Axiomatic Local Metric Derivatives for Low-Level Fractionality with Mittag-Leffler Eigenfunctions

In this contribution, we build up an axiomatic local metric derivative that exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level fractionality, whenever the order parameter is close to $1$. This version of deformed or metric derivative may be a possible alternative to the versions by Jumarie and the inappropriately so-called local fractional derivative also based on the Jumarie's approach. With rules similar to the classical ones, but with a solid axiomatic basis in the limit pointed out here, we present our results and some comments on the limits of validity for the controversial formalism found in the literature of the area.Comment: 5 page

Effects on the Non-Relativistic Dynamics of a Charged Particle Interacting with a Chern-Simons Potential

The hydrogen atom in two dimensions, described by a Schr\"odinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$. The only possible states correspond to $l=0$. How the result depends on the topological mass of the photon is also discussed. In the case $n=1$, the energy of the fundamental state corresponding to different choice for the photon mass scale are found to be comprehended in the interval $-3,5 \times 10^{-3} eV \leq E \leq -9,0 \times 10^{-2} eV$, corresponding to a mean radius of the electron in the range $(5.637 \pm 0.005) \times 10^{-8}$~cm $\leq \leq (48.87 \pm 0.03) \times 10^{-8}$~cm. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.Comment: 6 pages, 5 figure

A Discussion on Massive Gravitons and Propagating Torsion in Arbitrary Dimensions

In this paper, we reassess a particular $R^{2}$-type gravity action in D dimensions, recently studied by Nakasone and Oda, taking now torsion effects into account. Considering that the vielbein and the spin connection carry independent propagating degrees of freedom, we conclude that ghosts and tachyons are absent only if torsion is non-propagating, and we also conclude that there is no room for massive gravitons. To include these excitations, we understand how to enlarge Nakasone-Oda's model by means of explicit torsion terms in the action and we discuss the unitarity of the enlarged model for arbitrary dimensions.Comment: 11 page

Non-Linear Supersymmetric σ\sigma -Models and their Gauging in the Atiyah-Ward Space-Time

We present a supersymmetric non-linear \s-model built up in the $N=1$ superspace of Atiyah-Ward space-time. A manifold of the K\"ahler type comes out that is restricted by a particular decomposition of the K\"ahler potential. The gauging of the \s-model isometries is also accomplished in superspace.Comment: 15 pages, Latex, no figure