7,423 research outputs found
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 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 upto
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 Cabibbo-Kobayashi-Maskawa matrix, ,
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 from being moduli symmetric (i.e.
) is controlled by the small difference between two of the
eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli
symmetric depending on only three parameters. Our parametrization gives
very good fits to the available data including CP-violation. Our value of and other parameters associated with the ` unitarity
triangle' 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, , 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 . 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 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
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
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