Related papers: Mathematica and Fortran programs for various analy…
We consider the order parameter $u=\left<{\rm Tr}\phi^2\right>$ as function of the running coupling constant $\tau \in \mathbb{H}$ of asymptotically free $\mathcal{N}=2$ QCD with gauge group $SU(2)$ and $N_f\leq 3$ massive hypermultiplets.…
The traditional approach for studying the physics of the strong interactions employs a basic computational construct originally proposed by Wilson in the 1970s. Over the years additional enhancements have been added to this formulation to…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do…
Using all available data on the deep-inelastic cross-sections at HERA at x<0.01, we look for geometric scaling of the form \sigma^{\gamma^*p}(\tau) where the scaling variable \tau behaves alternatively like \log(Q^2)-\lambda Y, as in the…
In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the $\mathcal{N}=4$ super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling…
Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the…
Quantum chromodynamics, most commonly referred to as QCD, is a relativistic quantum field theory for the strong interaction between subatomic particles called quarks and gluons. The most systematic way of calculating the strong interactions…
It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties,and contain in particular IR generated ghost poles and cuts. As an outcome the rigorous background perturbation theory is…
In recent times, three-dimensional (3D) metamaterials have undergone a revolution driven mainly by the popularization of 3D-printing techniques, which has enabled the implementation of modern microwave and photonic devices with advanced…
We construct a non Abelian model for SU(2) QCD in Euclidean three-dimensional spacetime and study its different phases. The model contains a center vortex sector coupled to a dual effective field encoding information about how the vortices…
Quantum-dot Cellular Automata (QCA) may offer a viable alternative of traditional transistor-based technology at the nanoscale. When modeling a QCA circuit, the number of degrees of freedom necessary to describe the quantum mechanical state…
A manifestly Lorentz-covariant calculus based on two matrix-coordinates and their associated derivatives is introduced. It allows formulating relativistic field theories in any even-dimensional spacetime. The construction extends a…
We present a complete set of Fortran 90 modules that can be used to write very compact, efficient, and high level QCD programs. The modules define fields (gauge, fermi, generators, complex, and real fields) as abstract data types, together…
I construct "fake algebraic curves" in $Cp^2$. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset Cp^2$ homeomorphic to a non-singular…
We construct an associative differential algebra on a two-parameter quantum plane associated with a nilpotent endomorphism $d$ in the two cases $d^{2}=0$ and $d^3=0$ $(d^2\neq 0).$ The correspondent curvature is derived and the related non…
We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group with some emphasis on the exact solutions of the RG…
In this work the determination of low-energy bound states in Quantum Chromodynamics is recast so that it is linked to a weak-coupling problem. This allows one to approach the solution with the same techniques which solve Quantum…
We present an approach to the spectrum and analytic functional calculus for quaternionic linear operators, following the corresponding results concerning the real linear operators. In fact, the construction of the analytic functional…