6,634 research outputs found
The Heine-Stieltjes correspondence and a new angular momentum projection for many-particle systems
A new angular momentum projection for systems of particles with arbitrary
spins is formulated based on the Heine-Stieltjes correspondence, which can be
regarded as the solutions of the mean-field plus pairing model in the strong
pairing interaction G ->Infinity limit. Properties of the Stieltjes zeros of
the extended Heine-Stieltjes polynomials, of which the roots determine the
projected states, and the related Van Vleck zeros are discussed. The
electrostatic interpretation of these zeros is presented. As examples,
applications to n nonidentical particles of spin-1/2 and to identical bosons or
fermions are made to elucidate the procedure and properties of the Stieltjes
zeros and the related Van Vleck zeros. It is shown that the new angular
momentum projection for n identical bosons or fermions can be simplified with
the branching multiplicity formula of U(N) supset O(3) and the special choices
of the parameters used in the projection. Especially, it is shown that the
solutions for identical bosons can always be expressed in terms of zeros of
Jacobi polynomials. However, unlike non-identical particle systems, the
n-coupled states of identical particles are non-orthogonal with respect to the
multiplicity label after the projection.Comment: 14 pages LaTeX with no figur
Constraining the Mass of the Photon with Gamma-Ray Bursts
One of the cornerstones of modern physics is Einstein's special relativity,
with its constant speed of light and zero photon mass assumptions. Constraint
on the rest mass m_{\gamma} of photons is a fundamental way to test Einstein's
theory, as well as other essential electromagnetic and particle theories. Since
non-zero photon mass can give rise to frequency-(or energy-) dependent
dispersions, measuring the time delay of photons with different frequencies
emitted from explosive astrophysical events is an important and
model-independent method to put such a constraint. The cosmological gamma-ray
bursts (GRBs), with short time scales, high redshifts as well as broadband
prompt and afterglow emissions, provide an ideal testbed for m_{\gamma}
constraints. In this paper we calculate the upper limits of the photon mass
with GRB early time radio afterglow observations as well as multi-band radio
peaks, thus improve the results of Schaefer (1999) by nearly half an order of
magnitude.Comment: 25 pages, 2 tables, Accepted by Journal of High Energy Astrophysic
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