Linear Hamiltonians on homogeneous Kähler manifolds of coherent states

Details Linear Hamiltonians on homogeneous Kähler manifolds of coherent states Linear Hamiltonians on homogeneous Kähler manifolds of coherent states

2004-08-19

arxiv.org/abs/math/0408254v1

An. Univ. Timi\c{s}oara Ser. Mat.-Inform. Vol. XXXIX (2001) 31-56

Mathematics

Differential Geometry

22 pages, LATEX2E, ams fonts, The Fifth International Workshop on Differential Geometry and Its Applications, September 18-22,

Scientific paper

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equations of motion with holomorphic polynomials coefficients. For hermitian symmetric manifolds the equations of motion are matrix Riccati equations. It is presented the simplest example of the non-symmetric space $SU(3)/S(U(1)\times U(1)\times U(1))$ where the polynomials describing the equations of motion have the maximum degree 3.

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