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.

     

Relativistic Compton scattering from a relativistic maxwellian distribution of electrons

Using an earlier developed relativistic differential cross section formula for Compton scattering of photons from a given momentum distribution of electrons, an expression for the differential cross section is derived for the case of a relativistic Boltzmann distribution.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Statistical mechanics of relativistic plasmas

Based on the Klimontovich method of construction of a relativistic statistical mechanics the binary correlation function of a relativistic plasma is considered. Up to the order e⁴ for spatially homogeneous systems the relativistic binary correlation function can be expressed by the relativistic dielectric tensor, where higher-order correlation functions are neglected.In the case of thermodynamic equilibrium the relativistic dielectric tensor is calculated. The corresponding binary correlation function is determined up to the first relativistic order. The result is compared with those of Trubnikov/Kosachev (1968) and Krizan (1969).     

Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction

Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.     

Operators in a relativistic fock space for fermions

We extend the definition of creation and annihilation operators for a particle in an arbitrary state in Fock space to the relativistic case. We pay special attention to the metric in this space and to the phase convention that leads to anticommutation relations for these operators. The same conventions also apply in the case of several types of fermions.This work was supported in part by Drexel University     

One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

We study a simple microscopic model for the one-dimensional stochastic motion of a (non-)relativistic Brownian particle, embedded into a heat bath consisting of (non-)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic conservation laws for the microscopic collision processes, provided one additionally assumes probabilistic independence of the initial momenta. It is shown that, in the non-relativistic case, the integral criteria do correctly identify the Maxwellian momentum distributions as stationary (invariant) solutions. Subsequently, we apply the same criteria to the relativistic case. Surprisingly, we find here that the stationary momentum distributions differ slightly from the standard Jüttner distribution by an additional prefactor proportional to the inverse relativistic kinetic energy.     

Dielectric response of a relativistic degenerate electron plasma in a strong magnetic field

The longitudinal dielectric response of a relativistic ultra-degenerate electron plasma in a strong magnetic field is obtained via a relativistic generalization of the Hartree self-consistent field method. Dispersion relations and damping conditions for plasma oscillations both parallel and perpendicular to the magnetic field are obtained. We also give detailed results for the zero-field case. Applications to white dwarf stars and pulsars are given.     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.     

Comparison of the Newtonian and relativistic predicted trajectories for a low-speed periodically delta-kicked system

The dynamics of a periodically delta-kicked Hamiltonian system moving at low speed (i.e., at speed much less than the speed of light) is studied numerically. In particular, the trajectory of the system predicted by Newtonian mechanics is compared with the trajectory predicted by special relativistic mechanics for the same parameters and initial conditions. We find that the Newtonian trajectory, although close to the relativistic trajectory for some time, eventually disagrees completely with the relativistic trajectory, regardless of the nature (chaotic, nonchaotic) of each trajectory. However, the agreement breaks down very fast if either the Newtonian or relativistic trajectory is chaotic, but very much slower if both the Newtonian and relativistic trajectories are nonchaotic. In the former chaotic case, the difference between the Newtonian and relativistic values for both position and momentum grows, on average, exponentially. In the latter nonchaotic case, the difference grows much slower, for example, linearly on average.     

Analytically solving the relativistic Dirac-Coulomb equation for atoms and molecules

A method of solving the Schr?dinger equation in an analytically expanded form reported previously is extended to the relativistic case and a general method of exactly solving the Dirac-Coulomb equation has been proposed for atoms and molecules. Some problems characteristic of the relativistic case are discussed. Test applications to the hydrogen-like, helium-like atoms are satisfactory, implying a high potentiality of the proposed method also for the relativistic case.     

Operators in a relativistic fock space for fermions

We extend the definition of creation and annihilation operators for a particle in an arbitrary state in Fock space to the relativistic case. We pay special attention to the metric in this space and to the phase convention that leads to anticommutation relations for these operators. The same conventions also apply in the case of several types of fermions.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

On relativistic thermodynamics

The thermodynamics of moving bodies is developed from first principles. To do this, it is necessary to augment the laws of thermodynamics with a new principle, which asserts the impossibility of thermal equilibrium between bodies in relative motion. Clausius' theorem is generalized to heat flow between moving systems, and leads naturally to the identification of heat and temperature as Lorentz scalars. The formulation of relativistic statistical mechanics is carried out and the correspondence with classical quantities is made. The quantum distribution laws are generalized to the relativistic case, and are found to differ from their accepted relativistic form.     

拉曼型自由电子激光器中相对论电子运动稳定性的比较研究

拉曼型自由电子激光器作为一种兆瓦级高功率毫米波、太赫兹波辐射源, 其电子的运动稳定性对整体器件的性能至关重要.本文采用科尔莫戈罗夫熵方法, 以典型的麻省理工学院公布的实验数据为例, 比较研究拉曼型正向导引磁场和反向导引磁场两类自由电子激光器中相对论电子的运动稳定性. 结果表明:摇摆器绝热压缩磁场对电子运动的稳定性无实质性影响, 但对电子运动影响大; 电子束自身场在拉曼型正向导引磁场自由电子激光器中使电子运动稳定性变差, 而在拉曼型反向导引磁场自由电子激光器中则可改善电子运动稳定性. 关键词： 拉曼型自由电子激光器 相对论电子运动稳定性 科尔莫戈罗夫熵 电子束自身场     

Laser-driven recollisions generalized to relativistic energies

The important process of laser-driven recollisions, where electrons are accelerated by strong laser fields and return to their parent ions, breaks down if the laser intensities imply relativistic electron dynamics. In this case, the Lorentz force drags the electrons away in the laser propagation direction, which inhibits recollisions. Here, a variety of schemes are discussed and compared which generalize the concept of recollisions to the relativistic regime. Additional static electric fields, antisymmetric initial states, and tailored laser pulses are suitable for weakly to moderately relativistic energies, whereas standing waves, preaccelerated ions, positronium, and counterpropagating consecutive pulses allow for recollisions up to the highly relativistic regime.     

Low-frequency longitudinal oscillations in a plasma with a relativistic electron component

Ion-sound oscillations in a three-dimensional plasma with relativistic electron component are studied. It is established that in this case ion-sound oscillations can exist only at electron and ion temperatures much less than the rest mass of the ions. In particular, it is shown that for an electron-positron plasma at relativistic temperatures ion-sound is impossible. The problem of ion-sound excitation by a charged particle beam is considered. Corresponding increments in beam instability are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 24–27, December, 1985.     

Non-linear relativistic diffusions

We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles.     

Energy spectrum of a relativistic two-dimensional hydrogen-like atom in a constant magnetic field of arbitrary strength

We compute, via a variational mixed-base method, the energy spectrum of a two-dimensional relativistic atom in the presence of a constant magnetic field of arbitrary strength. The results are compared to those obtained in the non-relativistic and spinless case. We find that the relativistic spectrum does not present s states.     

Relativistic Boltzmann theory for a plasma: VI. The relativistic Landau equation

The relativistic Landau equation is obtained as the Fokker-Planck approximation to the relativistic Boltzmann equation. It is shown that, as far as the transport coefficients are concerned, both equations yield identical results in the dominant term approximation. Special attention is given to Møller-, Bhabha- and Mott-scattering processes. In the case of relativistic electron-electron collisions a detailed determination of the Coulomb logarithm is given.