Critical dimension of Spectral Triples
It is open the possibility of imposing requisites to the quantisation of Connes' Spectral Triples in such a way that a critical dimension D=26 appears.
physics.gen-ph↗
arXiv subjects
Alejandro Rivero
Publications and source records attributed to Alejandro Rivero.
The 115 GeV signal from nuclear physics
According standard models of nuclei, steepest variations of binding energy at the drip lines should happen for nuclear masses of 45, 68, 92, 115, 175 and 246 GeV. We explore the coincidence of these masses with another ones from well known HEP research and we wonder how much, of it, is an experimental measurement coming from low energy research.
hep-ph↗
Distance to the drip lines
It can be found that with the adequate measure, the beta stability line is equidistant from neutron and proton drip lines. We explore this fact and its predictive potentiality in the simplest case, the classic liquid drop formula.
nucl-th↗
Standard Model Masses and Models of Nuclei
We note an intriguing coincidence in nuclear levels, that the subshells responsible for doubly magic numbers happen to bracket nuclei at the energies of the Standard Model bosons. This could show that these bosons actually contribute to the effective mesons of nuclear models.
nucl-th↗
Democritus as Taoist
While similarities do naturally exist between tao and other philosophical systems, for the specific case of Democritus we can argue also the chronological parallels, the parallels in the posterior development (alchemy and mathematics) and the textual parallelism.
physics.hist-ph↗
Flashes of noncommutativity
Noncommutativity lays hidden in the proofs of classical dynamics. Modern frameworks can be used to bring it to light: *-products, groupoids, q-deformed calculus, etc.
math.HO↗
A Short Lecture on Divergences
We present some clues to the study of the renormalization group, at graduate level, as well as some bibliographical pointers to classical resources. Just the kind of things one had liked to hear when starting to study the subject.
hep-th↗
Around Poincare duality, in discrete spaces
We walk out the landscape of K-theoretic Poincare Duality for finite algebras. It paves the way to get continuum Dirac operators from discrete noncommutative manifolds.
hep-th↗
Discrete spectral triples converging to dirac operators
We exhibit some series of discrete spectral triples converging to the canonical spectral triple of a finite dimensional manifold. Thus the non-go theorem of Goekeler and Schuecker is reasonably bypassed.
math-ph↗
Lessons from Numerical Analysis
It is reviewed how Renormalization Group, species doubling and CKM mixing are known to appear in numerical analysis: Butcher group, parasitic solutions and higher order methods
hep-th↗
Rhythmos, Diathige, Trope
It is argued that properties of Democritus' atoms parallel those of volume forms in differential geometry. This kind of atoms has not "size" of finite magnitude. ----- Se arguye que las propiedades de los atomos de Democrito son paralelas a las de sus formas de volumen en geometria diferencial. Este tipo de atomos no tiene tamanno de magnitud finita.
physics.hist-ph↗
Dream of a Christmas lecture
We recall the origins of differential calculus from a modern perspective. This lecture should be a victory song, but the pain makes it to sound more as an oath for vendetta, coming from Syracuse two milenia before.
physics.soc-ph↗
Connes' Tangent Groupoid and Strict Quantization
We address one of the open problems in quantization theory recently listed by Rieffel. By developping in detail Connes' tangent groupoid principle and using previous work by Landsman, we show how to construct a strict, flabby quantization, which is moreover an asymptotic morphism and satisfies the reality and traciality constraints, on any oriented Riemannian manifold. That construction generalizes the standard Moyal rule. The paper can be considered as an introduction to quantization theory from Connes' point of view.
math.DG↗
Some conjectures looking for a NCG theory
It is pointed out that ambiguities in the regularization of actions with second derivatives seem to happen with the same multiplicity that the standard model of elementary particles
hep-th↗
A short derivation of Feynman formula
The complex exponential weighting of Feynman formalism is seen to happen at the classical level. (Finiteness of) Feynman path integral formula is suspected then to appear as a consistency condition for the existence of certain Dirac measures over functional spaces.
quant-ph↗
Introduction to the Tangent Grupoid
We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.
dg-ga↗
Renormalization in 1D Quantum Mechanics: contact interactions
We build a toy model of the Wilson-Kogut renormalization group in one dimensional Quantum Mechanics. With it, we show how the RG flow in the space of 1-D S matrices of finite range defines, as renormalized interactions, the known four parametric set of contact interactions, thus providing a suitable framework for its study.
hep-th↗