Related papers: Symmetries and wavelets
The purpose of this paper is to articulate an observation that many interesting type of wavelets (or coherent states) arise from group representations which are not square integrable or vacuum vectors which are not admissible. This extends…
The contributions to the deep inelastic scattering structure function which arise from emission of zero, one, two or three resolvable gluons and any number of unresolvable ones are computed to order ${\bar \alpha}_{S}^{3}$. Coherence…
Theory of laminated turbulnece includes continuous layer of turbulence (statistical description, kinetic equations, Zakharov-Kolmogorov spectra, etc) AND discrete layer of turbulence (isolated groups of interacting waves, no…
We present a detailed analysis of the symmetry properties of a four-quark wave function and its solution by means of a variational approach for simple Hamiltonians. We discuss several examples in the light and heavy-light meson sector.
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
The continuous wavelet transform has become a widely used tool in applied science during the last decade. In this article we discuss some generalizations coming from actions of closed subgroups of $\mathrm{GL}(n,\mathbb{R})$ acting on…
Quantum field theories can exhibit various generalized symmetry structures, among which higher-group symmetries and non-invertible symmetry defects are particularly prominent. In this work, we explore a new general scenario in which these…
The branching processes in parton showers are studied in perturbative QCD for both quark and gluon jets. The emphasis is on the nature of fluctuations of both the parton multiplicities and the spatial patterns of the final states. Effective…
The chiral and heavy quark symmetries of QCD are reviewed. These symmetries are used to predict some low-momentum properties of hadrons containing a single heavy quark. (Lectures given at the CCAST Symposium on Particle Physics at the Fermi…
In this paper we consider a singular wave equation with distributional and more singular non-distributional coefficients and develop tools and techniques for the phase-space analysis of such problems. In particular we provide a detailed…
In this paper novel classes of 2-D vector-valued spatial domain wavelets are defined, and their properties given. The wavelets are 2-D generalizations of 1-D analytic wavelets, developed from the Generalized Cauchy-Riemann equations and…
I review the basics of perturbative QCD, including infrared divergences and safety, collinear and $k_T$ factorization theorems, and various evolution equations and resummation techniques for single- and double-logarithmic corrections. I…
QCD jets, produced copiously in heavy-ion collisions at LHC and also at RHIC, serve as probes of the dynamics of the quark-gluon plasma (QGP). Jet fragmentation in the medium is interesting in its own right and, in order to extract…
A general discussion is presented of the possible symmetries responsible for confinement of color and of their evidence in lattice simulations. The consequences on the phase diagram of $QCD$ are also analyzed.
Within the framework of light-cone quantisation we derive the complete and exact overlap representation of skewed parton distributions for unpolarised and polarised quarks and gluons. Symmetry properties and phenomenological applications…
The robustness of two widespread multifractal analysis methods, one based on detrended fluctuation analysis and one on wavelet leaders, is discussed in the context of time-series containing non-uniform structures with only isolated…
The class of generalized shearlet dilation groups has recently been developed to allow the unified treatment of various shearlet groups and associated shearlet transforms that had previously been studied on a case-by-case basis. We consider…
The observation of quark and gluon jets has played a crucial role in establishing Quantum Chromodynamics [QCD] as the theory of the strong interactions within the Standard Model of particle physics. The jets, narrowly collimated bundles of…
Wavelets offer significant advantages for the analysis of problems in quantum mechanics. Because wavelets are localized in both time and frequency they avoid certain subtle but potentially fatal conceptual errors that can result from the…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…