2,269 research outputs found

### Quantum Geometric Description of Cosmological Models

This is a written version of the review talk given at the meeting on
"Interface of Gravitational and Quantum Realms" at IUCAA, Pune during December
2001. The talk reviewed the recent work of Martin Bojowald on Loop Quantum
Cosmology.Comment: 14 pages, Latex, no figures. To appear in Mod. Phys. Lett.

### Classical and Quantum Aspects of Gravitation and Cosmology

These are the proceedings of the XVIII Conference of the Indian Association
for General Relativity and Gravitation (IAGRG) held at the Institute of
Mathematical Sciences, Madras, INDIA during Feb. 15-17, 1996. The Conference
was dedicated the late Prof. S. Chandrasekhar.
The proceedings consists of 17 articles on:
- Chandrasekhar's work (N. Panchapkesan);
- Vaidya-Raychaudhuri Lecture (C.V. Vishveshwara)
- Gravitational waves (B.R. Iyer, R. Balasubramanian)
- Gravitational Collapse (T.P. Singh)
- Accretion on black hole (S. Chakrabarti)
- Cosmology (D. Munshi, S. Bharadwaj, G.S. Mohanty, P. Bhattacharjee);
- Classical GR (S. Kar, D.C. Srivatsava)
- Quantum aspects (J. Maharana, Saurya Das, P. Mitra, G. Date, N.D. Hari
Dass)
The body of THIS article contains ONLY the title, contents, foreword,
organizing committees, preface, list of contributed talks and list of
participants. The plenery talks are available at:
http://www.imsc.ernet.in/physweb/Conf/ both as post-script files of individual
articles and also as .uu source files. For further information please send
e-mail to [email protected]: 12 pages, latex, needs psfig.tex macros. Latex the file run.tex.
These Proceedings of the XVIII IAGRG Conference are available at
http://www.imsc.ernet.in/physweb/Conf/ MINOR TYPO's in the ABSTRACT correcte

### Irreducible Modules of Finite Dimensional Quantum Algebras of type A at Roots of Unity

Specializing properly the parameters contained in the maximal cyclic
representation of the non-restricted A-type quantum algebra at roots of unity,
we find the unique primitive vector in it. We show that the submodule generated
by the primitive vector can be identified with an irreducble highest weight
module of the finite dimensional A-type quantum algebra which is defined as the
subalgebra of the restricted quantum algebra at roots of unity.Comment: LaTeX(2e), 17 page

### Isolated Horizon, Killing Horizon and Event Horizon

We consider space-times which in addition to admitting an isolated horizon
also admit Killing horizons with or without an event horizon. We show that an
isolated horizon is a Killing horizon provided either (1) it admits a
stationary neighbourhood or (2) it admits a neighbourhood with two independent,
commuting Killing vectors. A Killing horizon is always an isolated horizon. For
the case when an event horizon is definable, all conceivable relative locations
of isolated horizon and event horizons are possible. Corresponding conditions
are given.Comment: 14 pages, Latex, no figures. Some arguments tightened. To appear in
Class. Quant. Gra

### Asymptotic analysis and spectrum of three anyons

The spectrum of anyons confined in harmonic oscillator potential shows both
linear and nonlinear dependence on the statistical parameter. While the
existence of exact linear solutions have been shown analytically, the nonlinear
dependence has been arrived at by numerical and/or perturbative methods. We
develop a method which shows the possibility of nonlinearly interpolating
spectrum. To be specific we analyse the eigenvalue equation in various
asymptotic regions for the three anyon problem.Comment: 28 pages, LaTeX, 2 Figure

### Classical and Quantum Mechanics of Anyons

We review aspects of classical and quantum mechanics of many anyons confined
in an oscillator potential. The quantum mechanics of many anyons is complicated
due to the occurrence of multivalued wavefunctions. Nevertheless there exists,
for arbitrary number of anyons, a subset of exact solutions which may be
interpreted as the breathing modes or equivalently collective modes of the full
system. Choosing the three-anyon system as an example, we also discuss the
anatomy of the so called ``missing'' states which are in fact known numerically
and are set apart from the known exact states by their nonlinear dependence on
the statistical parameter in the spectrum.
Though classically the equations of motion remains unchanged in the presence
of the statistical interaction, the system is non-integrable because the
configuration space is now multiply connected. In fact we show that even though
the number of constants of motion is the same as the number of degrees of
freedom the system is in general not integrable via action-angle variables.
This is probably the first known example of a many body pseudo-integrable
system. We discuss the classification of the orbits and the symmetry reduction
due to the interaction. We also sketch the application of periodic orbit theory
(POT) to many anyon systems and show the presence of eigenvalues that are
potentially non-linear as a function of the statistical parameter. Finally we
perform the semiclassical analysis of the ground state by minimizing the
Hamiltonian with fixed angular momentum and further minimization over the
quantized values of the angular momentum.Comment: 44 pages, one figure, eps file. References update

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