Anomalous behavior of a scalar particle in a globally regular space-time of a Schwarzschild black hole

The curved space-time Klein-Gordon equation in a globally regular space-time of a Schwarzschild black hole is solved, and its exact solution is obtained. The wave functions of a scalar particle inside the black hole are discussed by means of numerical analysis. The anomalous behaviors of the scalar particle in the central region of the black hole and in the interior neighborhood of the Schwarzschild event horizon are studied with the help of approximate solutions, which are compared with the exact one in these two regions.     

Green function of an electron and a scalar particle in external electromagnetic fields of special form

Using the results of [1], the relation between Green functions of an electron and a scalar particle in external electromagnetic fields of the following structure is investigated:H=[n×E]+H _an where n is a constant unit vector. The causative Green functions of an electron and a scalar particle are found in a field which is a combination of a longitudinal electric wave and a plane wave propagating in a single direction (alongn).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–63, July, 1982.     

Light-front wave function of a relativistic composite system in an explicitly solvable model

The light-front wave function of a composite system, consisting of two scalar particles, interacting by means of massless scalar particle exchange (the Wick-Cutkosky model) is calculated. The wave function obtained concides with that in the Coulomb potential at non-relativistic relative particle momentum, but in the relativistic region depends not only on the relative momentum, but, due to retardation of interaction, also on an additional variable having the form of a unit vector. It is emphasized that for the correct parametrization of the nuclear and hadronic wave functions at relativistic relative momenta, it is necessary to take into account their dependence on this additional variable.     

Scattering and Bound States of the Dirac Particle for q-Parameter Hyperbolic Pöschl-Teller Potential

The one-dimensional Dirac particle for equal scalar and vector asymmetric q-parameter hyperbolic PöschlTeller potential (qHPT) is solved in terms of hypergeometric functions. The scattering and bound states are obtained by using the properties of the equation of continuity of the wave functions. We calculat in details the transmission and reflection coefficients.     

A model for symmetries in nonlinear transport

A model for a Rayleigh particle suspended in a rarefied gas in internal equilibrium is constructed. It is shown that the macroscopic evolution of this system can be described by using nonlinear unilateral transfer flows which are gradients of particular scalar functions. These functions are constructed according to a general theory of nonlinear irreversible processes proposed previously by van Kampen.     

Spinless relativistic particle in energy-dependent potential and normalization of the wave function

The problem of normalization related to a Klein-Gordon particle subjected to vector plus scalar energy-dependent potentials is clarified in the context of the path integral approach. In addition the correction relating to the normalizing constant of wave functions is exactly determined. As examples, the energy dependent linear and Coulomb potentials are considered. The wave functions obtained via spectral decomposition, were found exactly normalized.     

Causal green function in relativistic quantum mechanics

The causal Green function or Feynman propagator for the free-field Klein-Gordon equation and related singular functions, defined as distributions, are related to the causal time-boundary data. Probability densities and amplitudes are defined in terms of the solutions of the Klein-Gordon equation for a complex scalar field interacting with an electromagnetic field. The convergence of the perturbation expansion of the solution of the Klein-Gordon equation for a charged scalar particle in an external field is shown for well-behaved electromagnetic potentials. Other relativistic wave equations are discussed briefly.     

On quantization of polynomial momentum observables

The paper is devoted to quantization of polynomial momentum observables in the cotangent bundle of a smooth manifold. A quantization procedure is proposed allowing to quantize a wide class of functions which are polynomials of any order in the momenta. As an application of the proposed approach, quantum mechanics of a scalar particle in curved space-time is studied.     

Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to a polarized laser beam: spatially varying reflection matrix

Three-dimensional vector radiative transfer in a semi-infinite, Rayleigh scattering medium exposed to a polarized, Gaussian laser beam directed perpendicular to the surface is studied. The focus of this investigation is the 4×4, spatially varying reflection matrix that can be used to determine the normally backscattered radiation when the polarization of the incident radiation is specified. An inverse integral transform is used to construct the spatially varying reflection matrix from the generalized reflection matrix found in a previous study. The elements of this matrix depend on location specified by optical radius and azimuthal angle. The azimuthal variation is found by performing part of the inverse transform analytically, while the radial variation is described by five functions that are calculated numerically via an inverse Hankel transform. Benchmark numerical results for these five functions are presented, and the effects of beam radius and particle concentration are discussed. Expressions that describe the behavior of the reflection functions at small and large optical radii are developed, and comparisons are made to the one-dimensional and scalar situations. The scalar approximation fails to predict the three-dimensional effects produced by the polarized beam, and even when the incident radiation is unpolarized, the error in the scalar reflection function can be as high as 20%.     

Path integral for a neutral spinning particle in interaction with a rotating magnetic field and a scalar potential

In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding wave functions are also deduced.     

Scalar Statistics along Inertial Particle Trajectory in Isotropic Turbulence

The statistics of a passive scalar along inertial particle trajectory in homogeneous isotropic turbulence with a mean scalar gradient is investigated by using direct numerical simulation. We are interested in the influence of particle inertia on such statistics, which is crucial for further understanding and development of models in non-isothermal gas-particle flows. The results show that the scalar variance along particle trajectory decreases with the increasing particle inertia firstly; when the particle＇s Stokes number St is less than 1.0, it reaches the minimal value when St is around 1.0, then it increases if St increases further. However, the scalar dissipation rate along the particle trajectory shows completely contrasting behavior in comparison with the scalar variance. The mechanical-to-thermal time scale ratios averaged along particle, （r）p, are approximately two times smaller than that computed in the Eulerian frame r, and stay at nearly 1.77 with a weak dependence on particle inertia. In addition, the correlations between scalar dissipation and flow structure characteristics along particle trajectories, such as strain and vorticity, are also computed, and they reach their maximum and minimum, 0.31 and 0.25, respectively, when St is around 1.0.     

The Continual Approach in the Yang-Mills Theory in the External Non-Abelian Field

The theory of Yang-Mills field in interaction with matter fields is considered in the presence of external gauge field. A closed expression for the generating functional of the Green functions is obtained, and a detailed analysis of the Green functions of the scalar, spinor, ghost and Yang-Mills fields is performed. The path-integral solution for all these Green functions is obtained, which includes the functional averaging over the classical trajectories in the space of commuting and anticommuting variables, the latter being anociated with the particle spin and isospin. For illustration an arbitrary Abelian-like external field is considered, as well as non-Abelian-like constant external field.     

Particle number in kinetic theory

We provide a derivation for the particle number densities on phase space for scalar and fermionic fields in terms of Wigner functions. Our expressions satisfy the desired properties: for bosons the particle number is positive, for fermions it lies in the interval between zero and one, and both are consistent with thermal field theory. As applications we consider the Bunch-Davies vacuum and fermionic preheating after inflation.Received: 18 May 2004, Revised: 27 August 2004, Published online: 20 October 2004     

Inclusive and Deep-Inelastic Scattering from a Dressed Structureless Nucleon

Nonperturbative polaron variational methods are used to study inclusive scattering in the context of the scalar Wick-Cutkosky model. We derive the structure functions for a scalar point-like nucleon surrounded by a cloud of strongly interacting mesons from the Compton amplitude that is obtained in a recent variational calculation based on the particle (or worldline) representation. In zeroth variational order, a covariant exponentiated form is obtained, which is identical to the one suggested by Vineyard for scattering of slow neutrons from quantum liquids. In first order, the much richer dependence of the structure function on momentum and energy transfer, which emerges, is evaluated numerically. We study the -evolution and the perturbative as well as the scaling limit of our variational structure functions. Finally, the momentum sum rule is derived and evaluated in order to determine the momentum fraction carried by the neutral mesons inside the dressed nucleon. Received May 30, 1997; revised December 19, 1997; accepted for publication January 30, 1998     

Quantum Potential in Relativistic Dynamics

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential.     

惯性颗粒所见被动标量统计特性的DNS与模型研究

本文采用DNS方法,对惯性颗粒所见各向同性湍流中具有平均标量梯度的被动标量场统计特性进行了研究。结果表明：惯性对颗粒温度脉动强度,两相温度关联,自相关特性以及颗粒热流与两相交叉热流的统计特性具有明显的影响。在PDF方法的框架下,系统地推导了非等温气固两相流的PDF方程,且基于朗之万随机体系对方程进行了封闭,并利用前面的...     

Green functions of scalar particles in stochastic fields

A variational method of evaluating functional integrals is proposed. This method is used to investigate the asymptotic behavior of the scalar-particle Green functions in stochastic fields. The equations for the Green functions in Euclidean space in stochastic fields are written. The solutions of these equations are represented in the form of a functional integral and then they are averaged over Gaussian stochastic fields. The variational method formulated above is used to evaluate the asymptotic behavior of these Green functions. The following equations are considered in this paper: a stochastic contribution to the mass of a scalar particle, a gauge stochastic field, and a weak stochastic contribution to the flat metric of Euclidean space.     

Feynman diagrams to three loops in three-dimensional field theory

The two-point integrals contributing to the self-energy of a particle in a three-dimensional quantum field theory are calculated to two-loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to three-loop order. For almost every integral an expression in terms of elementary and dilogarithm functions is obtained. For two integrals, the master integral and the Mercedes integral, a one-dimensional integral representation is obtained with an integrand consisting only of elementary functions. The results are applied to a scalar λφ⁴ theory.     

惯性颗粒所见被动标量统计特性的直接数值模拟研究

本文采用直接数值模拟方法,对惯性颗粒所见均匀各向同性湍流中具有平均标量梯度的被动标量场统计特性进行了研究。模拟结果表明:与颗粒所见流体速度的自相关特性不同,颗粒所见标量的自相关特性随颗粒惯性的增加而单调减少;颗粒所见标量脉动能随颗粒惯性的增加先减少再增大,在St≈1.0的临界颗粒附近达到最小值,而颗粒所见标量耗散率随颗粒惯性的变化行为与颗粒所见标量脉动能的变化行为相反;数值模拟的结果进一步揭示,在St≈1.0时颗粒所见流体标量脉动能和耗散率的极值是因为St≈1.0的临界颗粒聚集于低涡量、高应变区域和标量场在高应变区域形成强耗散的片状结构所致。     

Topological Aharonov-Bohm Effect of Neutral Scalar Particle on Noncommutative Space

We study the interactions between a neutral scalar particle and electromagnetic fields on noncommutative space. Because of the noncommutativity of space, neutral particle can couple to electromagnetic fields at the tree level, and the interaction strength is represented by a new coupling constant. We find that on noncommtuative space the topological Aharonov-Bohm effect is nontrivial even for neutral scalar particle.