Vector coherent state theory of the generic representations of so(5) in an so(3) basis

For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use vector coherent state techniques to develop an algorithm for constructing the matrices for arbitrary finite-dimensional irreps of the SO(5) Lie algebra in an SO(3) basis. The SO(3) subgroup of SO(5) is defined by regarding SO(5) as linear transformations of the five-dimensional space of an SO(3) irrep of angular momentum two. A need for such irreps arises in the nuclear collective model of quadrupole vibrations and rotations. The algorithm has been implemented in MAPLE, and some tables of results are presented.Comment: 20 pages, uses multirow.sty, submitted to J. Math. Phy

Coherent state triplets and their inner products

It is shown that if H is a Hilbert space for a representation of a group G, then there are triplets of spaces F_H, H, F^H, in which F^H is a space of coherent state or vector coherent state wave functions and F_H is its dual relative to a conveniently defined measure. It is shown also that there is a sequence of maps F_H -> H -> F^H which facilitates the construction of the corresponding inner products. After completion if necessary, the F_H, H, and F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H is often easier to evaluate in F_H than F^H. Thus, we obtain integral expressions for the inner products of coherent state and vector coherent state representations. These expressions are equivalent to the algebraic expressions of K-matrix theory, but they are frequently more efficient to apply. The construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it contained errors that are being correcte

Optimization of selectivity by tuning column temperatures for series-coupled capillary columns in dual-oven gas chromatographic systems

A method has been developed and evaluated for optimization of the selectivity of series-coupled capillary columns in a twin-oven gas chromatographic system in the shortest possible analysis time. The temperatures of either one or both columns were varied independently (partial optimization) or simultaneously (overall optimization), in order to separate the maximum number of sample components. The method is based upon computer-aided calculation of Kováts indices of the coupled columns by means of second and third order (polynomial) functions of the temperatures of the individual columns. The applicability and limitations of the methods are discussed and illustrated with separations of a synthetic hydrocarbon mixture of 33 components

Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations

It is shown here and in the preceeding paper (quant-ph/0201129) that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of generalizing its counterparts. In this paper, we focus on the construction of quantum models for algebraic systems with intrinsic degrees of freedom. Semi-classical partial quantizations, for which only the intrinsic degrees of freedom are quantized, arise naturally out of this construction. The quantization of the SU(3) and rigid rotor models are considered as examples.Comment: 31 pages, part 2 of two papers, published versio

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Comment: 29 pages, part 1 of two papers, published versio

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper: These are systems with an SL(2,\Rl) gauge symmetry and the complications arise because non -- compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the spectrum of the Master Constraint does not contain the point zero. However, the minimum of the spectrum is of order $\hbar^2$ which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to $\hbar$ normal ordering constants). The physical Hilbert space can then be be obtained after subtracting this normal ordering correction.Comment: 33 pages, no figure

Maximum rates of N2 fixation and primary production are out of phase in a developing cyanobacterial bloom in the Baltic Sea

Although N2-fixing cyanobacteria contribute significantly to oceanic sequestration of atmospheric CO2, little is known about how N2 fixation and carbon fixation (primary production) interact in natural populations of marine cyanobacteria. In a developing cyanobacterial bloom in the Baltic Sea, rates of N2 fixation (acetylene reduction) showed both diurnal and longer-term fluctuations. The latter reflected fluctuations in the nitrogen status of the cyanobacterial population and could be correlated with variations in the ratio of acetylene reduced to 15N2 assimilated. The value of this ratio may provide useful information about the release of newly fixed nitrogen by a cyanobacterial population. However, although the diurnal fluctuations in N2 fixation broadly paralleled diurnal fluctuations in carbon fixation, the longer-term fluctuations in these two processes were out of phase

Pathophysiological classification of chronic rhinosinusitis

BACKGROUND: Recent consensus statements demonstrate the breadth of the chronic rhinosinusitis (CRS) differential diagnosis. However, the classification and mechanisms of different CRS phenotypes remains problematic. METHOD: Statistical patterns of subjective and objective findings were assessed by retrospective chart review. RESULTS: CRS patients were readily divided into those with (50/99) and without (49/99) polyposis. Aspirin sensitivity was limited to 17/50 polyp subjects. They had peripheral blood eosinophilia and small airways obstruction. Allergy skin tests were positive in 71% of the remaining polyp subjects. IgE was<10 IU/ml in 8/38 polyp and 20/45 nonpolyp subjects (p = 0.015, Fisher's Exact test). CT scans of the CRS without polyp group showed sinus mucosal thickening (probable glandular hypertrophy) in 28/49, and nasal osteomeatal disease in 21/49. Immunoglobulin isotype deficiencies were more prevalent in nonpolyp than polyp subjects (p < 0.05). CONCLUSION: CRS subjects were retrospectively classified in to 4 categories using the algorithm of (1) polyp vs. nonpolyp disease, (2) aspirin sensitivity in polyposis, and (3) sinus mucosal thickening vs. nasal osteomeatal disease (CT scan extent of disease) for nonpolypoid subjects. We propose that the pathogenic mechanisms responsible for polyposis, aspirin sensitivity, humoral immunodeficiency, glandular hypertrophy, eosinophilia and atopy are primary mechanisms underlying these CRS phenotypes. The influence of microbial disease and other factors remain to be examined in this framework. We predict that future clinical studies and treatment decisions will be more logical when these interactive disease mechanisms are used to stratify CRS patients