39 research outputs found
Noncommutative Quantum Mechanics Viewed from Feynman Formalism
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This
proof is based on the assumption of simple commutation relations between
position and velocity. We first study a nonrelativistic particle using Feynman
formalism. We show that Poincar\'{e}'s magnetic angular momentum and Dirac
magnetic monopole are the direct consequences of the structure of the sO(3) Lie
algebra in Feynman formalism. Then we show how to extend this formalism to the
dual momentum space with the aim of introducing Noncommutative Quantum
Mechanics which was recently the subject of a wide range of works from particle
physics to condensed matter physics.Comment: 11 pages, To appear in the Proceedings of the Lorentz Workshop
"Beyond the Quantum", eds. Th.M. Nieuwenhuizen et al., World Scientific,
Singapore, 2007. Added reference
Spin Hall effect of Photons in a Static Gravitational Field
Starting from a Hamiltonian description of the photon within the set of
Bargmann-Wigner equations we derive new semiclassical equations of motion for
the photon propagating in static gravitational field. These equations which are
obtained in the representation diagonalizing the Hamiltonian at the order
, present the first order corrections to the geometrical optics. The
photon Hamiltonian shows a new kind of helicity-magnetotorsion coupling.
However, even for a torsionless space-time, photons do not follow the usual
null geodesic as a consequence of an anomalous velocity term. This term is
responsible for the gravitational birefringence phenomenon: photons with
distinct helicity follow different geodesics in a static gravitational field.Comment: 6 page
Appearance of Gauge Fields and Forces beyond the adiabatic approximation
We investigate the origin of quantum geometric phases, gauge fields and
forces beyond the adiabatic regime. In particular, we extend the notions of
geometric magnetic and electric forces discovered in studies of the
Born-Oppenheimer approximation to arbitrary quantum systems described by matrix
valued quantum Hamiltonians. The results are illustrated by several physical
relevant examples
Angular Symmetry Breaking Induced by Electromagnetic Field
It is well known that velocities does not commute in presence of an
electromagnetic field. This property implies that angular algebra symmetries,
such as the sO(3) and Lorentz algebra symmetries, are broken. To restore these
angular symmetries we show the necessity of adding the Poincare momentum M to
the simple angular momentum L. These restorations performed succesively in a
flat space and in a curved space lead in each cases to the generation of a
Dirac magnetic monopole. In the particular case of the Lorentz algebra we
consider an application of our theory to the gravitoelectromagnetism. In this
last case we establish a qualitative relation giving the mass spectrum for
dyons.Comment: 19 page
Topological Force and Torque in Spin-Orbit Coupling System
The topological force and torque are investigated in the systems with
spin-orbit coupling. Our results show that the topological force and torque
appears as a pure relativistic quantum effect in an electromagnetic field. The
origin of both topological force and torque is the Zitterbewegung effect.
Considering nonlinear behaviors of spin-orbit coupling, we address possible
phenomena driven by the topological forces.Comment: 4 page