Related papers: Scattering Theory with Path Integrals
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
Path-integral for theories with degenerate vacua is investigated. The origin of the non Borel-summability of the perturbation theory is studied. A new prescription to deal with small coupling is proposed. It leads to a series, which at low…
Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole…
In recent years, we have established the iteration theory of the index for symplectic matrix paths and applied it to periodic solution problems of nonlinear Hamiltonian systems. This paper is a survey on these results.
The paper presents a method for calculation of non-spherical particle T-matrices based on the volume integral equation and the spherical vector wave function basis, and relies on the Generalized Source Method rationale. The developed method…
This paper introduces new asymptotic analysis used to derive the set of simplified nonclassical $P_N$ equations with anisotropic scattering.
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…
The cvariant path integral quantization of the theory of the scalar and spinor particles interacting through the abelian and non-Abelian Chern-Simons gauge fields is carried out and is shown to be mathematically ill defined due to the…
We reformulate the Casimir force in the presence of a non-trivial background. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials take place when a…
We give a brief survey for the recent development of inverse scattering theory on non-compact Riemannian manifolds. The main theme is the reconstruction of the manifold and the metric from the scattering matrix.
The S-matrices corresponding to PT-symmetric \rho-perturbed operators are defined and calculated by means of an approach based on an operator-theoretical interpretation of the Lax-Phillips scattering theory.
The closed-form $T$ matrices in the $^3S_1$$-$$^3D_1$ channels of EFT($\not/!/!/pi$) for $NN$ scattering with the potentials truncated at order $\mathcal{O}(Q^4)$ are presented with the nonperturbative divergences parametrized in a general…
We calculate the conductance of tubular-shaped nanowires having many potential scatterers at random positions. Our approach is based on the scattering matrix formalism and our results analyzed within the scaling theory of disordered…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
The cross section of elastic electron-proton scattering taking place in an electron gas is calculated within the Closed Time Path method. It is found to be the sum of two terms, one being the expression in the vacuum except that it involves…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized P\"oschl-Taylor potential, is calculated explicitly by considering the asymptotic behavior of the…
In this work, the transition matrix elements for inelastic electron--electron scattering are investigated. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in…
Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…
We study the convergence in $L^2$ of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in Physics and Chemistry, the approximate propagators considered here…