Related papers: Cutoff regulators in chiral nuclear effective fiel…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
We regularize in a continuous manner the path integral of QED by construction of a non-local version of its action by means of a regularized form of Dirac's $\delta$ functions. Since the action and the measure are both invariant under the…
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example…
In a previous companion paper [arXiv:0712.3532], we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators which have been used in the extra-dimension…
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…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
Gravity can be considered as an effective quantum field theory with reliable, but limited predictions. Though the influence of gravity on gauge and other interactions of elementary particles is still an open question. We calculate the…
We review our work on computations of the quantum corrections to the mass and the central charge of the susy kink. For the mass corrections, we find that the widely used momentum cut-off scheme gives an incorrect result, but we deduce…
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
The paper is devoted to the three-loop renormalization of the effective action for a two-dimensional non-linear sigma model using the background field method and a cutoff regularization in the coordinate representation. The coefficients of…
Stable reduction methods will be important in the evaluation of high-order perturbative diagrams appearing in QCD and mixed QCD-electroweak radiative corrections at the LHC. Differential reduction techniques are useful for relating…
We consider QED in a constant axial vector background (\AE ther). Further Lorentz invariance violations (LIV) might occur owing to radiative corrections. The phenomenology of this model is studied, clarifying issues related to the various…
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
Most calculations of quantum corrections in supersymmetric theories are made with the dimensional reduction, which is a modification of the dimensional regularization. However, it is well known that the dimensional reduction is not…
We apply a novel background independent regularization scheme, the $N$-cutoffs, to self-consistently quantize scalar and metric fluctuations on the maximally symmetric but non-compact hyperbolic space. For quantum matter fields on a…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of…
Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron…
During the past two decades, chiral effective field theory has evolved into a powerful tool to derive nuclear forces from first principles. Nearly all two-nucleon interactions have been worked out up to sixth order of chiral perturbation…
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…
We discuss the current status of chiral effective field theory in the three-nucleon sector and present selected results for nucleon-deuteron scattering observables based on semilocal momentum-space-regularized chiral two-nucleon potentials…