Topics in the Semiclassical Quantization of Gravitation
Author | : Bharat Vishnu Ratra |
Publisher | : |
Total Pages | : 276 |
Release | : 1986 |
Genre | : |
ISBN | : |
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Author | : Bharat Vishnu Ratra |
Publisher | : |
Total Pages | : 276 |
Release | : 1986 |
Genre | : |
ISBN | : |
Author | : Claus Gerhardt |
Publisher | : Springer |
Total Pages | : 206 |
Release | : 2018-04-14 |
Genre | : Science |
ISBN | : 3319773712 |
A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological constant. The hyperbolic equation then has a sequence of smooth solutions which are products of temporal eigenfunctions and spatial eigendistributions. Due to this "spectral resolution" of the wave equation quantum statistics can also be applied to the quantized systems. These quantum statistical results could help to explain the nature of dark matter and dark energy.
Author | : Esko Olavi Keski-Vakkuri |
Publisher | : |
Total Pages | : 114 |
Release | : 1995 |
Genre | : |
ISBN | : |
Author | : Herbert W. Hamber |
Publisher | : Springer Science & Business Media |
Total Pages | : 342 |
Release | : 2008-10-20 |
Genre | : Science |
ISBN | : 354085293X |
"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.
Author | : Abhay Ashtekar |
Publisher | : World Scientific |
Total Pages | : 356 |
Release | : 1991-07-03 |
Genre | : Science |
ISBN | : 9814571091 |
Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.
Author | : A. A. Komar |
Publisher | : Nova Science Publishers |
Total Pages | : 344 |
Release | : 1988 |
Genre | : Science |
ISBN | : |
Author | : Claus Kiefer |
Publisher | : OUP Oxford |
Total Pages | : 376 |
Release | : 2007-02-22 |
Genre | : Science |
ISBN | : 019921252X |
The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction -- the direct quantisation of Einstein's general theory of relativity and string theory -- are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone,string theory assumes that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantization of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is adetailed presentation of the main approaches employed in quantum general relativity: path-integral quantization, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantization of black holes, quantum cosmology, the indications of a discrete structure ofspacetime, and the origin of irreversibility.The second edition will add some sections on topical issues. These include loop quantum cosmology, dynamical triangulation, renormalization-group approach, primordial black holes, and information-loss problem for black holes. The second edition will also contain some pedagogical extensions.This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science.
Author | : Claus Kiefer |
Publisher | : Oxford University Press |
Total Pages | : 406 |
Release | : 2012-04-05 |
Genre | : Mathematics |
ISBN | : 0199585202 |
Quantum theory and Einstein's theory of relativity are at the centre of modern theoretical physics, yet, the consistent unification of both theories is still elusive. This book offers an up-to-date introduction into the attempts to construct a unified theory of "quantum gravity".
Author | : Sabine Hossenfelder |
Publisher | : Springer |
Total Pages | : 121 |
Release | : 2017-11-15 |
Genre | : Science |
ISBN | : 3319645374 |
This book summarizes recent developments in the research area of quantum gravity phenomenology. A series of short and nontechnical essays lays out the prospects of various experimental possibilities and their current status. Finding observational evidence for the quantization of space-time was long thought impossible. In the last decade however, new experimental design and technological advances have changed the research landscape and opened new perspectives on quantum gravity. Formerly dominated by purely theoretical constructions, quantum gravity now has a lively phenomenology to offer. From high precision measurements using macroscopic quantum oscillators to new analysis methods of the cosmic microwave background, no stone is being left unturned in the experimental search for quantum gravity. This book sheds new light on the connection of astroparticle physics with the quantum gravity problem. Gravitational waves and their detection are covered. It illustrates findings from the interconnection between general relativity, black holes and Planck stars. Finally, the return on investment in quantum-gravitation research is illuminated. The book is intended for graduate students and researchers entering the field.
Author | : Bei-Lok B. Hu |
Publisher | : Cambridge University Press |
Total Pages | : 615 |
Release | : 2020-03-05 |
Genre | : Science |
ISBN | : 0521193575 |
An overview of semi-classical gravity theory and stochastic gravity as theories of quantum gravity in curved space-time.