A. Shariati

NEUTRINO OSCILLATION IN A SPACE–TIME WITH TORSION

Using Einstein–Cartan–Dirac theory, we study the effect of torsion on neutrino oscillation. We see that torsion cannot induce neutrino oscillation, but affects it whenever oscillation exists for other reasons. We show that the torsion effect on neutrino oscillation is as important as the neutrino mass effect, whenever the ratio of neutrino number density to neutrino energy is ~ 1069cm-3/eV, or the number density of the matter is ~ 1069cm-3.

Autonomous multispecies reaction-diffusion systems with more-than-two-site interactions.

Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for the closedness of the evolution equations of the n-point functions are obtained. The average numbers of the particles at each site for one species and three-site interactions, and its generalization to the more-than-three-site interactions, are explicitly obtained. Generalizations of the Glauber model in different directions, using generalized rates, generalized numbers of states at each site, and generalized numbers of interacting sites, are also investigated.

Multispecies reaction-diffusion systems

Multispecies reaction-diffusion systems, for which the time evolution equations of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time dependence of the average densities in these cases are also studied. For the general case, the large-time behavior of the average densities has also been obtained.

THE UNIVERSAL R-MATRIX FOR THE JORDANIAN DEFORMATION OF sl(2), AND THE CONTRACTED FORMS OF so(4)

We introduce a universal R-matrix for the Jordanian deformation of U(sl(2)). Using Uh(so(4))=Uh(sl(2)) ⊕ U−h(sl(2)), we obtain the universal R-matrix for Uh(so(4)). Applying the graded contractions on the universal R-matrix of Uh(so(4)), we show that there exist three distinct R-matrices for all the contracted algebras. It is shown that Uh(sl(2)), Uh(so(4)), and all of these contracted algebras are triangular.

QUANTUM REFLECTION OF MASSLESS NEUTRINOS FROM A TORSION-INDUCED POTENTIAL

In the context of the Einstein–Cartan–Dirac model, where the torsion of the space–time couples to the axial currents of the fermions, we study the effects of this quantum-gravitational interaction on a massless neutrino beam crossing through a medium with a high number density of fermions at rest. We calculate the reflection amplitude and show that a specific fraction of the incident neutrinos reflects from this potential if the polarization of the medium is different from zero. We also discuss the order of magnitude of the fermionic number density in which this phenomenon is observable, in other theoretical contexts, for example, the strong gravity regime and the effective field theory approach.

SLh(2)-Symmetric Torsionless Connections

The most general SLh(2)–symmetric torsionless linear connection is constructed. This is done based on a recently proposed definition of a linear connection in noncommutative geometry. Part of the results can be obtained by using the singular map which relates the q-plane to the h–plane. There is also a part in the covariant derivative, linearconnection, and curvature which does not have any q-analogue. It is seen that the covariant derivative of the h-plane is ‘more classical’ or ‘less quantized’ than that of the q-plane.

Equivalence Principle and Radiation by a Uniformly Accelerated Charge

We address the old question of whether or not a uniformly accelerated charged particle radiates, and consequently, if weak equivalence principle is violated by electrodynamics. We show that radiation has different meanings; some absolute, some relative. Detecting photons or electromagnetic waves is not absolute, it depends both on the electromagnetic field and on the state of motion of the antenna. An antenna used by a Rindler observer does not detect any radiation from a uniformly accelerated co-moving charged particle. Therefore, a Rindler observer cannot decide whether or not he is in an accelerated lab or in a gravitational field. We also discuss the general case.

A TRIANGULAR DEFORMATION OF THE TWO-DIMENSIONAL POINCARÉ ALGEBRA

Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincares algebra, the algebra of functions on its group and its differential structure. It is seen that these dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf algebra is triangular, and its universal R-matrix is also constructed explicitly. We then find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.

Closedness of orbits in a space with SU(2) Poisson structure

The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically symmetric potential energies, it is only the Kepler problem for which all of the bounded orbits are closed. In analogy with the case of the ordinary space, a conserved vector (apart from the angular momentum) is explicitly constructed, which is responsible for the orbits being closed. This is the analog of the Laplace-Runge-Lenz vector. The algebra of the constants of the motion is also worked out.

DIRAC THEORY ON A SPACE WITH LINEAR LIE TYPE FUZZINESS

A spinor theory on a space with linear Lie type noncommutativity among spatial coordinates is presented. The model is based on the Fourier space corresponding to spatial coordinates, as this Fourier space is commutative. When the group is compact, the real space exhibits lattice characteristics (as the eigenvalues of space operators are discrete), and the similarity of such a \emph{lattice} with ordinary lattices is manifested, among other things, in a phenomenon resembling the famous \emph{fermion doubling} problem. A projection is introduced to make the dynamical number of spinors equal to that corresponding to the ordinary space. The actions for free and interacting spinors (with Fermi-like interactions) are presented. The Feynman rules are extracted and 1-loop corrections are investigated.