共查询到20条相似文献,搜索用时 15 毫秒
1.
S.I. Muslih 《Czechoslovak Journal of Physics》2002,52(8):919-925
The Hamilton-Jacobi method of quantizing singular systems is discussed. The equations of motion are obtained as total differential equations in many variables. It is shown that if the system is integrable, then one can obtain the canonical phase space coordinates and the set of the canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields. As an example we quantize the CP1 model using the canonical path integral quantization formalism to obtain the path integral as an integration over the canonical phase-space coordinates. 相似文献
2.
S.I. Muslih 《Czechoslovak Journal of Physics》2002,52(12):1303-1311
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for the relativistic particle in a plane wave lead us to obtain the canonical phase space coordinates without using any gauge fixing condition. As a result of the quantization, we get the Klein-Gordon theory for a particle in a plane wave. The path integral quantization for this system is obtained using the canonical path integral formulation method. 相似文献
3.
A complete angular momentum analysis of the integral equations of motion for four identical spinless particles is given. After separation of the variables associated with rotation, the equations of motion take the form of an infinite set of coupled integral equations in three continuous variables. In general, the four-particle kinematic factors in the integral kernels are expressed as bilinear combinations of factors of the three-particle kinematic factors type. For the case of a separable two-particle interaction the equations obtained are simplified so that they are reduced to coupled integral equations in two continuous variables. 相似文献
4.
This Letter is devoted to the integrability problem of planar nonlinear differential equations. We introduce a new method to detect local analytic integrability or to construct a singular series expansion of the first integral around a singular point for planar vector fields. The method allows to find new variables (essential variables) where the integrability problem is more feasible. The new method can be used in different context and is an alternative to all the methods developed up to now for any particular case. 相似文献
5.
S.I.Muslih 《理论物理通讯》2002,37(5):567-570
The Hamilton-Jacobi method of quantizing singular systems is discussed.The equations of motion are obtained as total differential equations in many variables.It is shown that if the system is integrable,one can obtain the canonical phase space coordinates and set of canonical Hamilton-Jacobi partial differential equations without any need to introduce unphysical auxiliary fields.As an example we quantize the O(2) nonlinear sigma model using two different approaches:the functional Schrodinger method to obtain the wave functionals for the ground and the exited state and then we quantize the same model using the canonical path integral quantization as an integration over the canonical phase-space coordinates. 相似文献
6.
V. G. Marikhin 《JETP Letters》2011,94(3):243-247
The problem of commuting quadratic quantum operators with a magnetic field has been considered. It has been shown that any such pair can be reduced to the canonical form, which makes it possible to construct an almost complete classification of the solutions of equations that are necessary and sufficient for a pair of operators to commute with each other. The transformation to the canonical form is performed through the change of variables to the Kovalevskaya-type variables; this change is similar to that in the theory of integrable tops. As an example, this procedure has been considered for the two-dimensional Schrödinger equation with the magnetic field; this equation has an additional quantum integral of motion. 相似文献
7.
Robert E. Kalaba Melvin R. Scott 《Journal of Quantitative Spectroscopy & Radiative Transfer》1973,13(6):509-515
A new technique is presented for the calculation of the eigenvalues and eigenfunctions of complex-valued symmetric kernels which occur in laser theory. The method combines some classical results of integral equations and complex variables with a recent technique for transforming Fredholm integral equations into a Cauchy system of differential equations. The procedure is flexible and accurate, whereas many of the classical techniques, such as Rayleigh-Ritz, yield results of doubtful accuracy for the kernels of laser theory. 相似文献
8.
Angles and rapidity variables which are simply related to the invariants of a five-particle process are derived and the connecting equations established. Classification of the different forms of the phase space integral, obtained by successive use of these equations, is given. The symmetric treatment clarifies the meaning of several (commonly used or here introduced) sets of variables. 相似文献
9.
用场方法来求解Whittaker方程.将一个场变量取作为其余场变量和时间的函数并对这个函数建立基本偏微方程.如能求得它的完全积分,那么Whittaker方程的解可由解代数方程来得到.
关键词:
场变量
基本偏微分方程
场方法
积分 相似文献
10.
在具有交叉对称的李模型中,写出了非弹性振幅的积分方程组,它们是Omne氏型的。在已知弹性振幅时,这积分方程组是可解的。在适当地写出这方程组时,可证明非齐次项是小的(在某些区域内),因而使解也有取小值的可能。 相似文献
11.
Bruce Turkington 《Journal of statistical physics》2013,152(3):569-597
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter. 相似文献
12.
Marcus Alfred Petero Kwizera James V. Lindesay H. Pierre Noyes 《Foundations of Physics》2004,34(4):581-616
We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described. 相似文献
13.
Sorokin SV 《The Journal of the Acoustical Society of America》2011,129(3):1315-1323
Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. 相似文献
14.
F. Gori 《Optics Communications》1974,11(4):365-367
It is shown that any integral imaging equation whose solutions are known can be used to generate a class of solvable integral equations via an affinity transformation. 相似文献
15.
A.L. Crosbie R.L. Dougherty 《Journal of Quantitative Spectroscopy & Radiative Transfer》1981,25(6):551-569
Exact integral equations are derived describing the source function and radiative flux in a two-dimensional, radially infinite cylindrical medium which scatters anisotropically. The problem is two-dimensional and cylindrical because of axisymmetric loading. Radially varying collimated radiation is incident normal to the upper surface while the lower boundary has no radiation incident upon it. The scattering phase function is represented by a spike in the forward direction plus a series of Legendre polynomials. The two-dimensional integral equations are reduced to a one-dimensional form by separating variables for the case when the radial variation of the incident radiation is a Bessel function. The one-dimensional form consists of a system of linear, singular Fredholm integral equations of second kind. Other more complex boundary conditions are shown to be solvable by a superposition of this basic Bessel function case. Diffusely incident radiation is also considered. 相似文献
16.
17.
Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies. 相似文献
18.
I.M. Narodetskiǐ 《Nuclear Physics A》1974,221(1):191-210
Within the framework of the Yakubovsky four-body equations the 0+ bound states of 4He are determined. The two-particle interactions used are of the separable Yamaguchi type and include spin-dependent forces. The problem is reduced to the solution of four coupled integral equations in two variables. The separable approximation of the kernels makes it possible to reduce the problem to a set of single variable integral equations. The separable approximation method employed is based on the Hilbert-Schmidt expansion applied to the kernels of four-body equations. The ground state energy of 4He is found to be ?45.73 MeV, the excited 0+ level lies at ?11.69 MeV. In conclusion we discuss the accuracy of various approximate methods in the four-nucleon problem. 相似文献
19.
A.L. Fymat R.E. Kalaba E. Zagustin 《Journal of Quantitative Spectroscopy & Radiative Transfer》1975,15(3):259-265
A new representation formula for the solution of the auxiliary integral equation for the source function in inhomogeneous, anisotropically scattering media is presented. It involves two new functions Φ and ψ of two variables instead of the original five variables. This generalizes earlier results of Kagiwada et al. (1969) and Sobolev (1972) applicable to homogeneous atmospheres. The corresponding Bellman-Krein formula for the resolvent kernel is also derived. The present representation for the solution of Fredholm integral equations of second kind with unsymmetric kernels provides a new approach to radiative transfer in anisotropic inhomogeneous media. 相似文献
20.
A numerical method is proposed for the approximate solution of a Cauchy-type singular integral equation (or an uncoupled system of such equations) of the first or the second kind and with a generalized kernel, in the sense that, besides the Cauchy singular part, the kernel has also a Fredholm part presenting strong singularities when both its variables tend to the same end-point of the integration interval. In this case any type of real or generally complex singularities in the unknown function of the integral equation may be present near the end-points of the integration interval. The method proposed consists simply in approximating the integrals in the integral equation by using an appropriate numerical integration rule with generally complex abscissas and weights, followed by the application of the resulting approximate equation at properly selected complex collocation points lying outside the integration interval. Although no proof of the convergence of the method seems possible, this method was seen to exhibit good convergence to the results expected in an example treated. 相似文献