Related papers: Regularization of singular terms in $N\bar{N}$ pot…
We suggest a regular potential model of $N\bar{N}$ interaction without any cut-off. The effect of singular terms of OBE potential, modified by annihilation is shown to be repulsive. The experimental data for S- and P-wave scattering lengths…
We discuss the regularization of attractive singular potentials $-\alpha _{s}/r^{s}$, $s\geq 2$ by infinitesimal imaginary addition to interaction constant $\alpha_{s}=\alpha_{s}\pm i0$. Such a procedure enables unique definition of…
The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation and taking the cut-off to infinity. Inclusion of contact interactions that depend on energy as well as momentum allows…
We study the radial Schr\"odinger equation for a particle of mass $m$ in the field of a singular attractive $g^2/{r^4}$ potential with particular emphasis on the bound states problem. Using the regularization method of Beane \textit{et…
We present an abstract result on removing regularization for singular potentials which are not semibounded from below. The relation between ``right'' regularizations and ``right'' self-adjoint extensions of the perturbed Schr\"odinger…
The renormalization procedure is proved to be a rigorous way to get finite answers in a renormalizable class of field theories. We claim, however, that it is redundant if one reduces the requirement of finiteness to S-matrix elements only…
The renormalisation of NN scattering in theories with zero-range interactions is examined using a cut-off regularisation where the cut-off is taken to infinity, dimensional regularisation (DR) with minimal subtraction, and DR with…
This paper examines the role that regularization plays in the definition of the potential used in effective field theory (EFT) treatments of the nucleon-nucleon interaction. I consider $NN$ scattering in $S$-wave channels at momenta well…
Regularization and renormalization is discussed in the context of low-energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Quantum anomalies in the inverse square potential are well known and widely investigated. Most prominent is the unbounded increase in oscillations of the particle's state as it approaches the origin when the attractive coupling parameter is…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
The truncated singular value decomposition may be used to find the solution of linear discrete ill-posed problems in conjunction with Tikhonov regularization and requires the estimation of a regularization parameter that balances between…
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that combine electrical and mechanical components on a common substrate. Here, the electrostatic-elastic case is considered, where an elastic membrane is allowed…
The J-matrix method of scattering was developed to handle regular short-range potentials with applications in atomic, nuclear and molecular physics. Its accuracy, stability, and convergence properties compare favorably with other successful…
We solve the Lippman-Schwinger equation (LSE) with a kernel that includes a regular finite-range potential and additional contact terms with derivatives. We employ distorted wave theory and dimensional regularization, as proposed in Physics…
Narrowing extends term rewriting with the ability to search for solutions to equational problems. While first-order rewriting and narrowing are well studied, significant challenges arise in the presence of binders, freshness conditions and…
The observed enhancement of $p\bar p$-production near the threshold in radiative decays of $J/\psi$ and $e^+e^-$-annihilations can be explained with final state interactions among the produced $N\bar N$ system, where the enhancement is…
The shallow-water system is a standard model for long waves in shallow water. The system is hyperbolic and, for a large class of initial data, solutions develop steep gradients leading to shock formation in finite time. Since such…
I critically discuss two of the potential inconsistencies pointed out in the recent manuscript by Epelbaum, Gasparyan, Gegelia and Meissner, published in Eur. Phys.J. A54, 186 (2018). The potential inconsistencies are: (i) a possible…