Related papers: Dimensional regularization applied to nuclear matt…
Low-energy nuclear structure and reactions can be described in a systematically improvable way using the framework of chiral effective field theory. This requires solving the quantum mechanical many-body problem with regularized nuclear…
An inverse boundary value problem for the 1+1 dimensional wave equation $(\partial_t^2 - c(x)^2 \partial_x^2)u(x,t)=0,\quad x\in\mathbb{R}_+$ is considered. We give a discrete regularization strategy to recover wave speed $c(x)$ when we are…
We illustrated via the sunset diagram that dimensional regularization 'deforms' the nonlocal contents of multi-loop diagrams with its equivalence to cut-off regularization scheme recovered only after sub-divergence were subtracted. Then we…
We study the regularization and renormalization of a finite range inverse cube potential in the two- and three-body sectors. Specifically, we compare and contrast three different regulation schemes frequently used to study few-body systems…
Non-stationary blind super-resolution is an extension of the traditional super-resolution problem, which deals with the problem of recovering fine details from coarse measurements. The non-stationary blind super-resolution problem appears…
I comment and summarize the principles underlying the Four Dimensional Regularization/Renormalization (FDR) approach to the UV and IR infinities. A few recent results are also reviewed.
We introduce a new class of effective interactions to be used within the energy-density-functional approaches. They are based on regularized zero-range interactions and constitute a consistent application of the effective-theory methodology…
A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…
A symmetry-preserving regularization procedure for dealing with the contact interaction model is proposed in this work. This regularization procedure follows a series of consistency conditions which are necessary to maintain gauge symmetry.…
Renormalization group methods can be applied to the nuclear many-body problem using the approach proposed by Shankar. We start with the two-body low momentum interaction V_{low k} and use the RG flow from the particle-hole channels to…
The utility of the non-relativistic large-charge EFT for physical systems, and neutron matter in particular, relies on controlled Schr\"odinger-symmetry breaking deformations due to scattering length and effective-range effects in the…
We study the ultraviolet problem for models of a finite-dimensional quantum mechanical system linearly coupled to a bosonic quantum field, such as the (many-)spin boson model or its rotating-wave approximation. If the state change of the…
In this paper, we study the iteration complexity of cubic regularization of Newton method for solving composite minimization problems with uniformly convex objective. We introduce the notion of second-order condition number of a certain…
Recently, deep learning based methods appeared as a new paradigm for solving inverse problems. These methods empirically show excellent performance but lack of theoretical justification; in particular, no results on the regularization…
Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data…
In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by…
Over the last decade, new developments in Similarity Renormalization Group techniques and nuclear many-body methods have dramatically increased the capabilities of ab initio nuclear structure and reaction theory. Ground and excited-state…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions…
Inverse problems are fundamental in fields like medical imaging, geophysics, and computerized tomography, aiming to recover unknown quantities from observed data. However, these problems often lack stability due to noise and…