Structure of quantum-mechanical relativistic two-body interactions for spinning particles

Relativistic constraint mechanics yields consistent systems of coupled Dirac equations for pairs of spinning particles. We explicitly connect these equations to the Bethe-Salpeter equation of quantum field theory and to the interactions of classical Fokker-Tetrode dynamics (and hence to classical relativistic field theory) to obtain versions of these equations governed by systems of (possibly noncoulombic) relativistic potentials whose detailed structures contain important relativistic effects like correct Darwin interactions. We recast the defining pair of Dirac equations in a number of equivalent but important forms—“external potential,” Sazdjian, hyperbolic, and Breit— and examine their interconnection. Since the potentials in these equations are no more singular than — 1/4r² we are able to solve appropriate versions of them nonperturbatively for the qˉq system to obtain a very good fit to the entire meson spectrum and for the e ⁺ e ⁻ system to calculate the positronium spectrum of QED correct through order α ⁴ .     

A relativistic correction to semiclassical charmonium

It is shown that the relativistic linear potentials, introduced by the author within the particle à la Wheeler-Feynman direct-interaction (AAD) theory, applied to the semiclassically quantized charmonium, yield energy spectrum comparable to that of some known models. Using the expansion of the relativistic linear AAD potentials in powers ofc ^–1, the charmonium spectrum, given as a rule by Bohr-Sommerfeld quantization of circular orbits, is extended up to the second order of relativistic corrections.     

Specificity of multiwave interaction of an electronic beam and electromagnetic field in a relativistic diffractive generator

The mechanisms of self-consistent interaction of tubular relativistic electronic beams with the fields of super-dimensional periodic structure of a relativistic diffractive generator have been studied in the area of 2π-type oscillations of fundamental mode. Numerical analysis was carried out with the use of the matrix multimode method in its nonstationary variation. The electromagnetic field profiles, their mode structure, and their radiation spectrum have been studied. The conditions for generating frequency stabilization concerned with the longitudinal resonance of the surface spatial harmonics and volume resonance at the cutoff frequency of the E _0n mode of cylindrical waveguide have been revealed.     

Quantum carpets of a slightly relativistic particle

We analyze the structures emerging in the spacetime representation of the probability density woven by a slightly relativistic particle caught in a one‐dimensional box. In particular, we evaluate the relativistic effects on the revival time and the specific changes produced in the intermode traces, which quantum carpets consist of. Moreover, we present a detailed mathematical analysis of such quantum carpets pursuing the approach of a kernel. Here we represent the probability distribution as a superposition of interfering Airy function‐type structures along straight world lines. We also show that this phenomenon can be enhanced by many orders of magnitude in semiconductors with narrow band‐gap (e.g. as in InSb) and small effective mass of the electron, whereby due to the strong nonparabolicity of the semiconductor conduction band, the electron energy vs momentum dispersion relation behaves in a pseudo‐relativistic way.     

Eigenvalue Spectrum of a Dirac Particle in Static and Spherical Complex Potential

It has been observed that a quantum theory need not be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac-charged particle in complex statically and spherically symmetric potentials. Complex Dirac–Eckart, complex Dirac–Rosen–Morse II, complex Dirac–Scarf and complex Dirac–Poschl–Teller potential are investigated.     

On Relativistic Mass Spectra of a Two-Particle System

Abstract

A relativistic two-particle system with time-asymmetric scalar and vector interactions in the two-dimensional space-time is considered within the frame of the front form of dynamics using the dynamical symmetry approach. The mass-shell equation may be represented in terms of the nonlinear canonical realization of the Lie algebra of the group SO(2, 1). This allows us to quantize the system and to obtain a closed form for the mass spectrum.     

Spectrum and mechanism of the acceleration of protons in a solar flare

Investigations based on neutron monitor data show that two components of relativistic cosmic rays are generated by a solar flare. The so-called prompt component comes from a flare with flight times and is characterized by an exponential spectrum with a parameter of E ₀ ≈ 0.5 Gev. Numerical simulation of the conditions in the flare current sheet of the Bastille flare demonstrated that such a spectrum is formed at a magnetic reconnection velocity of ∼10⁷ cm s⁻¹. The delayed component has a power law spectrum and is apparently formed during the diffusion of protons in the plasma of the interplanetary magnetic field.     

Perturbative and non-perturbative Kolmogorov turbulence in a gluon plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles n(p)∼p ^−ν with exponent ν≃2, which is larger than expected from relativistic 2↔2 scatterings. Using the approach of Zakharov, L’vov and Falkovich, we analyze possible Kolmogorov coefficients for relativistic (m≥4)-particle processes, which give at most ν=5/3 perturbatively for an energy cascade. We discuss non-perturbative scenarios which lead to larger values. As an extreme limit we find the result ν=5 generically in an inherently non-perturbative effective field theory situation, which coincides with results obtained by Berges et al. in large-N scalar field theory. If we instead assume that scaling behavior is determined by Schwinger–Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario, which would single out ν=2.     

The transparency of nuclei to nucleons and pions in a relativistic Glauber approximation

We present a selection of results obtained within the context of a relativistic eikonal model. First, results of relativistic Glauber calculations for the nuclear transparency extracted from photon-induced pion production are presented. Second, computed differential cross-sections for the ¹² C(p, 2p) are compared to data.     

周期量级激光脉冲的Thomson散射

用经典辐射理论对线偏振周期量级激光脉冲的线性Thomson散射进行分析，从理论上得到它可产生亚阿秒脉冲的结论. 计算显示，在电子相对论因子为50、激光脉冲中心波长为1μm、归一化光场强度为0.01的情况下，用包含1.5个光周期的激光脉冲，可获得0.2as(半高全宽)的散射脉冲输出. 还对光场载波包络初相φ_ce和电子进入光场的初相φ_in对散射脉冲的影响作了分析讨论，结果表明，在适当的φ_ce和φ_in条件下，能实现单个阿秒脉冲输出，并可对脉冲宽度和频率进行调谐. 关键词： 线性Thomson散射 周期量级激光脉冲 载波包络初相 阿秒脉冲     

Stability of the Relativistic Maxwellian in a Collisional Plasma

The relativistic Landau-Maxwell system is the most fundamental and complete model for describing the dynamics of a dilute collisional plasma in which particles interact through Coulombic collisions and through their self-consistent electromagnetic field. We construct the first global in time classical solutions. Our solutions are constructed in a periodic box and near the relativistic Maxwellian, the Jüttner solution.Acknowledgements The research is supported in part by NSF grants.     

The light-baryon spectrum in a relativistic quark model with instanton-induced quark forces

This is the second of a series of three papers treating light-baryon resonances up to 3 GeV within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces. In this paper we apply the covariant Salpeter framework (which we developed in the first paper, U. L?ring, K. Kretzschmar, B.Ch. Metsch, H.R. Petry, Eur. Phys. J. A 10, 309 (2001)) to specific quark model calculations. Quark confinement is realized by a linearly rising three-body string potential with appropriate spinorial structures in Dirac space. To describe the hyperfine structure of the baryon spectrum we adopt 't Hooft's residual interaction based on QCD-instanton effects and demonstrate that the alternative one-gluon exchange is disfavored on phenomenological grounds. Our fully relativistic framework allows to investigate the effects of the full Dirac structures of residual and confinement forces on the structure of the mass spectrum. In the present paper we present a detailed analysis of the complete non-strange-baryon spectrum and show that several prominent features of the nucleon spectrum such as, e.g., the Roper resonance and approximate “parity doublets” can be uniformly explained due to a specific interplay of relativistic effects, the confinement potential and 't Hooft's force. The results for the spectrum of strange baryons will be discussed in a subsequent paper, see U. L?ring, B.Ch. Metsch, H.R. Petry, this issue, p. 447. Received: 27 March 2001 / Accepted: 17 April 2001     

On a kinetic approach to the modulational stability of envelope solitons in a relativistic plasma in an external electric field

Summary The formation of envelope solitons is discussed in a relativistic plasma under the influence of a fluctuating electric field. We use the kinetic-theory approach for our analysis. Due to the larger inertia, only the electrons are considered to be relativistic and the ions to be nonrelativistic. A NLS equation is derived describing the motion of the solitary wave. This NLS equation actually comes from an approximation of a pair of equations which can be considered to be a relativistic generalisation of the Zakharov equation. We next discuss the exact form of the envelope solitary-wave solution of the NLS equation and the modulation stability of such a wave. When the density, momentum and energy of such wave packets are fixeda priori, conditions are derived for the parameters of the problem from such stability consideration.     

Quarkonia in a Gluonic Background Field

We give a systematic treatment of relativistic corrections to a Coulomb system of heavy quarks in a colour background field with a finite correlation time. The relativistic corrections turn out to be significant. Comparison with experiment favors a correlation time of 0.2−0.5 fm. We predict the ³S₁ − ¹S₀ and ³P₁ − ¹P₁ hyperfine splitting.     

Aharonov-Bohm and non-inertial effects on a Klein-Gordon oscillator with potential in the cosmic string space-time with a spacelike dislocation

In this paper, we investigate the analogue effect to the Aharonov-Bohm effect for bound states in a relativistic quantum system described by the Klein-Gordon oscillator in the cosmic string space-time with a spacelike dislocation. We assume the topological defects have an internal magnetic flux and then analyze the effect on the relativistic energy eigenvalue subject to a Cornell-type potential and subsequently with a Coulomb-type potential. We show the presence of various potential parameters, the torsion parameter as well the cosmic string modify the energy spectrum.     

Enhancement of high PT hadrons due to collapsing Z(3) walls in heavy-ion collisions

We discuss enhancement of multiplicities of hadrons at high transverse momentum due to multiple reflections of quarks from collapsing Z(3) interfaces in the QGP produced in relativistic heavy-ion collisions. By modeling the dependence of effective mass of the quarks on the Polyakov loop order parameter, we evaluate the reflection coefficient of quarks from collapsing Z(3) interfaces. We use the effective potential proposed by Pisarski for the Polyakov loop to determine the profile of the Z(3) interfaces and calculate the reflection probability for quarks. We discuss the formation of a network of these Z(3) walls in relativistic heavy-ion collisions, in the QGP phase. We do a numerical simulation to calculate the modifications in the thermal transverse momentum spectra of the quarks/anti-quarks that results from a collapsing wall. We then use the recombination model to calculate the transverse momentum spectrum of final hadrons. Our results show enhancement of high P _T hadrons, with the enhancement being stronger for heavier quarks. Further, we find that due to larger reflection coefficient for heavier quarks, the density of strange and charm quarks/anti-quarks increases inside the collapsing walls. This implies enhancement in the multiplicities of multi-strange and multi-charmed hadrons.     

Ionization of ytterbium atoms from an excited state

The cross sections of the photoionization and the electron impact-induced ionization of Yb atoms from the excited 6s6p(³ P ₁) state are numerically calculated. Matrix elements are computed in multielectron relativistic and nonrelativistic approximations with allowance for the superposition of configurations and a relaxation effect. The radial part of the electron wavefunction in a continuous spectrum is calculated using the solutions to one-configuration Hartree-Fock and Dirac-Fock equations. The cross sections calculated by a relativistic method are compared to those for a nonrelativistic approximation. The ratios of the radiation reduced matrix elements and the phase shifts of the wavefunctions of a continuous spectrum calculated for the 6p ɛs and 6p → ɛd transitions are compared to the values obtained by approximating the experimental dependences of the angular distribution of photoelectrons for the photoionization by ultraviolet radiation from an oriented excited state.     

The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

Nonextensive perfect hydrodynamics — a model of dissipative relativistic hydrodynamics?

We demonstrate that nonextensive perfect relativistic hydrodynamics (q-hydrodynamics) can serve as a model of the usual relativistic dissipative hydrodynamics (d-hydrodynamics) therefore facilitating considerably its applications. As an illustration, we show how using q-hydrodynamics one gets the q-dependent expressions for the dissipative entropy current and the corresponding ratios of the bulk and shear viscosities to entropy density, ζ/s and η/srespectively.      

Calculation of the Interelectronic-Interaction Correction to Radiative Recombination of an Electron with a Heavy He-Like Ion

We present a calculation of the interelectronic-interaction correction of first order in 1/Z for radiative recombination of an electron with a heavy He-like ion in the ground state. A rigorous relativistic treatment is demonstrated which includes the Coulomb, Breit and retarded parts of the interelectronic interaction. A complete relativistic evaluation is compared with two frequently used approximations. This revised version was published online in July 2006 with corrections to the Cover Date.