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7 papers · 2 filters
On geometrical representation of the Jacobian in a path integral reduction problem
S. N. Storchak
The geometrical representation of the Jacobian in the path integral reduction problem which describes a motion of the scalar particle on a smooth compact Riemannian manifold with t…
Classical and quantum integrability in 3D systems
M. Gadella, J. Negro, G. P. Pronko +1
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditi…
Kepler Problem in the Constant Curvature Space
G. Pronko
We present algebraic derivation of the result of Schrödinger [1] for the spectrum of hydrogen atom in the space with constant curvature.
Quantum superintegrable system for arbitrary spin
G. Pronko
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for…
On Z-graded loop Lie algebras, loop groups, and Toda equations
Kh. S. Nirov, A. V. Razumov
Toda equations associated with twisted loop groups are considered. Such equations are specified by Z-gradations of the corresponding twisted loop Lie algebras. The classification o…
Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2
A. V. Razumov, Yu. G. Stroganov, P. Zinn-Justin
Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that wh…