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Real Clifford algebras for arbitrary number of space and time dimensions as well as their representations in terms of spinors are reviewed and discussed. The Clifford algebras are classified in terms of isomorphic matrix algebras of real,…
In this paper, we analyze some properties regarding singular spinors and how they are connected. The method employed here consists of mapping the spinorial structure and also the adjoint structure. Such a mathematical device is useful to…
Recent work on algebraic formulations of holographic dualities in terms of large $N$ algebras has revealed a deep connection between the properties of the associated spectral functions and the emergence of a semiclassical spacetime and…
The recent discovery of a spin-0 Brout-Englert-Higgs boson leads to further enquire about other fundamental scalars. Supersymmetric theories involve, in relation with the electroweak breaking, five such scalars at least, two charged and…
The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…
The classical model of spinning particle is analyzed in details in two versions - with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes…
The usual spinor construction from one fermion yields four irreducible representations of the Virasoro algebra with central charge $c = 1/2$. The Neveu-Schwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$ module, and the…
Recently, D. S. Kim and T. Kim have studied applications of um- bral calculus associated with p-adic invariant integrals on Zp (see [6]). In this paper, we investigate some interesting properties arising from umbral calculus. These…
Inclusion relations of metric balls defined by the hyperbolic, the quasihyperbolic, the $j$-metric and the chordal metric will be studied. The hyperbolic metric, the quasihyperbolic metric and the $j$-metric are considered in the unit ball.
The spectral properties of two special classes of Jacobi operators are studied. For the first class represented by the $2M$-dimensional real Jacobi matrices whose entries are symmetric with respect to the secondary diagonal, a new…
The symmetries provided by representations of the centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$ are known to play an important role in the spin chain models originated in the planar anti-de Sitter/conformal field theory…
In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
The quaternions form a 4-dimensional Cayley-Dickson algebra. In this paper, we introduce the Tetranacci and Tetranacci-Lucas quaternions. Furthermore, we present some properties of these quaternions and derive relationships between them.
The paper lays the foundation for the study of unimodular rows using Spin groups. We show that elementary orbits of unimodular rows (of any length $n\geq 3$) are equivalent to elementary Spin orbits on the unit sphere. (This bijection is…
The isotropic Dunkl oscillator model in the plane is investigated. The model is defined by a Hamiltonian constructed from the combination of two independent parabosonic oscillators. The system is superintegrable and its symmetry generators…
The analytical relations in position, momentum and four-dimensional spaces are established for the expansion and one-range addition theorems of relativistic complete orthonormal sets of exponential type spinor wave functions and Slater…
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of…
An effective approach is presented to produce Schrodinger-like equation for the spinor components from Dirac equation. Considering electrostatic potential as a constant value yields a second-order differential equation that is comparable…
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…