Application of the coherent state formalism to multiply excited states

A general expression is obtained for the matrix element of an m-body operator between coherent states constructed from multiple orthogonal coherent boson species. This allows the coherent state formalism to be applied to states possessing an arbitrarily large number of intrinsic excitation quanta. For illustration, the formalism is applied to the two-dimensional vibron model [U(3) model], to calculate the energies of all excited states in the large-N limit.Comment: LaTeX (iopart); 10 pages; to be published in J. Phys.

Cosmic censorship of smooth structures

It is observed that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard $\R^4$. Similarly, a smooth 4-manifold homeomorphic to the product of a closed oriented 3-manifold $N$ and $\R$ and admitting a globally hyperbolic Lorentz metric is in fact diffeomorphic to $N\times \R$. Thus one may speak of a censorship imposed by the global hyperbolicty assumption on the possible smooth structures on $(3+1)$-dimensional spacetimes.Comment: 5 pages; V.2 - title changed, minor edits, references adde

A symmetry adapted approach to vibrational excitations in atomic clusters

An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be$_4$, H$_3^+$, Be$_3$ and Na$_3^+$ clusters.Comment: 8 pages with 2 tables, invited talk at `Atomic Nuclei & Metallic Clusters: Finite Many-Fermion Systems', Prague, Czech Republic, September 1-5, 199

Comment on ``Boson-realization model for the vibrational spectra of tetrahedral molecules''

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras.Comment: 9 pages Revtex, submitted February 199

A general algebraic model for molecular vibrational spectroscopy

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules.Comment: 35 pages TEX, submitted to Annals of Physics (N.Y.

A symmetry-adapted algebraic approach to molecular spectroscopy

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have identified interaction terms that were absent in previous formulations of the vibron model. The inclusion of these new interactions leads to reliable spectroscopic predictions. We illustrate the method for the D_3h triatomic molecules, H_3^+, Be_3 and Na_3, and the T_d molecules, Be_4 and CH_4.Comment: 16 pages with 4 tables, invited talk at `Symmetries in Science IX', August 6-10, 199