Graded Fock--like representations for a system of algebraically interacting paraparticles

We will present an algebra describing a mixed paraparticle model, known in the bibliography as "The Relative Parabose Set (\textsc{Rpbs})". Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom $P_{BF}^{(1,1)}$, we will study a class of Fock--like representations of this algebra, dependent on a positive integer parameter p (a kind of generalized parastatistics order). Mathematical properties of the Fock--like modules will be investigated for all values of p and constructions such as ladder operators, irreducibility (for the carrier spaces) and Klein group gradings (for both the carrier spaces and the algebra itself) will be established.Comment: 4 pages, 1 ref. updated with respect to the journ. versio

Variants of bosonisation in Parabosonic algebra. The Hopf and super-Hopf structures

Parabosonic algebra in finite or infinite degrees of freedom is considered as a $\mathbb{Z}_{2}$-graded associative algebra, and is shown to be a $\mathbb{Z}_{2}$-graded (or: super) Hopf algebra. The super-Hopf algebraic structure of the parabosonic algebra is established directly without appealing to its relation to the $osp(1/2n)$ Lie superalgebraic structure. The notion of super-Hopf algebra is equivalently described as a Hopf algebra in the braided monoidal category ${}_{\mathbb{CZ}_{2}}\mathcal{M}$. The bosonisation technique for switching a Hopf algebra in the braided monoidal category ${}_{H}\mathcal{M}$ (where $H$ is a quasitriangular Hopf algebra) into an ordinary Hopf algebra is reviewed. In this paper we prove that for the parabosonic algebra $P_{B}$, beyond the application of the bosonisation technique to the original super-Hopf algebra, a bosonisation-like construction is also achieved using two operators, related to the parabosonic total number operator. Both techniques switch the same super-Hopf algebra $P_{B}$ to an ordinary Hopf algebra, producing thus two different variants of $P_{B}$, with ordinary Hopf structure.Comment: 27 pages, some typos of the journal version are corrected and a couple of references adde

Effective Monopoles within Thick Branes

The monopole mass is revealed to be considerably modified in the thick braneworld paradigm, and depends on the position of the monopole in the brane as well. Accordingly, the monopole radius continuously increases, leading to an unacceptable setting that can be circumvented when the brane thickness has an upper limit. Despite such peculiar behavior, the quantum corrections accrued -- involving the classical monopole solution -- are shown to be still under control. We analyze the monopole's peculiarities also taking into account the localization of the gauge fields. Furthermore, some additional analysis in the thick braneworld context and the similar behavior evinced by the topological string are investigated.Comment: 7 pages, 1 figur

Paraboson quotients. A braided look at Green ansatz and a generalization

Bosons and Parabosons are described as associative superalgebras, with an infinite number of odd generators. Bosons are shown to be a quotient superalgebra of Parabosons, establishing thus an even algebra epimorphism which is an immediate link between their simple modules. Parabosons are shown to be a super-Hopf algebra. The super-Hopf algebraic structure of Parabosons, combined with the projection epimorphism previously stated, provides us with a braided interpretation of the Green's ansatz device and of the parabosonic Fock-like representations. This braided interpretation combined with an old problem leads to the construction of a straightforward generalization of Green's ansatz.Comment: 33 pages, Corrected a few misprints and typos of the journal versio

Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie algebras using the parabosonic (and parafermionic) extension of the Jordan Schwinger map. The differences between the Hopf algebraic and the graded Hopf superalgebraic structure on the parabosonic algebra are discussed.Comment: 11 pages, LaTex2e fil