The relativistic theory of fluctuation electromagnetic interactions of moving neutral particles with a flat surface

The problem concerning the fluctuation electromagnetic interaction of a neutral particle moving parallel to the boundary of a semi-infinite homogeneous isotropic medium characterized by a permittivity and permeability dependent on the frequency is considered in terms of the fluctuation electrodynamic theory within the relativistic formalism. It is assumed that, in the general case, the particle and the medium have different temperatures. Within the proposed approach, general expressions are derived both for conservative (normal to the boundary of the medium) and nonconservative (tangential) forces of the interaction between the particle and the medium and for the thermal heating (cooling) rate of the particle. In the nonrelativistic limit (c → ∞), the derived relationships coincide with nonrelativistic analogs available in the literature. It is demonstrated that the tangential force acting on the particle can be either accelerating or decelerating. There can occur a situation when the hot moving particle will be heated and the cold medium will be cooled. The interaction of the high-conductivity medium with a high-conductivity particle is analyzed numerically. The asymptotics of the radiative contributions to the heat flux and the tangential force is investigated. It is shown that the inclusion of the relativistic effects leads to a substantial increase in the tangential force and the heat flux at distances greater than 1 μm (as compared to the nonrelativistic case); however, the corresponding dependences exhibit a monotonic decreasing behavior over the entire range of studied distances (from zero to several hundreds of microns). __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 10, 2003, pp. 1729–1741. Original Russian Text Copyright ? 2003 by Dedkov, Kyasov.     

Nonlinear Schrödinger mechanics and the law of gravity

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.     

The nucleon and Δ-resonance masses in relativistic chiral effective-field theory

We study the chiral behavior of the nucleon and Δ-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the πN and πΔ one-loop contributions to the mass and field-normalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these manifestly relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the πN-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and Δ masses, while inclusion of the πΔ loops tends to spoil this agreement.     

Relativistic effects and spin observables in deuteron electrodisintegration

The influence of relativistic effects in deuteron electrodisintegration, in particular their manifestation in spin observables, is discussed. We have used a simple phenomenological approach by adding the lowest-order relativistic corrections to the nonrelativistic one-body current and including the kinematic wave-function boost. Furthermore, final-state interaction, meson-exchange currents and isobar configurations are included in order to study kinematic regions off the quasi-free case. Sizeable relativistic effects in many observables are found even at low energies.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

On the equivalence of standard and covariant perturbation series in non-polynomial pion lagrangian field theory

Recently a covariant perturbation approach has been developed to give a perturbation expansion of the chiral-invariant pion theory which does not depend on the choice of pion coordinates. We prove that this covariant approach is equivalent to standard perturbation theory. Our method explicitly shows how one can express covariant graphs by contributions of non-covariant ones and vice versa. We neglect contributions vanishing on the mass shell.     

Form factor for a two-particle system within a relativistic quasipotential approach: Case of arbitrary masses and of a vector current

A new relativistic form factor for a bound two-particle system was obtained for the case of a vector current. The present consideration was performed within the relativistic quasipotential approach based on the covariant Hamiltonian formulation of quantum field theory by going over to the three-dimensional relativistic configuration representation for the case of interaction between two relativistic spinless particles of arbitrary mass.

     

Influence of the momentum dependence of nuclear interactions on heavy-ion potentials

We analyse the momentum dependence of nucleus-nucleus interactions and compare the predictions for this dependence obtained from nonrelativistic Skyrme forces, from relativistic mean field models and from phenomenological ansätze used in data analyses. In all cases the momentum dependence is determined by the effective mass alone and is therefore the same for relativistic and nonrelativistic models.     

Electromagnetic and Axial Form Factors of Octet and Decuplet Baryons

We report from a study of the elastic electromagnetic and axial form factors of all lowest baryon states with flavors up, down, and strange along relativistic constituent-quark models. We consider the baryons as relativistic bound states of three constituent quarks and solve the eigenvalue problem of the invariant mass operator. The corresponding eigenstates are employed to calculate manifestly covariant form factors within the point form of Poincaré-invariant quantum mechanics. The electromagnetic and axial current operators are constructed along the spectator model in point-form relativistic dynamics. We have thus obtained covariant predictions for the electroweak form factors, for momentum transfers up to Q ² ~ 4 GeV², as well as the electric radii, magnetic moments, and axial charges. The theoretical results in general agree very well with existing phenomenological data. In cases, where no experimental information is yet available, the results are well compatible with data from lattice quantum chromodynamics.     

The Covariant Stark Effect

This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schrödinger equation with invariant evolution parameter, and represent mass eigenstates whose eigenvalues correspond to the well-known energy spectrum of the nonrelativistic theory. In analogy to the nonrelativistic case, the off-diagonal perturbation leads to a lifting of the degeneracy in the mass spectrum. In the covariant case, not only do the spectral lines split, but they acquire an imaginary part which is linear in the applied electric field, thus revealing induced bound state decay in first order perturbation theory. This imaginary part results from the coupling of the external field to the non-compact boost generator. In order to recover the conventional first order Stark splitting, we must include a scalar potential term. This term may be understood as a fifth gauge potential, which compensates for dependence of gauge transformations on the invariant evolution parameter.     

Gibbs ensembles in relativistic classical and quantum mechanics

Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.     

Form factor of a relativistic two-particle system within the relativistic quasipotential approach: Case of an arbitrary masses and a scalar current

A new relativistic form factor for a bound two-particle system was obtained for the case of a scalar current. The respective analysis was performed within the relativistic quasipotential approach based on a covariant Hamiltonian formulation of quantum field theory by going over to a three-dimensional relativistic configuration representation for the case of the interaction of two relativistic spinless particles that have arbitrary masses.     

Selection rules for dipole radiation from a relativistic bound state

Recently, in the framework of a relativistic quantum theory with invariant evolution parameter, solutions have been found for the two-body bound state, whose mass spectrum agrees with the nonrelativistic Schrödinger energy spectrum. In this paper, we study the radiative transitions of these states in the dipole approximation and find that the selection rules are identical with those of the usual nonrelativistic theory, expressed in a manifestly covariant form. In addition to the transverse and longitudinal polarizations of the nonrelativistic theory, we find a scalar transition, induced by the relative time coordinate, which is of the same type as the longitudinal transition, expressing the Lorentz covariance of the theory.     

Generalized boltzmann equation in a manifestly covariant relativistic statistical mechanics

We consider the relativistic statistical mechanics of an ensemble of N events with motion in space-time parametrized by an invariant historical time . We generalize the approach of Yang and Yao, based on the Wigner distribution functions and the Bogoliubov hypotheses to find approximate dynamical equations for the kinetic state of any nonequilibrium system, to the relativistic case, and obtain a manifestly covariant Boltzmann- type equation which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU) equation for indistinguishable particles. This equation is then used to prove the H-theorem for evolution in . In the equilibrium limit, the covariant forms of the standard statistical mechanical distributions are obtained. We introduce two-body interactions by means of the direct action potential V(q), where q is an invariant distance in the Minkowski space-time. The two- body correlations are taken to have the support in a relative O(2, 1)-invariant subregion of the full spacelike region. The expressions for the energy density and pressure are obtained and shown to have the same forms (in terms of an invariant distance parameter) as those of the nonrelativistic theory and to provide the correct nonrelativistic limit.     

Gauge-Independence and the Two-Body Problem in QED

I describe a gauge-independent approach to the relativistic two-body bound state and scattering problems in quantum field theory. The basic tool is an ordinary three-dimensional equation involving a potential operator V which gets contributions from both irreducible and reducible diagrams. In QED the resultant V is independent of the choice of covariant gauge used for the photon propagator, unlike the kernel in the Bethe–Salpeter equation. As an illustration, a problem concerning spin-independent level shifts in two-body bound states is analyzed.     

Relativistic Hamiltonian dynamics

A manifestly covariant relativistic hamiltonian dynamics is presented for a closed system of N particles in mutual interaction. The “no-interaction theorem” is overcome by use of relativistic center-of-mass variables instead of individual particle variables. The theory permits canonical quantization.