arXiv subjects

D. A. Kalinin

Publications and source records attributed to D. A. Kalinin.

3 recordsLinked to original sources

arXiv1997

Large Quantum mechanics in curved space and quantization of polynomial Hamiltonians

The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme are developed. These investigations are applied to quantization of the particle Hamiltonian in an appropriate curved space-time. As an example the energy eigenvalues in Einstein universe are calculated. In the last sections o the paper approximation for small values of momenta of the results previously obtained is considered as well as quantization of polynomial Hamiltonians of general type is discussed.

gr-qc↗

arXiv1996

Hamilton dynamics and $H$-planar curves

Hamilton flows on Kähler manifold for which all trajectories are $H$-planar curves (complex analog of geodesics) are considered. These flows are called $H$-planar. The equation which has to obey the Hamiltonian of $H$-planar Hamilton flow is received and the method of finding general solution of this equation is proposed. Trajectories of charged particles in magnetic fields of special form on Kähler manifolds of constant holomorphic sectional curvature are studied. Using the fact that Kähler manifolds of constant holomorphic sectional curvature admit $H$-projective mapping on flat space the equation of particle motion is reduced to an ordinary differential equation of second order.

dg-ga↗

arXiv1995

Quantization of Kähler manifolds admitting $H$-projective mappings

We discuss the quantization of mechanical systems for which the Hamiltonian vector fields of observables form the deformation of $n$-dimensional oscilator algebra. Because of this fact these systems can be considered as "deformations" of the harmonic oscillator. The set of abovementioned mechanical systems are realized at the classical level in the form of Kähler manifolds of constant holomorphic curvature. Such mechanical systems are quantized later with the help of the geometric quantization approach. We also discuss the quantization of more general Kähler manifolds (not necessarily of constant holomorphic curvature) admitting $H$-projective mappings.

dg-ga↗