141 research outputs found
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 . 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 . The only possible states correspond to . How the result
depends on the topological mass of the photon is also discussed. In the case
, the energy of the fundamental state corresponding to different choice
for the photon mass scale are found to be comprehended in the interval , corresponding to a mean
radius of the electron in the range ~cm
~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 -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
Lorentz-symmetry violation in scenarios of non-linear electromagnetic models: a preliminary inspection
In this contribution, our efforts consist in presenting and discussing the
status of a paper in progress we are working on to investigate how non-linear
electromagnetic effects couple to the parameters that signal Lorentz-symmetry
violation (LSV). Here, we realize LSV by means of a specific model, namely
Carroll-Field-Jackiw's. We set the formulation by considering a general
non-linear photonic Lagrangian (written in terms of the Lorentz-invariant
bilinears in the field-strength) that may be coupled to different operators
that carry the message of LSV. In possess of the polynomial equation expressing
the dispersion relation and the refractive index, one can find the results that
express how the (meta)material constitutive properties of the vacuum are
affected by the mixing of the parameters that measure LSV with the parameters
of the specific non-linear electrodynamic model under consideration. We expect
that our efforts might be of interest in connection with the experiments
carried out with the existing super-intense LASERs based on chirped pulse
amplification.Comment: 8 pages, no figures, Presented at the Ninth Meeting on CPT and
Lorentz Symmetry, Bloomington, Indiana, May 17-26, 202
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