Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group $Z_{n}$ of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group $D_{n}$ -- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group $Z_{n}$ of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group $D_{n}$ -- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.

Feb 19, 20070 citations

Quantum kinematics and geometry

Mario Schönberg

Il Nuovo CimentoFeb 1, 195725 citations

Quantum kinematics and the Lie group structure of non-Abelian quantum mechanics

Jorge Krause

A formalism of quantum kinematics which rests on the regular representation of a Lie group is proposed. This representation leads to explicit canonical commutation relations for non-Abelian dynamical variables which, together with the Lie algebra, define the kinematic algebra. Generalised equations of motion for the group-parameter-dependent operators, as well as generalised wave equations, are introduced over the group manifold considered as a background arena. The formalism proposed affords a method of geometric quantisation stemming directly from the observed symmetries of a system.A formalism of quantum kinematics which rests on the regular representation of a Lie group is proposed. This representation leads to explicit canonical commutation relations for non-Abelian dynamical variables which, together with the Lie algebra, define the kinematic algebra. Generalised equations of motion for the group-parameter-dependent operators, as well as generalised wave equations, are introduced over the group manifold considered as a background arena. The formalism proposed affords a method of geometric quantisation stemming directly from the observed symmetries of a system.

Journal of Physics A Mathematical and GeneralJun 21, 198517 citations

Quantum kinematics and geometric quantization

Zhao Qiang

Journal of Geometry and PhysicsDec 1, 19962 citations

Our previous work on quantum kinematics and coherent states over finite configuration spaces is extended: the configuration space is, as before, the cyclic group

Z_{n}

of arbitrary order n=2,3,..., but as its symmetry group a larger group -- the non-Abelian dihedral group

D_{n}

-- is taken. The corresponding group related coherent states are constructed and their overcompleteness proved. Our approach based on geometric symmetry can be used as a kinematic framework for matrix methods in quantum chemistry of ring molecules.