Quantum chromodynamics through the geometry of Möbius structures

Abstract

This paper describes a rigorous mathematical formulation providing a divergence free framework for QCD and the standard model in curved space-time. The starting point of the theory is the notion of covariance which is interpreted as (4D) conformal covariance rather than the general (diffeomorphism) covariance of general relativity. It is shown how the infinitesimal symmetry group (i.e. Lie algebra) of the theory, that is su(2, 2), is a linear direct sum of su(3) and the algebra κ ∼ = sl(2, C) × u(1), these being the QCD algebra and the electroweak algebra. Fock space which is a graded algebra composed of Hilbert spaces of multiparticle states, where the particles can be fermions such as quarks and electrons or bosons such as gluons and photons, is described concretely. Algebra bundles whose typical fibers are the Fock spaces are defined. Scattering processes are associated with covariant linear maps between the Fock space fibers which can be generated by intertwining operators between the Fock spaces. It is shown how quark-quark scattering and gluon-gluon scattering are associated with kernels which generate such intertwining operators. The rest of the paper focusses on QCD vacuum polarization in order to compute and display the (1 loop) running coupling for QCD at different scales. Through an easy application of the technique called the spectral calculus the densities associated with the quark bubble and the gluon bubble are computed

Observation of different scenarios in different temperatures in small and large collision systems

“…The soft process have many choices of formalisms such as Blast wave model with Boltzmann Gibb's statistics [19][20][21][22], Blast wave model with Tsallis statistics [23][24][25][26],Tsallis pareto-type function [27], Erlang distribution [28][29][30], Scwinger mechanism [31][32][33][34], Hagedorn distribution function [35], Standard distribution [36] etc. The p T region above 3 GeV/c is contributed for the hard process and is described by Quantum chromodynamics (QCD) calculus [37][38][39] or inverse power law which is also known as Hagedron function…”

Analysis of kinetic freeze out temperature and transverse flow velocity in nucleus-nucleus and proton-proton collisions at same center of mass energy

“…The hard scattering process contributes the spectrum in wide or low+high p T range that is described by the QCD calculus [36][37][38] or the Hagedorn function [28], which is an inverse power law as shown in the function below…”