Review of chiral perturbation theory

A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.     

πN scattering and electromagnetic corrections in the perturbative chiral quark model

We apply the perturbative chiral quark model to give predictions for the electromagnetic O(p²) low-energy couplings of the ChPT effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e²) radiative corrections to the πN scattering amplitude. We estimate the leading isospin-breaking correction to the strong energy shift of the π⁻p atom in the 1s state, which is relevant for the experiment “Pionic Hydrogen” at PSI.     

Probing the convergence of perturbative series in baryon chiral perturbation theory

Using the examples of pion-nucleon scattering and the nucleon mass we analyze the convergence of perturbative series in the framework of baryon chiral perturbation theory. For both cases we sum up sets of an infinite number of diagrams by solving equations exactly and compare the solutions with the perturbative contributions.     

Wronskian perturbation theory

We develop a perturbation method that generalizes an approach proposed recently to treat velocity-dependent quantum-mechanical models. In order to test the present approach we apply it to some simple trivial and nontrivial examples.     

A one-electron variant of direct perturbation theory for the treatment of scalar-relativistic effects

ABSTRACT

The different importance of scalar-relativistic two-electron contributions in second-order direct perturbation theory (DPT2) and the spin-free one-electron variant of exact two-component theory (SFX2C-1e) is analysed. The apparent discrepancy is traced back to the fact that SFX2C-1e is not ignoring the total DPT2 two-electron contribution rather just a so-called commutator term which originates from a rewrite of the small-component density (matrix) in terms of the related, though different kinetic-energy density (matrix). This commutator term is shown to be significantly smaller (10% and less) and to have, unlike the total DPT2 two-electron contribution, a negative sign. Based on our findings, we propose a one-electron variant of direct perturbation theory, referred to as DPT-1e, and report on its implementation for the computation of energies and first-order properties at the second-order level, i.e. DPT2-1e. Numerical results are presented for the hydrogen halide series HX, X=F, Cl, Br, I, and At, as well CuF and CuCl in order to investigate its performance in comparison to DPT2 and SFX2C-1e.     

A Hopf-like equation and perturbation theory for differential delay equations

We extend techniques developed for the study of turbulent fluid flows to the statistical study of the dynamics of differential delay equations. Because the phase spaces of differential delay equations are infinite dimensional, phase-space densities for these systems are functionals. We derive a Hopf-like functional differential equation governing the evolution of these densities. The functional differential equation is reduced to an infinite chain of linear partial differential equations using perturbation theory. A necessary condition for a measure to be invariant under the action of a nonlinear differential delay equation is given. Finally, we show that the evolution equation for the density functional is the Fourier transform of the infinite-dimensional version of the Kramers-Moyal expansion.     

Critical exponents and large-order behavior of perturbation theory

The principles of the recent calculations of critical exponents from three- and two-dimensional field theory are reviewed. They rely on the Callan-Symanzik equations, diagram calculations, and on the characterization of the asymptotic behavior of perturbation series at large order. We then present new results concerning the normalization of the large-order behavior.On leave of absence from INFN, Frascati.     

Symmetry-adapted many-body perturbation theory: use of the wave operator matrix elements

In this paper we develop a simple method for adapting the closed-shell many-body perturbation theory to an arbitrary point group symmetry taking account of various classes of diagrams exactly to all orders. The method consists in deriving a linear operator equation for the closed-shell wave-operatorW which is then symmetry-adapted to the pertinent point groupG. It is shown that the system of equations thus derived enables one to include orbital-diagonalh-h, p-p andh-p ladders to all orders in a perturbative framework. The way to generalise the method through inclusion of a larger classes of diagrams to all orders is also indicated. Finally, the connection of the present mode of development with the non-perturbative coupled-cluster formalisms is briefly indicated.     

Chiral perturbation theory: Introduction and recent results in the one-nucleon sector

We provide an introduction to the basic concepts of chiral perturbation theory and discuss some recent developments in the manifestly Lorentz-invariant formulation of the one-nucleon sector.     

运用线性量子变换理论和定态微扰论求解线型多原子分子振动的一般方法

采用键长伸缩和垂直键轴位移为内坐标,多维耦合谐振子、势函数中超过二次幂的项分别为零级近似和微扰的线型多原子分子振动模型,运用广义线性量子变换理论和定态微扰论对线型多原子分子振动进行了普遍求解,将线型多原子分子简谐振动能量本征值和态的求解转化成正定和半正定矩阵的对角化问题,微扰矩阵元、能量和波函数各级修正的计算转换到多维无耦合谐振子的本征表象中进行.并以CO2分子为例进行了具体求解.     

Effective Hamiltonian for bound states in Yukawa theory

A generalization of the Gell-Mann–Low theorem is applied to lowest nontrivial order to determine an effective Hamiltonian for two-fermion states in relativistic Yukawa theory. The consistency of the corresponding effective Schrödinger equation is thoroughly investigated in various aspects, among others the nonrelativistic and one-body limits, and the small-distance or large-momentum regime of the bound state solutions is discussed in detail.     

Gluon cascades and amplitudes in light-front perturbation theory

We construct the gluon wave functions, fragmentation functions and scattering amplitudes within the light-front perturbation theory. Recursion relations on the light-front are constructed for the wave functions and fragmentation functions, which in the latter case are the light-front analogs of the Berends–Giele recursion relations. Using general relations between wave functions and scattering amplitudes it is demonstrated how to obtain the maximally-helicity violating amplitudes, and explicit verification of the results is based on simple examples.     

表象变换和久期微扰理论在耦合杜芬方程中的应用

本文通过对耦合杜芬方程线性项的表象变换及非线性项的久期微扰理论的应用,将耦合杜芬方程转化为简正表象下的退耦合形式,由此可以很方便地得出耦合杜芬方程的解.为了验证该方法的正确性,设计了音叉耦合实验,观测到了振幅谱谱峰的劈裂以及"振滞回线"现象,这些实验结果都可以和之前所得的理论结果符合得很好.本文求解耦合非线性方程的方法...     

Generalized parton distributions for the nucleon in chiral perturbation theory

We complete the analysis of twist-two generalized parton distributions of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. Extending our previous study of the chiral-even isosinglet sector, we give results for chiral-even isotriplet distributions and for the chiral-odd sector. We also calculate the one-loop corrections for the chiral-odd generalized parton distributions of the pion.     

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments （MMs） in terms of Chiral Perturbation Theory （ChPT）.In particular,we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well.We also make predictions for the decuplet MMs at the same chiral order.Among them,the MMs of the Δ＋＋ and Δ ＋ are found to agree well with data within the experimental uncertainties.