Related papers: Dynamical Theory of Generalized Matrices
In the superalgebraic representation of spinors using Grassmann densities and derivatives with respect to them, a generalization of Dirac conjugation is introduced, which provides Lorentz-covariant transformations of conjugate spinors. It…
In a recent paper, we introduced a new way of treating systems of compounded angular momentum. We obtained the probability amplitudes for measurements on the systems and used these to derive the matrix treatment of compounded spin. However,…
We study solutions of the parametric set-theoretic reflection equation from an algebraic perspective by employing recently derived generalizations of the familiar shelves and racks, called parametric (p)-shelves and racks. Generic…
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…
The centralizer algebra of a matrix consists of those matrices that commute with it. We investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
In this paper we extend the idea of integration to generic algebras. In particular we concentrate over a class of algebras, that we will call self-conjugated, having the property of possessing equivalent right and left multiplication…
Spinorial methods have proven to be a powerful tool to study geometric properties of spin manifolds. Our aim is to continue the spinorial study of manifolds that are not necessarily spin. We introduce and study the notion of $G$-invariance…
We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second class constraints the Dirac brackets of the proposed theory represent the commutation relations for…
We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…
In this letter we present a theorem on the dynamics of the generalized Hubbard models. This theorem shows that the symmetry of the single particle Hamiltonian can protect a kind of dynamical symmetry driven by the interactions. Here the…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We propose a general action describing the dynamics of lightlike (LL) p-branes in any odd (p+1) world-volume dimensions. Next, we consider self-consistent coupling of \textsl{LL}-membranes (p=2) to D=4 Einstein-Maxwell system plus a D=4…
Several major open problems in cosmology, including the nature of inflation, dark matter, and dark energy, share a common structure: they involve spacetime-filling media with unknown microphysics, and can be probed so far only through their…
We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex…
A classical problem in dynamical systems is to measure the complexity of a map in terms of their orbits. One of the main tools we have to achieve this goal is entropy. However, many interesting families of dynamical systems have every…
We present a geometrical inspired study of the dynamics of $Dp$-branes. We focus on the usual nonpolynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize…
All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli)…
An overview of dynamical systems in accelerator physics is presented with a suggestion of a few issues to be addressed. Also mentioned are a few possible developments in the future. Technical details supporting the views are not presented.