The region of validity of perturbation theory

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

The region of validity of perturbation theory

Abstract

We present a study of the region of validity of perturbation theory applied to rough surface scattering. We solve numerically the case of a periodic surface or grating varying in one dimension. For a statistical ensemble of gratings with a sufficiently long period one may obtain a good approximation of rough surface scattering. We use this to test the validity of perturbation theory.

Only the perfect conductor case was considered. We find that as the grazing angle becomes small the perturbation result for the TE (E horizontal) polarization remains valid, while for the TM (E vertical) polarization it breaks down. The results show that the perturbation results should be used carefully when being compared with experimental data at grazing angles.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Generalized perturbation theory of classical fluids in the critical region

Perturbation theories of classical fluids are extended in the critical region by decomposition of the attractive part of the pair interaction. The generalized theory is in agreement with scaling, has the correct dependence on dimensionality and on the range of the forces and offers a method to compute critical indices.     

Ring wave solutions of a n+1-dimensional Sine-Gordon model

The dynamical properties of the ring wave solutions of the model psi(tt)- nabla (n) (2)psi+sin psi+ varepsilon sin (psi/2)+alphapsi(t)=0 (00, alpha=0 (or alpha>0) the return effect of the ring wave does not occur only for well defined values of varepsilon. It will be shown numerically that the dissipative perturbation alphapsi(t) (alpha>0) stabilizes both the velocity and the wave profile of the ring wave when the return effect does not occur. (c) 1997 American Institute of Physics.     

Fundamental domains and light-cone string field theory

It is shown that light-cone string field theory leads to a very simple specification of the fundamental domain over which the moduli are to be integrated for multiloop string and superstring amplitudes, as well as clarifying related questions.     

On the light-cone quantization of non-abelian gauge theory

The implications of periodic boundary conditions in the light-cone quantization of non-abelian fields are studied. Formulation of the theory in the singularity-free case is presented. Some consequences of field singularities are discussed.     

The linear meson model and chiral perturbation theory

We compare the linear meson model and chiral perturbation theory in next to leading order in the quark mass expansion. In particular, we compute the couplings – of chiral perturbation theory as functions of the parameters of the linear model. They are induced by the exchange of scalar mesons. We use a phenomenological analysis of the effective vertices of the linear model in terms of pseudoscalar meson masses and decay constants. Our results for the agree with previous phenomenological estimates. Received: 21 April 1997 / Published online: 20 February 1998     

Degenerate perturbation theory and its application to the Hubbard model

Projection operators are incorporated in the canonical transformation to derive an analytical infinite series of a degenerate perturbation expansion. The theory is used to calculate the ground state energy of a half-filled s-band Hubbard model to seventh order.     

一类广义Sine-Gordon扰动方程的解析解

利用同伦映射方法研究了一类广义Sine-Gordon方程. 首先引入一个同伦变换. 然后构造了原方程解的迭代关系式. 最后得到了问题的解析解. 关键词： 孤子 扰动 同伦映射     

Schwinger model in the light-cone representation

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the discretized light-cone quantization of gauge fields are discussed.     

On the light-cone formulation of classical non-abelian gauge theory

For a classical Yang-Mills field which is periodic in the longitudinal light-cone coordinate: (a) a gauge condition is formulated, (b) the presence of field singularities in this gauge is shown, and (c) the relevance of these singularities to the topological charge is demonstrated.Also of the Science Sector, UNESCO