topological analysis has been performed on the total electron density of the two forms of ozonemolecule,c2v and d3h ,to investigate the nature of chemical bonds ,molecular structure , atomiccharges and electrical properties. while these concepts have been completely discussed usingclassical models the emphasize in this work is based on quantum theory of atoms in molecules(qtaim). because the d3...

This article is based on a talk given in Dijon for the 2000 summer school “Topological and Geometrical Methods: Applications to Dynamical Systems”. The standard definitions of the monodromy invariant for completely integrable classical systems are reviewed, and the link to the quantum monodromy observed in the joint spectrum of commuting operators is explained. The mathematical treatment relies...

In [1], a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space—or history-theory analogue—is the set of objects, Ob(Q), in a (small) category Q. The quantum states in this approach are cross-sections of a bundle A ; K[A] of Hilbert spaces over Ob(Q). The Hilbert spaces K[A], A ∈ Ob(Q), depend stron...

We study the deformation (Moyal) quantisation of gravity in both the ADM and the Ashtekar approach. It is shown, that both can be treated, but lead to anomalies. The anomaly in the case of Ashtekar variables, however, is merely a central extension of the constraint algebra, which can be “lifted”. Finally we write down the equations defining physical states and comment on their physical content....

In the Chern-Simons formulation of Einstein gravity in 2+1 dimensions the phase space of gravity is the moduli space of flat G-connections, where G is a typically non-compact Lie group which depends on the signature of space-time and the cosmological constant. For Euclidean signature and vanishing cosmological constant, G is the three-dimensional Euclidean group. For this case the Poisson struc...

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This true even for quantum in infrared. Using octonions as coordinates, we construct pre-spacetime, pre-quantum Lagrangian dynamics. We show that symmetries this space unify standard model particle physics with $SU(2)_R$ chiral gravity. The algebra octonionic yields spinor states which c...

With the rapid rise in interest in microand nano-mechanical and electromechanical devices it will soon be necessary to consider the quantum aspects of the behaviour of such mechanical devices in the same way as the development of microand nano-scale electronic devices forces us to consider quantum finite size and interference effects as well as single electron effects (Drexler 1992, Cleland & R...

In bosonic field theories the low-energy scattering of solitons that saturate Bogomol’nyi-type bounds can be approximated as geodesic motion on the moduli space of static solutions. In this paper we consider the analogous issue within the context of supersymmetric field theories. We focus our study on a class of N = 2 non-linear sigma models in d = 2 + 1 based on an arbitrary Kähler target mani...