BRST COHOMOLOGY OF THE HALL EFFECT ON THE SPHERE

Antonio L\'opez Almorox and Carlos Tejero Prieto

Key words: BRST Cohomology, Hall effect, Symplectic reduction.

1991 Math. Subject Classification: 17B81, 58F06, 58F05, 53C80.

Abstract: Symplectic reduction associated with the invariance
under rotations of Hall effect on a sphere is analyzed.
Angular momenta  are in this case irreducible second class
constraints and the subvariety of constant energy determines
a non trivial $U(1)$-principal fibre bundle over a sphere
whose radius depends on the energy and the topological charge
of the magnetic Hall field. BRST differentials are constructed
and their cohomologies are studied, giving a geometrical
interpretation of the ghost and antighost fields.
The relationship between energy and angular momenta allow us
to define a super-Poisson structure for the trajectories
with constant angular momentum but the induced  BRST charge
must be modified by a derivation of total ghost degree $-1$ in
order to obtain the BRST-operator.