Zero Energy Modes of Massless Fermions in S3R Spacetime

The Dirac-type equation on topology is worked out and the complete set of solutions in the particular physical case of the zero-energy modes of the massless field quanta is derived. Unlike the Minkowskian case, the 1/2fermionic vacua on the manifold is made of nontrivial static modes of defined chirality.     

U(1) gauge theory of the quantum hall effect

The solution of the Klein-Gordon equation for a complex scalar field in the presence of an electrostatic field orthogonal to a magnetostatic field is analyzed. Considerations concerning the quantum Hall-type evolution are presented also. Using the Hamiltonian with a self-interaction term, we obtain a critical value for the magnetic field in the case of the spontaneous symmetry breaking.     

The $$SO(3,1) \times U(1)$$-gauge invariant approach to charged bosons in relativistic magnetars

Using a perturbative method, we investigate solutions of the Klein–Gordon equations for a charged massive field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions. By imposing various conditions on the parameters, one gets the energy quantization law and simple polynomial forms of the Heun’s functions, which can be used in computing first-order transition amplitudes.     

<Emphasis Type="Italic">SO</Emphasis>(3,1)-Invariant Approach to Dipole Radiation

The aim of the present work is to revisit the theory of the dipole radiation, within an SO(3,1)-gauge invariant formulation, by solving the Maxwell equations. Thus, we obtain the two interconnected components, A _B , B=1,2, of the vector potential A, in terms of Hankel and Legendre polynomials. Finally, for the pure dipole-like radiation, the observables, regarded as phasors, the Umov–Poynting vector components and the well-known Larmor formula for the effective radiated power are explicitly derived.     

Scalar particles mass spectrum and localization on FRW branes embedded in a 5D de Sitter bulk

In this paper, we study the scalar fields evolving on a FRW brane embedded in a five-dimensional de Sitter bulk. The scale function and the warp factor, solutions of the Einstein equations, are employed in the five-dimensional Gordon equation describing the massive scalar field, whose wave function depends on the cosmic time and on the extra-dimension. We point out the existence of bounded states and find a minimum value of the effective four-dimensional mass. For the test (scalar) field envelope along the extra-dimension, we derive the corresponding Schrödinger-like equation which is formally that for the Pöschl-Teller potential. Accordingly, we have obtained the quantization law for the mass parameter of the tested scalar field.