Related papers: Dimensional regularization applied to nuclear matt…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) \phi^4 scalar theory in 4-dimensions, we explictly analyze, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic…
When a nonrelativistic particle interacts with a scalar quantum field, the standard perturbation theory leads to a dependence of the energy of its ground state on an undefined parameter---"momentum cutoff"---due to the ultraviolet…
While it is usually stated that dimensional regularization (DR) has no direct physical interpretation, consensus has recently grown on the idea that it might be endowed with special physical properties that would provide the mechanism that…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
A method of cut-off regularization is proposed to evaluate vacuum corrections in nuclear matter in the framework of the Hartree approximation. Bulk properties of nuclear matter calculated by this method are a good agreement with results…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
To regularize the three-body problem, Minlos and Faddeev suggested a modification of zero-range model, which diminishes interaction at the triple-collision point. The analysis reveals that this regularization results in four alternatives…
This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…
A second-order regularity theory is developed for solutions to a class of quasilinear elliptic equations in divergence form, including the $p$-Laplace equation, with merely square-integrable right-hand side. Our results amount to the…
It is proven by explicit construction that regularization by dimensional reduction can be formulated in a mathematically consistent way. In this formulation the quantum action principle is shown to hold. This provides an intuitive and…
We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'')…
We first briefly review some aspects of the techniques of dealing with ultraviolet divergences in Feynman amplitudes in an Euclidian $D$-dimensional space-time. Next we consider compactification of a $d$-dimensional ($d\leq D$) subspace.…
So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…
We use a combination of effective field theory and the renormalization group to determine the impact of radiative corrections on the nucleon-nucleon potential and the binding energy of the deuteron. In order to do so, we present a modified…
The present lectures are a practical guide to the calculation of radiative corrections to the Green functions in quantum field theory. The appearance of ultraviolet divergences is explained, their classification is given, the…
Neural radiance fields, or NeRF, represent a breakthrough in the field of novel view synthesis and 3D modeling of complex scenes from multi-view image collections. Numerous recent works have shown the importance of making NeRF models more…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of…