Berry phase for spin--1/2 particles moving in a spacetime with torsion

Berry phase for a spin--1/2 particle moving in a flat spacetime with torsion is investigated in the context of the Einstein-Cartan-Dirac model. It is shown that if the torsion is due to a dense polarized background, then there is a Berry phase only if the fermion is massless and its momentum is perpendicular to the direction of the background polarization. The order of magnitude of this Berry phase is discussed in other theoretical frameworks.Comment: 9 pages. Some typos corrected, a discussion on propagating torsion is added, accepted for publication in Eur. Phys. J. C (2001

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)} \oplus {\rm 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 of the contracted algebras. It is shown that \Uh{\sl(2)}, \Uh{\so(4)}, and all of these contracted algebras are triangular.Comment: LaTeX, 8 page

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 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.Comment: 8 pages, LaTe

A Triangular Deformation of the two Dimensional Poincare Algebra

Contracting the $h$-deformation of \SL(2,\Real), we construct a new deformation of two dimensional Poincar\'e algebra, the algebra of functions on its group and its differential structure. It is also shown that the Hopf algebra is triangular, and its universal R matrix is also constructed explicitly. Then, we find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.Comment: 11 pages, LaTeX, Two figures upon reques