Renormalized Path Integral for the Two-Dimensional Delta-Function Interaction

A path-integral approach for delta-function potentials is presented. Particular attention is paid to the two-dimensional case, which illustrates the realization of a quantum anomaly for a scale invariant problem in quantum mechanics. Our treatment is based on an infinite summation of perturbation theory that captures the nonperturbative nature of the delta-function bound state. The well-known singular character of the two-dimensional delta-function potential is dealt with by considering the renormalized path integral resulting from a variety of schemes: dimensional, momentum-cutoff, and real-space regularization. Moreover, compatibility of the bound-state and scattering sectors is shown.Comment: 26 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchange

Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Comment: 3 pages, 3 figure

Comprehensive application of a coupled-channel complex scaling method to the KbarN-piY system

We have applied the coupled-channel complex scaling method (ccCSM) to K^{bar}N-\pi Y system. One advantage of ccCSM is that resonant states as well as scattering states can be treated in the same framework. For the interactions in the system, we have constructed a meson-baryon potential-matrix by basing on the chiral SU(3) theory and respecting the K^{bar}N scattering length obtained in the Martin's analysis. For future purpose to apply it more complicated system such as K^{bar}NN, we adopt a local Gaussian form in the r-space. We have investigated both the non-relativistic (NR) and the semi-relativistic (SR) kinematics. In the SR case, two types of the potentials are obtained. To test the constructed potentials, we have calculated scattering amplitudes and searched resonances. One resonance pole, corresponding to \Lambda(1405), is found in isospin I=0 system around (1419, -20) MeV ((1425, -25) or (1419, -13) MeV) on complex-energy plane with the NR (SR) kinematics. Mean distance between meson and baryon in the resonant state is 1.3 - i0.3 fm (1.2 - i0.5 fm) for NR (SR), in which the states are treated as Gamow states. In addition, we have observed a signature of another pole in lower-energy region involving large decay width, although they are unstable against the change of scaling angle \theta. This may correspond to the lower pole of the double-pole of \Lambda(1405) discussed in literature to date.Comment: 51 pages, 17 figures, to appear in Nuclear Physics

High-Reynolds-number Batchelor-model asymptotics of a flow past an aerofoil with a vortex trapped in a cavity

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