Konstantinos Kanakoglou

Mass hierarchy, mass gap and corrections to Newton’s law on thick branes with Poincaré symmetry

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with

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

m^2\ge 0

Mass hierarchy and mass gap on thick branes with Poincare symmetry

m2≥0, in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza–Klein (KK) excitations and to analytically compute the corrections to Newton’s law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall–Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken–Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar–tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

Ladder Operators, Fock-Spaces, Irreducibility and Group Gradings for the Relative Parabose Set Algebra

The mathematical structure of a mixed paraparticle system ( co bining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be describe d for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it wil l be shown that these realizations possess the valuable representation-theoretic property o f transferring invariably the super-Hopf structure. Finally two classes of virtual applications wil l be outlined: The first is of interest for both mathematics and mathematical physics and deals with th e representation theory of infinite dimensional Lie superalgebras, while the second is of inter es in theoretical physics and has to do with attempts to determine specific classes of solutions of t he Skyrme model.The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation‐theoretic property of transferring invariably the super‐Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, while the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.

Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras

We will present and study an algebra describing a mixed paraparticle model, known in the bibliography as The Relative Parabose Set (RPBS). Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom P(1,1)BF, we will construct a class of Fock–like representations of this algebra, dependent on a positive 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 -gradings (for both the carrier spaces and the algebra itself) will be established.

On a class of Fock-like representations for Lie Superalgebras

We present a preliminary attempt to establish the existence of hidden nonlinear symmetries of the SU(N) Skyrme model which could, in principle, lead to the further integration of the system. An explicit illustration is given for the SU(2) symmetry group.