A direct proof of completeness of squeezed odd-number states

A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squeezed number states $D(\xi)|2m+1>; D(\xi) = \exp(({\xi}a^{\dagger2}-{\xi}^*{a^2})/2)$ is given. The proof entails evaluation of an integral involving Jacobi polynomials. This is achieved by the use of Racah identities.Comment: 6 pages, latex, no figure

Jack polynomials, generalized binomial coefficients and polynomial solutions of the generalized Laplace's equation

We discuss the symmetric homogeneous polynomial solutions of the generalized Laplace's equation which arises in the context of the Calogero-Sutherland model on a line. The solutions are expressed as linear combinations of Jack polynomials and the constraints on the coefficients of expansion are derived. These constraints involve generalized binomial coefficients defined through Jack polynomials. Generalized binomial coefficients for partitions of $k$ upto $k=6$ are tabulated.Comment: 19 pages, latex, no figures, 12 tables Minor typographical errors in some of the equations and the tables have been correcte

The Schwinger SU(3) Construction - II: Relations between Heisenberg-Weyl and SU(3) Coherent States

The Schwinger oscillator operator representation of SU(3), studied in a previous paper from the representation theory point of view, is analysed to discuss the intimate relationships between standard oscillator coherent state systems and systems of SU(3) coherent states. Both SU(3) standard coherent states, based on choice of highest weight vector as fiducial vector, and certain other specific systems of generalised coherent states, are found to be relevant. A complete analysis is presented, covering all the oscillator coherent states without exception, and amounting to SU(3) harmonic analysis of these states.Comment: Latex, 51 page

Scheme to Measure Quantum Stokes Parameters and their Fluctuations and Correlations

We propose a scheme to measure quantum Stokes parameters, their fluctuations and correlations. The proposal involves measurements of intensities and intensity- intensity correlations for suitably defined modes, which can be produced by a combination of half wave and quarter wave plates.Comment: Submitted to the Journal of Modern Optic

Parametrization of the quark mixing matrix involving its eigenvalues

A parametrization of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix, $V$, is presented in which the parameters are the eigenvalues and the components of its eigenvectors. In this parametrization, the small departure of the experimentally determined $V$ from being moduli symmetric (i.e. $|V_{ij}|=|V_{ji}|$) is controlled by the small difference between two of the eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli symmetric $V$ depending on only three parameters. Our parametrization gives very good fits to the available data including CP-violation. Our value of $\sin 2\beta\approx 0.7$ and other parameters associated with the ` unitarity triangle' $V_{11}V_{13}^{*}+V_{21}V_{23}^{*}V_{31}V_{33}^{*}=0$ are in good agreement with data and other analyses.Comment: Latex, 11 pages, no figure

Is the quark- mixing matrix moduli symmetric?

If the unitary quark- mixing matrix, $V$, is moduli symmetric then it depends on three real parameters. This means that there is a relation between the four parameters needed to parametrize a general $V$. It is shown that there exists a very simple relation involving |V_{11}|^2, |V_{33}|^2,\orh and \oet. This relation is compared with the present experimental data. It is concluded that a moduli symmetric $V$ is not ruled out.Comment: 7 pages, Latex, 1 figur

Parametrizing the mixing matrix : A unified approach

A unified approach to parametrization of the mixing matrix for $N$ generations is developed. This approach not only has a clear geometrical underpinning but also has the advantage of being economical and recursive and leads in a natural way to the known phenomenologically useful parametrizations of the mixing matrix.Comment: 8 pages, LaTe