The equations of Wilson's renormalization group in dimension 4 and analytic renormalization

Wilson's renormalization group equations are introduced and investigated in the framework of perturbation theory with respect to the deviation of the renormalization exponent from its bifurcation value. We consider the case when the dimension is equal to 4. An exact solution of these equations is constructed using analytic renormalization of the projection Hamiltonians.     

On the stationary perturbation theory in quantum mechanics

A simple method is proposed for solving the Shcrödinger equation in the presence of a perturbation. Formally exact expressions are obtained in the form of infinite series for the energies and wave functions without assuming that the perturbation is small. Under the additional assumption that it is small (in accordance with a well-defined criterion of smallness) the obtained results yield directly the results of Schrödinger's perturbation theory. The developed approach contains in compact form various formulations of perturbation theory. The calculations use neither the complex technique of projection operators nor the complicated formalism of Green's functions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 33–36, November, 1980.     

An exact iterative solution of the atom-surface scattering problem for realistic potentials

A general method, based on high order distorted wave perturbation theory, is developed to obtain exact reflection intensities for low energy atoms scattered by solid surfaces. Resonance shapes are calculated using projection techniques to obtain uniform convergence. Important differences with the hard corrugated wall model arise when the calculations for a corrugated Morse potential are compared with experiment for helium scattered by a Cu(110) surface.     

Application of Lie transform perturbation method for multidimensional non-Hermitian systems

Three-dimensional non-Hermitian systems are investigated using classical perturbation theory based on Lie transformations. Analytic expressions for total energy in terms of action variables are derived. Both real and complex semiclassical eigenvalues are obtained by quantizing the action variables. It was found that semiclassical energy eigenvalues calculated with the classical perturbation theory are in very good agreement with exact energies and for certain non-Hermitian systems second-order classical perturbation theory performed better than the second-order Rayleigh–Schroedinger perturbation theory.     

A creative factor and two-step processes

Some questions concerning the creative factor contained in perturbation theory of two-step processes are examined. It is shown that perturbation theory is justifiable by deriving the propagator by means of a projection method and using a generalized optical potential.     

Borel summation of perturbation series in quantum mechanics and field theory

The Borel summation of factorial divergent perturbation series is considered. The relation between the asymptotics of the coefficients in the series and the character of the exact function singularity is established. The applicability limits for the improved perturbation theory are obtained. The results are tested on a number of physical problems for which the exact solutions are available.     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Gauge model of a crack

The paper proposes a model of a crack system as local symmetry breaking for a group of 3D rotations compensated by fictitious fields that make Lagrangian equations of elastic energy density covariant in the effective Riemannian space. Equilibrium equations are solved using the perturbation theory with the number of notches being a small parameter, and exact expressions are derived for stress and gauge fields in a 2D problem by applying Hilbert transform to orthogonal Chebyshev polynomials. The model is generalized to nonlinear elasticity (deformation theory of plasticity) and statistical mesomechanics models. Also presented is a solution for stress concentration in a system of arbitrarily oriented cracks which takes into account their mutual influence at any order of the perturbation theory and reduces to a system of linear equations with explicit exact solutions.     

Projection operators in classical kinetic theory

Zwanzig's projected kinetic equation is rederived by a perturbation method. A choice of projection is proposed which, in conjunction with appropriate initial-value conditions, yields kinetic equations for the two time distribution functions of phase subsets for a system in equilibrium. These equations are generalizations of the Fokker-Planck equations in which the dissipative terms are non-Markoffian.

It is shown that exact equations for the van Hove self and distinct correlation functions are particular cases of these equations.     

Shear in a perturbed Friedmann universe

For perturbed Friedmann models of vanishing and positive curvature the time development of shear is computed by means of a linear perturbation theory. As for the smallness of the perturbation functions mathematically exact and physically meaningful conditions are stated. The shear is computed for different stages of the universe.     

Perturbative solution of the schwinger model

One interesting question for the exactly solvable Schwinger model is how to infer the exact solution from perturbation theory. We give a systematic procedure of deriving the exact solution from Feynman diagrams of arbitrary order for arbitraryn-point functions. As a byproduct, we derive from perturbation theory exact integral equations that then-point functions have to obey. This work was supported by a research stipendium of the University of Vienna.     

Critical exponents predicted by grouping of Feynman diagrams in φ4 model

Different perturbation theory treatments of the Ginzburg‐Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical exponents consistent with the known exact solutions in two dimensions. The usual perturbation theory is reorganized by appropriate grouping of Feynman diagrams of φ⁴ model with O(n) symmetry. As a result, equations for calculation of the two‐point correlation function are obtained which allow to predict possible exact values of critical exponents in two and three dimensions by proving relevant scaling properties of the asymptotic solution at (and near) the criticality. The new values of critical exponents are discussed and compared to the results of numerical simulations and experiments.     

Nonparabolicity and exciton effects in two-photon absorption in zincblende semiconductors

The two-photon absorption coefficient is calculated from perturbation theory for direct-gap zincblende semiconductors using exact nonparabolic energies and matrix elements. The enhancement due to exciton effects is included. The results are compared to experiment and to other theories including the tunneling or Keldysh theory.     

递推与迭代在量子力学近似计算中的应用

综述了非简并微扰论和简并微扰论的递推形式，一维阶梯位势透射系数的递推计算及变化法的迭代形式，在给定的精度下，利用上述方法可以得到与精确解完全一致的效果。     

The Born-Infeld action from conformal invariance of the open superstring

We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.     

Radiative mass generation in perturbation theory and the renormalization group

The mechanism of dynamical mass generation is investigated in perturbation theory for the spontaneously broken supersymmetry model of O'Raifeartaigh. The generated mass obeys an homogeneous renormalization group equation. The compatibility of the perturbation solution with the exact solutions spectrum of the renormalization group equation is shown.     

Photon energy spectrum of electron-positron bremsstrahlungin the center-of-mass system

Formulae for the total cross section of electron-positron bremsstrahlung in the center-of-mass system are given which are exact in lowest-order perturbation theory. The resulting photon spectra are compared with those of electron-electron bremsstrahlung.Received: 1 August 2003, Revised: 2 September 2003, Published online: 30 October 2003     

Perturbation theory for bending potentials

An efficient perturbative method is developed to facilitate the treatment of the anharmonicity of bending degrees of freedom. The Rosen-Morse and sec² potentials are transformed so that perturbation theory may be applied easily. For a model problem it is found that the difference between the energy levels obtained from perturbation theory and the exact energy levels is less than 0·1 cm^-1 for the first six energy levels.     

Perturbation theory calculation of high-order bound-bound transitions

We have calculated the transition rate for high-order bound-bound transitions in hydrogen by using the approximate perturbation theory result of Bebb and Gold. We find that there is a considerable amount of discrepancy between the results of our calculation and those of the exact perturbation theory calculation of Gontier and Trahin.     

Wave function renormalization in heavy baryon chiral perturbation theory

We establish exact relations between relativistic form factors and amplitudes for single-baryon processes and the corresponding quantities calculated in the framework of heavy baryon chiral perturbation theory. A crucial ingredient for the proper matching is the first complete treatment of baryon wave function renormalization in heavy baryon chiral perturbation theory.