Suemi Rodríguez-Romo

Multivectorial representation of Lie groups

In vector spaces of dimensionn=p+q a multivector (Clifford) algebraC(p, q) can be constructed. In this paper a multivectorC(p, q) representation, riot restricted to the bivector subalgebraC2(p, q), is developed for some of the Lie groups more frequently used in physics. This representation should be especially useful in the special cases of (grand) unified gauge field theories, where the groups used do not always have a simple tensor representation.

A multivectorial Dirac equation

The multivectorial generalization of the Cartan map, for C(1,3) space‐time Clifford algebra and an arbitrary gauge group in an isotopic space, is applied to the standard Dirac equation to generate the multivectorial Dirac equation. Using both geometrical and physical reasoning, a particular case discussed by Reifler and Morris [J. Math. Phys. 26, 2059 (1985)] is projected from the general multivectorial Dirac equation, to discuss the properties and limitations associated to their quaternion model. The use of the general multivectorial Dirac equation, which can be defined on any space‐time manifold, is also illustrated.

Multivectorial generalization of the Cartan map

A multivectorial generalization of the spinors to vectors Cartan map is constructed, with space‐time as a base space, constructed from spinors (Dirac spinors and spinors pairs being particular cases) onto a multivector space with two internal symmetries: one of them is the fundamental space‐time Clifford group C(1,3) and the other an ‘‘isotopic space’’ (in multivectorial representation) related with the more common gauge groups. The algebraic properties of this map and of the operators representing observables are studied. The inversion map is also presented. The quaternion projection of the map is shown as are its properties and its mathematical and physical meaning. The procedure presented here is compared with other spinor‐vector maps used in the literature.

Oscillations in the kinetics of ethylcyanoacrylate nanoparticles intended as skin drug carriers

Ethylcyanoacrylate nanoparticles (40–100 nm) were synthesized to act as potential skin drug carriers. A novel multiscale non-linear model, based on an oscillatory mechanism, which includes polymerization, de-polymerization, re-polymerization and cluster dynamics, is shown to fit the kinetics experimental data and it is used to estimate the amount of potentially histotoxic by-products (i.e. residual monomers or very low molecular weight oligomers).

Some Quantum-like Hopf Algebras which Remain Noncommutative when q = 1

Starting with only three of the six relations defining the standard (Manin) GLq(2), we try to construct a quantum group. The antipode condition requires some new relations, but the process stops at a Hopf algebra with a Birkhoff–Witt basis of irreducible monomials. The quantum determinant is group-like but not central, even when q = 1. So, the two Hopf algebras constructed in this way are not isomorphic to the Manin GLq(2), all of whose group-like elements are central. Analogous constructions can be made starting with the Dipper–Donkin version of GLq(2), but these turn out to be included in the two classes of Hopf algebras described above.

Actions of GLq (2,C) on C(1,3) and its four dimensional representations

A complete classification is given of all inner actions on the Clifford algebra C(l,3) defined by representations of the quantum group GLq (2,C)qm ≠1, which are not reduced to representations of two commuting “q-spinors”. As a consequence of this classification it is shown that the space of invariants of every GLq (2,C)-action of this type, which is not an action of SLq (2,C), is generatedby 1 and the value of the quantum determinant for the given representation.

Geometrical content of the Fierz identities

The (generalized) Fierz identities are shown to reduce to a single equation, a relation between the elements of a multivector Clifford algebra. For this purpose we use a multivectorial generalization of the spinors to vectors Cartan’s map. The method is put in a general form such that the vectors correspond to spacetime as a base space and isotopic symmetries, represented as a multivector group, are also included. A particular case is the representation of spacetime by its even part Clifford algebra only, through quaternions. This subalgebra is projected and analyzed.

Implementation of the boundary element method for detecting defects by transient thermography on an aluminum plate

This paper deals with the application of a numerical method to a non-destructive testing, describing the thermal behavior of surface flaws. This article was focused only to the two-dimensional case by solving the overall heat transfer model and applying boundary element method (BEM), to obtain the temperature variation versus time for different areas of the sample surface. The study of the changes in the temperature and the cooling profiles of the flow of heat energy through a material, interpreted for damage in the material, shows thermal conductivity as a criterion in locating damage by the thermographic technique and the computational BEM. Transient thermography was employed for the inspection of defects in an aluminum homogeneous plate (no damage) and on an heterogeneous plate (i.e., simulating damage). The results from the simulation are compared with experimental values found in the literature and show a good agreement.

On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras

We deal with some matters needed to construct concrete left Hopf algebras for inhomogeneous quantum groups produced as noncommutative symmetries of fermionic and bosonic creation/annihilation operators. We find a map for the bidimensional fermionic case, produced as in Manins [Quantum Groups and Non-commutative Hopf Geometry (CRM Univ. de Montreal, 1988)] seminal work, named preantipode that fulfills all the necessary requirements to be left but not right on the generators of the algebra. Due to the complexity and importance of the full task, we consider our result as an important step that will be extended in the near future.

2D massless QED Hall half-integer conductivity and graphene

Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system C-non-invariant under fermion–antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature, the main features of the quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to e2/h for the Hall conductivity. For typical values of graphene the plateaus of the Hall conductivity are also reproduced.