Effective Lagrangian and equations for valence quark and gluon Green's functions

Starting from the QCD Lagrangian and separating background and valence degrees of freedom, one arrives at the effective Lagrangian for valence quarks and gluons. Each term in the Lagrangian contains a product of valence quark and gluon operators acting at the end of the fundamental or adjoint string, made of the background field. A simple procedure is described how to obtain from the Lagrangian self-coupled equations for quark and gluon Green's function.     

A wave automaton for Maxwell's equations

This paper presents an extension to electromagnetic fields of the wave automaton, which was introduced in recent years for describing wave propagation in inhomogeneous media. Using elementary processes obeying a discrete Huygens' principle and satisfying fundamental symmetries such as time reversal and reciprocity, this new wave automaton is capable of modeling Maxwell's equations in 3+1 dimensions. It supplements the methods that were developed early for scalar and spinor fields. Received 19 July 2001     

Axioms for Euclidean Green's functions

We establish necessary and sufficient conditions for Euclidean Green's functions to define a unique Wightman field theory.Supported by the National Science Foundation under grant GP 31239X.Supported in part by the Air Force Office of Scientific Research, contract AF 44620-70-C-0030.     

One self-consistent closure for chains of equations for Green's functions. An anisotropic heisenberg model

This article present a self-consistent approach to computation of the correlation function in the method of Green's functions. The basis for the approach is representation of the desired Green's function in the form of a chain of fractions that is subsequently closed. The closure is based on the use of concrete relations imposed on the higher-order correlation functions. General expressions for the correlation functions and conditions for self-consistency of the computations are presented. The method has been tested by computing the magnetization and critical temperature in a Heisenberg model with arbitrary anisotropy parameter. We obtain general expressions for these quantities. The critical temperature obtained is less than the corresponding value given by the molecular-field approximation. The latter approximation also leads to an overestimate of the magnetization values. It is shown that no critical transition is possible for any value of the anisotropy parameter. The corresponding inequalities are obtained. The method is compared with a method for self-consistent computation of correlation functions that was proposed earlier by the author.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 1, pp. 46–52, January, 1996.     

Fisher information as the basis for Maxwell's equations

Maxwell's equations of classical electrodynamics may be derived on the following statistical basis. Consider a gedanken experiment whereby the mean space-time coordinate for photons in an electromagnetic field is to be determined by observation of one photon's space-time coordinate. An efficient (i.e. optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. The Fisher information I is a simple functional of the probability law governing space-time coordinates of the “particles” of the field. This probability law is modeled as the source-free Poynting energy flow density, i.e., the ordinary local intensity in the optical sense, or, the square of the four-vector potential. When the Fisher information is extremized subject to an additive constraint term in the total interaction energy, Maxwell's equations result.     

Axioms for Euclidean Green's functions II

We give new (necessary and) sufficient conditions for Euclidean Green's functions to have analytic continuations to a relativistic field theory. These results extend and correct a previous paper.with an Appendix by Stephen SummersSupported in part by the National Science Foundation under Grant MPS 73-05037 A01.Alfred P. Sloan Foundation Fellow.     

Nonsteady perturbation theory for Green's functions

A simple method is proposed for uncoupling a complex chain of Green's function (GF) equations when the initial GF is coupled simultaneously with several higher-order GF. Uncoupling of the chain of equations of motion for the nuclear spin anticommutator Green's function provides an example of the use of this method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 126–133, August, 1978.     

Euclidean Green's functions for Jaffe fields

We extend the axioms for Euclidean Green's functions recently proposed by Osterwalder and Schrader to Jaffe fields.     

Green's functions for body-centred cubic lattices

The presented paper contains the tables of Green's functions for bcc lattices for outband frequencies 1·0/ _m 1·6. The central-force model is used, the interaction with 8 nearest and 6 next-nearest neighbours is considered and the number of different Green's functions is fairly decreased by symmetry. Numerical difficulties arising by computing Green's functions are discussed. The derivation of symmetry relations for a dynamical matrix is generalized for the matrix of Green's functions.     

Maxwell's equations in divergence form for general media with applications to MHD

Maxwell's equations in media with general constitutive relations are reformulated in covariant form as a system of divergence equations without constraints. Our reformulation enables us to express general electro-magneto-fluid problems as hyperbolic systems in divergence form. We illustrate this method on the MHD problem. In the absence of constraints, a general representation is derived for the characteristics form for first-order systems of quasi-linear partial differential equations in vector fields and scalars. Using this covariant formulation of characteristics, we find that the principle of covariance imposes a very rigid structure on the infinitesimally small amplitude waves in MHD. To demonstrate the power of the reformulation, we study numerically ultra-relativistic wave breaking using the divergence formulation of MHD.This material is based upon work supported by NSF grant AST 84-51725. Some of the work has been performed at the Department of Applied Mathematics, Caltech     

Vacuum electrodynamics of accelerated systems: Nonlocal Maxwell's equations

The nonlocal electrodynamics of accelerated systems is discussed in connection with the development of Lorentz‐invariant nonlocal field equations. Nonlocal Maxwell's equations are presented explicitly for certain linearly accelerated systems. In general, the field equations remain nonlocal even after accelerated motion has ceased.     

Method of Green's functions in the theory of quantum kinetic equations. I

The solution of the dynamic equation is strongly degenerate for systems with an infinite number of degrees of freedom. A causality principle is stated, whereby the particular solution of the dynamic equation, which is at the same time a solution of the kinetic equation, can be selected. The principle is applied here to the multitime formalism of correlation functions. A basis is thus obtained for the method of Green's time-temperature functions in the theory of kinetic equations.The author thanks all those who have discussed the topics in this paper with him, particularly V. L. Bonch-Bruevich, D.A. Kirzhnits, V.M. Fain, E.S. Fradkin, and A. S. Shekhter.     

AnO(3, 1) approach to Maxwell's equations

Using the principal series representations of the Lorentz group, a method parallel to that of Gelfand and Yaglom is suggested to obtain Maxwell's equations, which dispenses with the arbitrary introduction of a degenerate transformation with respect to which the photon equations are invariant. The method also gives subsidiary conditions which, in conjunction with the masslessness of the particle, yield the Lorentz condition and the correct values of photon polarization.     

Double-time Green's functions for crystals with defects

A general method for the calculation of the double-time Green's function of displacements for a crystal with arbitrary symmetry and arbitrary point defect is given in a harmonic approximation. Green's function is derived in two forms. In the first form Green's function of the ideal crystal is modified by the defect, in the second form Green's function of the defect molecule is modified by the ideal part of the crystal.     

Green's functions for open-shell atoms and molecules

Green's functions for atoms and molecules with a degenerate ground state are evaluated by means of tensorial analysis. The final results obtained are of simple character allowing the usual diagrammatic approach via Wick's theorem for non-degenerate ground states. As an example the ionization of a σ orbital of O₂ is considered and an equivalent approach to the frozen orbital approximation is discussed.     

Theoretical application of z-dependent gain coefficient to describe amplified spontaneous emission

Based on the geometrical modeling of the unified gain coefficient and the reported amplified spontaneous emission (ASE) output energy measurement ε(ASE) versus amplifying excitation length, l(AMP) in a KrF laser oscillator, we managed, as an example, to explain the ASE output energy behavior both numerically and analytically. In this approach, introducing the ASE gain-coefficient profile for the KrF laser, g(0,KrF)(ASE), was not avoidable. It was found that while the g(0,KrF)(ASE) profile follows the introduced gain-modeling formulation, it is, however, slightly lower than the KrF laser gain profile, g(0,KrF)(exp), deduced from the measurements reported by different researchers. The present approach, up to the present time, is able to explain all of the existing ambiguities on understanding the ASE behavior.     

Tailored nearfield Green's functions for arbitrary geometries

An iterative technique, taken from the field of optics, is used to obtain tailored Green's functions suitable for the evaluation, in the nearfield, of pressure fluctuations generated by turbulent flow in the vicinity of solid boundaries. Comparisons are made with the analytical solution for the solid sphere, and with results obtained using conventional boundary element method (BEM) for the case of a thick semi-infinite plate. A divergence issue in the case of the solid sphere is resolved by the introduction of a relaxation factor. The performance of the iterative approach is found to be comparable to that of conventional BEM, except at irregular frequencies, where the bandwidth of the error is slightly larger than that of the conventional BEM. The main advantage of the iterative approach is a significantly reduced computational cost, which allows for higher surface mesh densities and a broader useful frequency range.     

Commutator Green's functions for a spin Hamiltonian

All the commutator Green's functions are calculated for the Heisenberg spin Hamiltonian in the Hartree-Fock approximation. It is shown further that the Tyablikov transverse commutator Green's function corresponds to the Hartree—Fock approximation only for the longitudinal part of the Heisenberg spin Hamiltonian, and to obtain the longitudinal part of the commutator Green's function to the same accuracy as the Tyablikov transverse commutator Green's function it is necessary to go over to the Hartree—Fock approximation only with respect to the transverse part of the Heisenberg spin Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 62–65, December, 1980.     

Maxwell's equations in Segal's model: Solutions and their invariance

We determine all smooth solutions of Maxwell's equation in Segal's universe; furthermore we show that the group of diffeomorphisms stabilizing the space of solutions of these equations is the conformal group of Segal's model.Aspirant du F.N.R.S.