Three-loop β-function for the bosonic non-linear sigma model

We present a calculation of the three-loop metric β-function for the bosonic non-linear sigma model. We also construct the action whose equations of motion coincide with the vanishing of the β-function. It is found to be the effective action derived from string scattering amplitudes.     

Four-loop β-function for the N = 1 and N = 2 supersymmetric non-linear sigma model in two dimensions

A superspace calculation of the four-loop β-function is presented for two-dimensional N= 1,2 supersymmetric non-linear σ-models. It is concluded that besides the one-loop contribution which vanishes on Ricci-flat manifolds, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for the superstring are discussed.     

Perturbative series and the 1/N expansion for the QED β-function

A comparison of the 5-loop perturbative series and the 1/N expansion for the QED renormalization group β-function in the Minimal Subtraction scheme is performed. The good agreement between two expansions is found which proves that the MS β-function is adequately described by both series.     

Feynman propagator for the δ-function potential

A new derivation of the Feynman propagator for the Dirac δ-function potential is presented.     

Exact expression for decoherence factor in the time-dependent generalized Cini model

The present letter finds the complete set of exact solutions of the time-dependent generalized Cini model by making use of the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation and, based on this, the general explicit expression for the decoherence factor is therefore obtained. This study provides us with a useful method to consider the geometric phase and topological properties in the time-dependent quantum decoherence process.     

Analytical five-loop expressions for the renormalization group QED β-function in different renormalization schemes

We obtain analytical five-loop results for the renormalization group ??-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are discussed.     

The four-loop dilaton β-function

We employ the identity derived by Curci and Paffuti relating the metric and dilaton β-functions for the bosonic σ-model to deduce the O(α′³) (four-loop) dilaton β-function from the O(α′³) (three-loop) metric β-function. We also give details of an explicit four-loop calculation in partial confirmation of our result.     

Asymptotics of a τ-function arising in the two-dimensional Ising model

The short-distance assymptotics of the -function associated to the 2-point function of the two-dimensional Ising model is computed as a function of the integration constant defined from the long-distance behavior of the -function. The result is expressible in terms of the Barnes double gamma function (equivalently, the BarnesG-function).Supported in part by the National Science Foundation, Grant No. DMS-90-01794     

A generalized Peierls–Nabarro model for kinked dislocations

We present a generalized Peierls–Nabarro model for curved dislocations incorporating directly the Peierls energies for both straight dislocations and dislocation kinks. In our model, the anisotropic elastic energy is calculated efficiently using the discrete Fourier transform on the discrete lattice sites of the slip plane, and the discreteness in both the elastic energy and the misfit energy is included. We have used our model to calculate the kink migration and nucleation energies of the 30° dislocations in silicon. The results agree well with those obtained using atomistic potentials and first principles calculations, and the experimental results.     

Shell model calculations for the allowed Gamow-Teller β-decays of light nuclei

The allowed Gamow-Teller β-decay information of Li,Be,B,C,and N isotopes under the frame work of nuclear shell model is calculated herein.Theoretical results of Q values,half-lives,excitation energies,log ft values,branching fractions,and β-delayed proton/neutron emission probabilities are tabulated and compared with experimental data.The deviations from the observations are also analyzed.The 11Be nucleus is well known for its anomaly ground state Jπ=1/2+.Thus,we compared the theoretical energy levels with the experimental data and the agreements for low excitation states are consistent.The quenching factor is also evaluated and discussed.     

Construction of the two-dimensional sine-Gordon model for β<8π

We present a rigorous renormalization group construction of the two-dimensional massless and massive quantum sine-Gordon models in finite volume for the range 0<<8. We prove analyticity in the coupling constant , which implies the convergence of perturbation theory. The field correlation functions and their generating functional are analyzed and shown to have the short distance asymptotics of the free field theory. In the massive case the bounds are uniform in volume and we also obtain uniform estimates on the long distance decay of correlations.Research supported by NSF Grant PHY-9001178Research supported by the Natural Sciences and Engineering Research Council of Canada     

Resonances and antibound states for the dressed one-dimensional δ-function potential

We calculate resonances, antibound states and two new light induced states of the dressed one-dimensional attractive δ-function potential, as function of α₀ — the free electron quiver motion amplitude in a monochromatic electromagnetic field, in the range 0<α₀<150 a.u. We describe also our method, adequate to the numerical solution of the Schrödinger equation for this particular potential.     

How much can one break chiral symmetry in the linear sigma model?

We show that the hedgehog soliton solution describing the nucleon in theSU(3) ×SU(3) linear sigma model breaks down when the pion mass becomes too large.On leave of absence from the Laboratoire de Physique Théorique, Université de Nice, parc Valrose, F-06034 Nice Cedex, France