Geometry Fields And Cosmology
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Geometry, Fields and Cosmology
Author: B.R. Iyer
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-09
This volume is based on the lectures given at the First Inter University Graduate School on Gravitation and Cosmology organized by IUCAA, Pune, in 1989. This series of Schools have been carefully planned to provide a sound background and preparation for students embarking on research in these and related topics. Consequently, the contents of these lectures have been meticulously selected and arranged. The topics in the present volume offer a firm mathematical foundation for a number of subjects to be de veloped later. These include Geometrical Methods for Physics, Quantum Field Theory Methods and Relativistic Cosmology. The style of the book is pedagogical and should appeal to students and research workers attempt ing to learn the modern techniques involved. A number of specially selected problems with hints and solutions have been included to assist the reader in achieving mastery of the topics. We decided to bring out this volume containing the lecture notes since we felt that they would be useful to a wider community of research workers, many of whom could not participate in the school. We thank all the lecturers for their meticulous lectures, the enthusiasm they brought to the discussions and for kindly writing up their lecture notes. It is a pleasure to thank G. Manjunatha for his meticulous assistence over a long period, in preparing this volume for publication.
STUDIES ON GRAVITATIONAL FIELD EQUATIONS AND IMPORTANT RESULTS OF RELATIVISTIC COSMOLOGY
We live in this universe. Hence, it is essential to understand the origin, evolution and ultimate fate of the universe. This can be, effectively, done by constructing mathematical models of the universe, using Einstein's theory of gravitation and other modified theories of gravitation. The models, thus, obtained can be compared with the present day observations, to decide about the shape, physics, and origin of the universe. With this motivation we have taken up the investigations in this book entitled "STUDIES ON GRAVITATIONAL FIELD EQUATIONS AND IMPORTANT RESULTS OF RELATIVISTIC COSMOLOGY". This book comprises of six chapters and deals with some spatially homogeneous isotropic and anisotropic cosmological models of the universe in some modified theories of gravitation.
Geometric Approaches to Quantum Field Theory
The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.