54,704 research outputs found
Supersymmetric methods in the traveling variable: inside neurons and at the brain scale
We apply the mathematical technique of factorization of differential
operators to two different problems. First we review our results related to the
supersymmetry of the Montroll kinks moving onto the microtubule walls as well
as mentioning the sine-Gordon model for the microtubule nonlinear excitations.
Second, we find analytic expressions for a class of one-parameter solutions of
a sort of diffusion equation of Bessel type that is obtained by supersymmetry
from the homogeneous form of a simple damped wave equations derived in the
works of P.A. Robinson and collaborators for the corticothalamic system. We
also present a possible interpretation of the diffusion equation in the brain
contextComment: 14 pages, 1 figur
Majorana neutrino oscillations in vacuum
In the context of a type I seesaw scenario which leads to get light
left-handed and heavy right-handed Majorana neutrinos, we obtain expressions
for the transition probability densities between two flavor neutrinos in the
cases of left-handed and right-handed neutrinos. We obtain these expressions in
the context of an approach developed in the canonical formalism of Quantum
Field Theory for neutrinos which are considered as superpositions of
mass-eigenstate plane waves with specific momenta. The expressions obtained for
the left-handed neutrino case after the ultra-relativistic limit is taking lead
to the standard probability densities which describe light neutrino
oscillations. For the right-handed neutrino case, the expressions describing
heavy neutrino oscillations in the non-relativistic limit are different respect
to the ones of the standard neutrino oscillations. However, the right-handed
neutrino oscillations are phenomenologically restricted as is shown when the
propagation of heavy neutrinos is considered as superpositions of
mass-eigenstate wave packets.Comment: 25 pages, abstract changed, two sections added, some references adde
Contractions, Hopf algebra extensions and cov. differential calculus
We re-examine all the contractions related with the
deformed algebra and study the consequences that the contraction process has
for their structure. We also show using
as an example that, as in the undeformed case, the contraction may generate
Hopf algebra cohomology. We shall show that most of the different Hopf algebra
deformations obtained have a bicrossproduct or a cocycle bicrossproduct
structure, for which we shall also give their dual `group' versions. The
bicovariant differential calculi on the deformed spaces associated with the
contracted algebras and the requirements for their existence are examined as
well.Comment: TeX file, 25 pages. Macros are include
- β¦