34 research outputs found
Construction of a photon position operator with commuting components from natural axioms
A general form of the photon position operator with commuting components
fulfilling some natural axioms is obtained. This operator commutes with the
photon helicity operator, is Hermitian with respect to the Bialynicki-Birula
scalar product and defined up to a unitary transformation preserving the
transversality condition. It is shown that, using the procedure analogous to
the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac
magnetic monopole, the photon position operator can be defined by a flat
connection in some trivial vector bundle over . This observation enables us to reformulate quantum mechanics of
a~single photon on .Comment: 19 pages, some corrections, to appear in Phys. Rev.
Anyons, group theory and planar physics
Relativistic and nonrelativistic anyons are described in a unified formalism
by means of the coadjoint orbits of the symmetry groups in the free case as
well as when there is an interaction with a constant electromagnetic field. To
deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell
groups.Comment: 22 pages, journal reference added, bibliography update
Quantization on a 2-dimensional phase space with a constant curvature tensor
Some properties of the star product of the Weyl type (i.e. associated with
the Weyl ordering) are proved. Fedosov construction of the *-product on a
2-dimensional phase spacewith a constant curvature tensor is presented.
Eigenvalue equations for momentum p and position q on a 2-dimensional phase
space with constant curvature tensors are solved.Comment: 33 pages, LaTeX, Annals of Physics (2003