Point Green Function Research Articles

Quantum inverse problem and green functions for the Heisenberg ferromagnet

The local spin operators of the anisotropic Heisenberg ferromagnet are expressed in terms of the quantum scattering data (the quantum inverse problem). Thus a finite algorithm for calculating the Green function is obtained. By an appropriate limiting procedure in the expression for the four point Green function we get the four point Green function for the isotropic XXX-model and reproduce the known formulae for the nonlinear Schrödinger equation.

Integral representation of Green's functions for asymptotically free field theories

The renormalization-group equation is used to construct an integral representation for the renormalized $n$-point Green's function of an asymptotically free theory. The integral is over a finite range of the coupling parameter. The significance of this result is discussed.

Ultraviolet Finiteness of All Quantum Loops in Gauge Supersymmetry

The arbitrary $n$-point Green's functions of spontaneously broken gauge supersymmetry are shown to be ultraviolet finite to arbitrary loop order for $Ng~2$ (where $4N$ is the number of Fermi coordinates) when the spontaneous breaking preserves global supersymmetry.

Comparison between large-order estimates and perturbation series in a scalar field theory with Gaussian propagator

We use the Phi/sup 4/ field theory with a Gaussian propagator as a model to compare large-order estimates of perturbation theory with the actual calculation of the first terms of the perturbative expansion. Although this field theory, as it stands, has no physical content, it has the following advantages: All Feynman diagrams are finite and easily calculable analytically; we have calculated eight (seven) terms in the expansion of the zero-, two- (and four-) point Green's functions in arbitrary dimension. Furthermore, the leading term in the large-order estimate can also be calculated analytically. We have actually extended the calculation to the Phi/sup 2M/ interaction. Comparison between the large-order estimate and the perturbation series shows that the agreement is best for lower dimensions. Finally, we use the knowledge of the large-order estimate to study various resummation methods.

Strong coupling in the quantum field theory with nonlocal nonpolynomial interaction

In the relativistic quantum field theory the representation for theS-matrix elements is obtained for any coupling constantsg in the case of a one component scalar field ϕ(x) with nonlocal nonpolynomial interaction ℒ I (ϕ)=gU(ϕ) when the causal function is bounded in the Euclidean region 0≦D c (x ≦D c (0)<∞ and the function |U(u)|≦1 for realu. It is proved that the two point Green function is bounded in the physical region of momenta variablep 2.

Conformal-Invariant Green Functions Without Ultraviolet Divergences

It is known that conformal invariance, with anomalous dimensions, determines the 2- and 3-point functions in relativistic quantum field theory up to some constants. It is then natural to use these to construct the skeleton-graph expansion of the general $n$-point Green function. We demonstrate that this leads to well-defined conformal-invariant expressions, for non-exceptional external momenta, given by ordinary convergent (Riemann) integrals. This also applies to the integrals in the Schwinger-Dyson equation for the 2- and 3-point functions. These results support in particular conjectures recently advanced by Migdal---including self-consistency of conformal invariance. All results are derived for (pseudo-) scalar Yukawa theory.

The optical potential of the deuteron (H3, He3) and the two (three) nucleon vibration coupling

We present a closed expression for the exact deuteron (H3, He3) optical potential in terms of higher point Green functions. This form is well suited to study its energy dependence. Intermediate resonances due to two (three) particle phonon coupling are suggested and the coupling constants are identified with the Migdal parameters.

The six-point Green function and the application of Faddeev's theory to the many body problem

Integral equations for the 6-point Greenfunction are established and a Faddeev-like part extracted. We give a qualitative solution of our integral equation in the sense of the renormalized RPA. The connection of the mass operatorM, K andT matrices with “higher” point Greenfunctions is discussed.

An integral equation for the six-point green function and the many body problem

An integral equation for the 6-point Green function is established and a Faddeev-like part extracted. We sketch a solution of our integral equation in the sense of the RPA. The connection of the mass operator with the 6, 10, 14, … -point Green function is discussed.