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