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.     

Kinetic Green's functions

It is shown that the theory of kinetic Green's functions coincides completely with the theory of vacuum Green's functions after the choice of the operatorO ^?1 in its overall part. An expression for the energy of the system is obtained directly in terms of the mass operators. An equation is given that is a generalization of the Boltzmann equation and has the same mathematical structure.     

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.     

电磁学中的格林函数

文章回顾了电磁学中的格林函数理论与格林函数方法。首先,引入标量波动方程对应的格林函数,并与信号系统中的冲击响应函数作类比。其次,引入矢量波动方程对应的并矢格林函数,包括均匀和非均匀介质中的格林函数,并探讨其与电磁理论中的互易定理、等效原理之间的联系。最后,介绍了考虑介质的运动效应和电磁场的量子效应下的格林函数理论。此外,文章也探讨了电磁格林函数在无线通信、电磁兼容等工程领域的应用。     

Approximation of Green's functions

Special symmetries of the Green's functions of a non-relativistic many fermion-system and conservation laws, expressible by hermitian generators, are formulated as relations for a Green's function operator. Approximations for the Green's functions, defined as partial summations of the perturbation expansion, and consistent with the symmetries and conservation laws are presented.     

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.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.     

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.     

Fast analytical approximation for arbitrary geometries in diffuse optical tomography

Diffuse optical tomography is a novel imaging technique that resolves and quantifies the optical properties of objects buried in turbid media. Typically, numerical solutions of the diffusion equation are employed to construct the tomographic problem when media of complex geometries are investigated. Numerical methods offer implementation simplicity but also significant computation burden, especially when large three-dimensional reconstructions are involved. We present an alternative method of performing tomography of diffuse media of arbitrary geometries by means of an analytical approach, the Kirchhoff approximation. We show that the method is extremely efficient in computation times and consider its potential as a real-time three-dimensional imaging tool.     

Green's functions for off-shell electromagnetism and spacelike correlations

The requirement of gauge invariance for the Schwinger-DeWitt equations, interpreted as a manifestly covariant quantum theory for the evolution of a system in spacetime, implies the existence of a five-dimensional pre-Maxwell field on the manifold of spacetime and proper time . The Maxwell theory is contained in this theory; integration of the field equations over restores the Maxwell equations with the usual interpretation of the sources. Following Schwinger's techniques, we study the Green's functions for the five-dimensional hyperbolic field equations for both signatures ± [corresponding to O(4, 1) or O(3, 2) symmetry of the field equations] of the proper time derivative. The classification of the Green's functions follows that of the four-dimensional theory for massive fields, for which the mass squared may be positive or negative, respectively. The Green's functions for the five-dimensional field are then given by the Fourier transform over the mass parameter. We derive the Green's functions corresponding to the principal part _P and the homogeneous function ₁ ; all of the Green's functions can be expressed in terms of these, as for the usual field equations with definite mass. In the O(3, 2) case, the principal part function has support for x²², corresponding to spacelike propagation, as well as along the light cone x²=0 (for =0). There can be no transmission ofinformation in spacelike directions, with this propagator, since the Maxwell field, obtained by integration over , does not contain this component of the support. Measurements are characterized by such an integration. The spacelike field therefore can dynamically establish spacelike correlations.     

Existence of Green's functions for dilute Bose gases

Some properties of finite volume Green's functions are obtained, and the infinite volume limit is shown to exist for the multi-time Green's functions of a dilute Bose gas, constructed with the operators of the quasi-local algebra (see Theorem IV.5).     

On the dyadic Green's functions for Beltrami fields

A simple derivation of the Green's functions for Beltrami fields is presented for use with time-harmonic electromagnetism in homogeneous biisotropic media.     

Two-particle Green's functions in non-equilibrium matter

The method of the derivation of two-particle Green's functions in non-equilibrium matter is developed. The closed set of equations for the vertex functions and also for the two-particle Green's functions is obtained by means of the summation of the series of irreducible diagrams. The solution of such equations completely defines the two-particle Green's functions in matter.