257 research outputs found
On the Geometry of the Batalin-Vilkovisky Formalism
An invariant definition of the operator of the Batalin-Vilkovisky
formalism is proposed. It is defined as the divergence of a Hamiltonian vector
field with an odd Poisson bracket (antibracket). Its main properties, which
follow from this definition, as well as an example of realization on
K\"ahlerian supermanifolds, are considered. The geometrical meaning of the
Batalin-Vilkovisky formalism is discussed.Comment: 11 pages , UGVA---DPT 1993/03--80
Multi-center MICZ-Kepler systems
We present the classical solutions of the two-center MICZ-Kepler and
MICZ-Kepler-Stark systems. Then we suggest the model of multi-center
MICZ-Kepler system on the curved spaces equipped with -invariant
conformal flat metrics.Comment: 7 pages, typos corrected, refs added. Contribution to the Proceedings
of International Workshop on Classical and Quantum Integrable systems,
24-28.01.2007, Dubna, Russi
3D Oscillator and Coulomb Systems reduced from Kahler spaces
We define the oscillator and Coulomb systems on four-dimensional spaces with
U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the
three-dimensional oscillator and Coulomb systems specified by the presence of
Dirac monopoles. We find the Kahler spaces with conic singularity, where the
oscillator and Coulomb systems on three-dimensional sphere and two-sheet
hyperboloid are originated. Then we construct the superintegrable oscillator
system on three-dimensional sphere and hyperboloid, coupled to monopole, and
find their four-dimensional origins. In the latter case the metric of
configuration space is non-Kahler one. Finally, we extend these results to the
family of Kahler spaces with conic singularities.Comment: To the memory of Professor Valery Ter-Antonyan, 11 page
Quantum oscillator on complex projective space (Lobachewski space) in constant magnetic field and the issue of generic boundary conditions
We perform a 1-parameter family of self-adjoint extensions characterized by
the parameter . This allows us to get generic boundary conditions for
the quantum oscillator on dimensional complex projective
space() and on its non-compact version i.e., Lobachewski
space() in presence of constant magnetic field. As a result, we
get a family of energy spectrums for the oscillator. In our formulation the
already known result of this oscillator is also belong to the family. We have
also obtained energy spectrum which preserve all the symmetry (full hidden
symmetry and rotational symmetry) of the oscillator. The method of self-adjoint
extensions have been discussed for conic oscillator in presence of constant
magnetic field also.Comment: Accepted in Journal of Physics
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