Related papers: Why Are Renormalons Always In The Same Place ?
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
The sonar transform in geometric tomography maps functions on the Euclidean half-space to integrals of those functions over hemispheres centered on the boundary hyperplane. We obtain sharp $L^p$-$L^q$ estimates for this transform and new…
Fourier transformations of several functions of one and two variables are evaluated and then used to derive some integral and series identities. It is shown that certain double Mordell integrals can be reduced to a sum of products of…
The question posed in the title is answered in terms of a simple pictorial argument that is manifestly symmetric between the two functions that are Legendre transform of each other.
Inversion of Radon transforms is the mathematical foundation of many modern tomographic imaging modalities. In this paper we study a conical Radon transform, which is important for computed tomography taking Compton scattering into account.…
The star transform is a generalized Radon transform mapping a function of two variables to its integrals along "star-shaped" trajectories, which consist of a finite number of rays emanating from a common vertex. Such operators appear in…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
Within the exact renormalisation group approach, it is shown that stability properties of the flow are controlled by the choice for the regulator. Equally, the convergence of the flow is enhanced for specific optimised choices for the…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…
For the reconstruction problem, the universal representation of inverse Radon transforms implies the needed complexity of the direct Radon transforms which leads to the additional contributions. In the standard theory of generalized…
A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities,…
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
The renormalization issue of the reparameterization invariance in heavy quark effective theory and NRQCD is investigated. I argue that the renormalization of the transformation of the heavy quark field under the variation of the velocity…
We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the…
We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal…
Derivations of Borns Rule are of interest because they tell us what's connected to what in quantum mechanics if we ever need to change or modify it.
Using the background field method, we, in the large $N_f$ approximation, calculate the beta function of scalar quantum electrodynamics at the first nontrivial order in $1/N_f$ by two different ways. In the first way, we get the result by…
It is shown that a change of variable in 1-dim Schroedinger equation applied to the Borel summable fundamental solutions [Giller] is equivalent to Borel resummation of the fundamental solutions multiplied by suitably chosen…
The Quantum Chromodynamics (QCD) coupling $\alpha_s$ is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In…