Validity Of Perturbation Theory Research Articles

Laser-induced charge transfer in the LiH 3+ quasi-molecule

The laser-induced charge-transfer cross section for Li 3+ + H collisions is calculated using the perturbation approach of Copelang and Tang, and is compared to the collision-induced cross section. The validity of perturbation theory and the use of simple criteria based on the Landau-Zener formula to extend the usefulness of the theory are examined.

Supersymmetry at ordinary energies. II.Rinvariance, Goldstone bosons, and gauge-fermion masses

We explore the observable consequences of supersymmetry, under the assumption that it is broken spontaneously at energies of order 300 GeV. Theories of this sort tend automatically to obey a global $R$ symmetry, which presents us with a choice among phenomenologically unacceptable alternatives. If the $R$ symmetry is broken by scalar vacuum expectation values of order 300 GeV, there will be a semiweakly coupled light Goldstone boson, similar to an axion. If it is not broken by such vacuum expectation values but is broken by quantum-chromodynamic (QCD) anomalies, then there will be a light ninth pseudoscalar meson. If it is not broken by QCD anomalies, then the asymptotic freedom of QCD is lost at high energies, killing the hope of an eventual meeting of the electroweak and strong couplings within the regime of validity of perturbation theory. We also confront the problem of an uncomfortably light gluino. A general analysis of gaugino masses shows that the gluino mass is at most of order 1 GeV, and in many cases much less.

Meson-current corrections to the magnetic moment of the deuteron within an extended Lee model

The magnetic moment of the deuteron is calculated within an extended Lee model which allows the use of realistic deuteron wave functions. The meson-current corrections which are due to the dynamical effects of the π − -meson are computed rigorously and analysed in detail. Conclusions are drawn about the validity of perturbation theory and about the importance of norm and off-shell renormalization corrections.

Perturbation theory for undoubled lattice fermions

I study a class of lattice versions of QED with fermions with the aim of clarifying the relationship between the fermion spectrum (doubled or not), continuous chiral symmetry, the range of the lattice interactions, and the validity of perturbation theory. Theories of this class with an undoubled spectrum, such as the formulation due to Drell, Weinstein, and Yankielowicz (DWY), have infinite-range interactions and infrared-divergent perturbation series. The infrared singularities can be removed by a resummation of the series. I then carry out a renormalization program for DWY QED after which the $a\ensuremath{\rightarrow}0$ limit of the theory is finite and coincides with continuum QED. Finally, I consider the nonperturbative structure of DWY QED.

Suppression of Higgs flavor-changing neutral currents in a class of gauge theories

It is shown that the masses of neutral Higgs particles in the minimal $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ left-right-symmetric gauge theory which mediate flavor-changing interactions can be as large as necessary without running into conflict with experiment or with the validity of perturbation theory.

The Fröhlich Hamiltonian: mathematical results. III. Perturbation theory

We prove the validity of perturbation theory for the polaron model. After obtaining the usual results for the Hamiltonian without cut-off, we derive the effective mass and energy shift for the Hamiltonian with cut-off. We also introduce a simplified model whose exact eigenvalue and eigenvector can be computed.

Some aspects of instantons

We study various effects associated with Euclidean instanton solutions. By means of an instructive example, we discuss how the probability of tunnelling among vacuum states in Minkowski space is connected with stationary (instanton) solutions in Euclidean space. Next we examine the cluster decomposition properties of non-Abelian gauge theories and indicate how these are recovered in the presence of instanton solutions. The validity of perturbation theory in these field theories is discussed. We show that perturbative analyses are only tenable in the deep Euclidean region, unless there is an intrinsic scale. Finally, we examine the role that instantons have in providing violations of otherwise conserved quantum numbers. We study, in particular, how fermion number nonconservation results by a careful examination of the path integral for the fermion-generating functional.

Homogeneous Renormalization Group Equations

A set of homogeneous renormalization group equations is derived on the basis of the inhomogeneous Callan-Symanzik equations in the neutral scalar theory, and the relation of these equations to those of Weinberg and of MacDowell is discussed. This set of homogeneous equations is further extended to quantum electrodynamics. As distinguished from the conventional Callan-Symanzik equations, the differential operator in these new equations can be regarded as the generator of renormalization group without approximations. Using this property, the general solution of the homogeneous renormalization group equations is obtained. Finally, in view of the infrared stability of electrodynamics, the validity of perturbation theory in the sliding coupling constant 1s examined by explicitly constructing the perturbation solution in the infrared limit. It 1s shown that the latter deviates from the exact solution.

Perturbation theory in thermosphere dynamics

It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.

Local Model Potentials for Metals: Limitations and Applications

The suitability and usefulness of local model potentials as approximate replacements for more accurate nonlocal potentials are discussed. The properties of a general local potential, which includes as subcases the empty-core potential, the optimized model potential (OMP), and the point-ion potential, are reviewed. Scattering properties of "linearly screened" and "minimum-perturbation" local model potentials are calculated and the usefulness of phase-shift matching as a selection criterion for potentials is discussed. Properties of the local OMP are studied in detail and particular emphasis is given to the relation between ion-core cancellation in real space and the validity of perturbation theory. A nonlinear Fermi-Thomas model is used to calculate an optimum core radius for each metal. This core radius is found to correlate well with the Pauling ionic radius. The calculated core radii are used to extend the local OMP to the entire Periodic Table and thence to study trends in elemental properties. A striking correlation is observed between superconducting transition temperature and a parameter characterizing the electron-phonon interaction in terms of the local OMP.

Validity of perturbation theory. I. The single band gap model

A simple test of the validity of perturbation theory in the evaluation of energy differences between different crystal structures for sp- bonded metals is provided by a model in which the effect of only one band gap is considered. This model, which was previously discussed semi-quantitatively by Harrison and by Pick and Blandin, is here solved exactly for a local pseudopotential. Former ideas concerning the nature of 'Brillouin zone-Fermi surface interactions' are discussed in the light of perturbation theory and this more exact model.

Statistical Mechanics of Open Systems

We have generalized Kubo's treatment of isolated nonequilibrium systems to open systems in contact with thermal reservoirs. When the system is in contact with one reservoir and is subject to a weak external field, the deviation of the average of any quantity from its equilibrium value is related to a time-correlation function which incorporates the effect of the reservoir. A corollary is an isothermal fluctuation-dissipation theorem, which gives an explicit expression in terms of a time-correlation function for the rate at which energy flows from the driving field into the reservoir via the system. As an application, we compute the complex conductivity of a Lorentz gas. We also obtain an expression for the stationary nonequilibrium distribution of a system in contact with several reservoirs at slightly differing temperatures and chemical potentials. The Onsager coefficients, which relate the heat and particle fluxes to the differences among the reservoir parameters, are then explicitly expressed in terms of suitable time-correlation functions and their symmetry is exhibited. The validity of perturbation theory in finding the linear deviation from equilibrium of the $\ensuremath{\Gamma}$-space ensemble density is also discussed.