Related papers: Exotic smoothness and particle physics
In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.
Usually, the topology of a 4-manifolds $M$ is restricted to admit a global hyperbolic structure $\Sigma\times\mathbb{R}$. The result was obtained by using two conditions: existence of a Lorentz structure and causality (no time-like closed…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
We investigate on exotic tetraquark hadrons of the kind [cs][cbar sbar] by computing their spectrum and decay modes within a constituent diquark-antidiquark model. We also compare these predictions with the present experimental knowledge.
In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…
An axiomatics for indistinguishability of elementary particles in terms of hidden variables is presented in a manner which depart from the standard approaches usually given to hidden variables. Quantum distribution functions are also…
We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.
Various ideas associated with exotic hadrons, and hadronic structure in general, are briefly reviewed.
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
A connection between differential geometry and soliton equations is discussed
After quick survey of some key results and open questions about the structure of singularities of minimal surfaces, we discuss recent work~\cite{Sim23} on singularities of stable minimal hypersurfaces, including some simplifications of the…
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…
We investigate the geometric and topological structure of equidistant decompositions of Riemannian manifolds.
The properties of exotic stars are investigated. In particular, we study objects made entirely of dark matter and we take into account intrinsic anisotropies which have been ignored so far. We obtain exact analytical solutions to the…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.
Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
The molecular picture and the constituent-quark model of exotic hadrons are reviewed, with application to the states recently discovered in the hidden-charm and hidden beauty sectors, and to other configurations.