From Quark to Infinite Dimensionality

This article gives a overall picture of how the universe works from the likelihood that our universe is infinite dimensional at the nanometer scale of an indestructible quark. The article explains that we only can perceive for sure up to 4 dimensions of physical reality. However, the speculation in this article seems very clear that likely we are seeing activity in the 5th dimension in particle physics experimentation explaining the EPR paradox and other mysteries seen in particle physics. Finally, the article shows why the Mendeleev Chart has historically listed possible stable atoms without giving the exact number possible. The way protons and other hadrons are composed of six quarks and six antiquarks held together by gluons leads to the inevitable conclusion that only 108 stable atoms can exist. Being stable means the protons in an atom are composed of 3 quarks/antiquarks having charge 1. Recent discoveries in particle physics research demonstrates that there exists a particle named the pentaquark composed of five quarks. The article explains that pentaquarks have been identified in recent particle research. It is not known yet whether the pentaquark leads to a different proton that leads in turn to a pentaquark atom. New particle research will likely answer this question

A NOTE ON BUNDLE GERBES AND INFINITE-DIMENSIONALITY

Let (P,Y ) be a bundle gerbe over a fibre bundle Y →M. We show that if M is simply connected and the fibres of Y →M are connected and finite-dimensional, then the Dixmier–Douady class of (P,Y ) is torsion. This corrects and extends an earlier result of the first author.

$\epsilon$-convertibility of entangled states and extension of Schmidt rank in infinite-dimensional systems

By introducing the concept of $\epsilon$-convertibility, we extend Nielsen's and Vidal's theorems to the entanglement transformation of infinite-dimensional systems. Using an infinite-dimensional version of Vidal's theorem we derive a new stochastic-LOCC (SLOCC) monotone which can be considered as an extension of the Schmidt rank. We show that states with polynomially-damped Schmidt coefficients belong to a higher rank of entanglement class in terms of SLOCC convertibility. For the case of Hilbert spaces of countable, but infinite dimensionality, we show that there are actually an uncountable number of classes of pure non-interconvertible bipartite entangled states.