystal. It is shown that the use of the parametric X-ray radiation under the condition of multi-wave diffraction allows essential decreasing of the value of threshold beam density for the coherent generation. Estimation for the critical current density for the coherent X-ray generation in some crystals is also obtained.Анализ оптимальных условий для реализации рентгеновского лазера на свободных электронах проведен в случае, когда электроны излучают в кристалле. Показано, что использование параметрического рентгеновского излучения в условиях многоволновой дифракции позволяет существенно уменьшить величину пороговой плотности пучка для получения когерентного излучения. Получена также оценка для критической плотности для когерентной генерации рентгеновского излучения в некоторых кристаллахАналіз оптимальних умов для реалізації рентгенівського лазера на вільних електронах проведений у випадку, коли електрони випромінюють у кристалі. Показано, що використання параметричного рентгенівського випромінювання в умовах багатохвильової дифракції дозволяє істотно зменшити величину порогової густини пучка для одержання когерентного випромінювання. Отримана також оцінка критичної густини для когерентної генерації рентгенівського випромінювання в деяких кристалах

Angular momentum of the physical electron

The angular momentum of the physical electron, modelled as a Dirac fermion coupled to the electromagnetic field, is found to be hbar/2, the same as that of a bare Dirac fermion and independent of the size of the electric charge.Comment: revision, 3 pages pd

Self-Similar Factor Approximants

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are named the self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of the self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions which include a variety of transcendental functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties.Comment: 22 pages + 11 ps figure

Parametric X-rays from ultrarelativistic electrons in a crystal : theory and possibilities of practical utilization

The detailed theory of parametric X-rays from charged particles in a crystal is considered. It is shown that this radiation is due to the diffraction of the particle's electromagnetic field. Some features of the parametric X-rays allow us to separate this radiation from other radiation types. Methods of the experimental investigation and uses of parametric X-rays are discussed.Dans cet article on présente la théorie détaillée de l'émission de rayons X lors du passage de particules chargées dans les cristaux. On montre que cette émission provient de la diffraction du champ électromagnétique propre de la particule et possède des particularités spécifiques qui permettent de la distinguer des autres mécanismes d'émission. Les méthodes expérimentales utilisées dans l'étude de l'émission paramétrique des rayons X sont discutées également

Theoretical investigation of the parametric X-ray features

The numerical calculation of the parametric X-ray spectral and angular distributions for different crystals is performed. Their dependence on the particle energy is discussed.Dans cet article on présente les calculs numériques de la distribution spectrale et angulaire des rayons X paramétriques pour différents cristaux. On analyse leurs variations en fonction de l'énergie des particules