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Author: F. G. Friedlander
Publisher: Cambridge University Press
Published: 1975
Total Pages: 298
ISBN-13: 0521205670
DOWNLOAD EBOOK →This book gives a rigourous discussion of the local effects of curvature on the behaviour of waves. In the course of this discussion many techniques are developed which are also needed for a study of more general problems, in which the gravitational field itself plays a dynamical role.
Author: Peter Collas
Publisher: Springer
Published: 2019-03-21
Total Pages: 109
ISBN-13: 3030148254
DOWNLOAD EBOOK →This book explains and develops the Dirac equation in the context of general relativistic quantum mechanics in a range of spacetime dimensions. It clarifies the subject by carefully pointing out the various conventions used and explaining how they are related to each other. The prerequisites are familiarity with general relativity and an exposure to the Dirac equation at the level of special relativistic quantum mechanics, but a review of this latter topic is given in the first chapter as a reference and framework for the physical interpretations that follow. Worked examples and exercises with solutions are provided. Appendices include reviews of topics used in the body of the text. This book should benefit researchers and graduate students in general relativity and in condensed matter.
Author: A. Lichnerowicz
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 292
ISBN-13: 9401721262
DOWNLOAD EBOOK →For seventy years, we have known that Einstein's theory is essentially a theory of propagation of waves for the gravitational field. Confusion enters, however, through the fact that the word wave, in physics, implies sometimes repetition and sometimes not. This confusion is often increased by he use of Fourier transforms, by which a disturbanse which appears to be without repetition is resolved into periodic wave-trains with all frequencies. But, in a general curved space-time, we have nothing corresponding to Fourier transforms. Here, we consider systematically waves corresponding to the propagation of discontinuities of physical quantities describing either fields (essentially electromagnetic fields and gravitational field), or the motion of a fluid, or together, in magnetohydrodynamics, the changes in time of a field and of a fluid. The main equations, for the different studied phenomena, constitute a hyperbolic system and the study of a formal Cauchy problem is possible. We call ordinary waves the case in which the derivative of superior order appearing in the system are discontinuous at the traverse of a hypersurface, the wave front ; we call shock waves the case where the derivatives of an order inferior by one are discontinuous at the traverse of a wave front. XI xii PREFACE From 1950, many well-known scientits (Taub, Synge, Choquet-B ruhat, etc.) have studied the corresponding equations for different physical phenomena : systems associated to the electromagnetic and gravitational fields, to hydrodynamics and to magnetohydrodynamics.
Author: Stephen A. Fulling
Publisher: Cambridge University Press
Published: 1989-08-24
Total Pages: 332
ISBN-13: 9780521377683
DOWNLOAD EBOOK →The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.
Author: Jurgen Audretsch
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 555
ISBN-13: 1461538149
DOWNLOAD EBOOK →Quantum mechanics and quantum field theory on one hand and Gravity as a theory of curved space-time on the other are the two great conc- tual schemes of modern theoretical physics. For many decades they have lived peacefully together for a simple reason: it was a coexistence wi- out much interaction. There has been the family of relativists and the other family of elementary particle physicists and both sides have been convinced that their problems have not very much to do with the problems of the respective other side. This was a situation which could not last forever, because the two theoretical schemes have a particular structural trait in common: their claim for totality and universality. Namely on one hand all physical theories have to be formulated in a quantum mechanical manner, and on the other hand gravity as curved space-time influences all processes and vice versa. It was therefore only a question of time that physically relevant domains of application would attract a general int- est, which demand a combined application of both theoretical schemes. But it is immediately obvious that such an application of both schemes is - possible if the schemes are taken as they are. Something new is needed which reconciles gravity and quantum mechanics. During the last two de- des we are now doing the first steps towards this more general theory and we are confronted with fundamental difficulties.
Author: Melvin Lax
Publisher: Courier Corporation
Published: 2001-01-01
Total Pages: 514
ISBN-13: 0486420019
DOWNLOAD EBOOK →High-level text applies group theory to physics problems, develops methods for solving molecular vibration problems and for determining the form of crystal tensors, develops translational properties of crystals, more. 1974 edition.
Author: Leonard Parker
Publisher: Cambridge University Press
Published: 2009-08-20
Total Pages: 472
ISBN-13: 1139480855
DOWNLOAD EBOOK →Quantum field theory in curved spacetime has been remarkably fruitful. It can be used to explain how the large-scale structure of the universe and the anisotropies of the cosmic background radiation that we observe today first arose. Similarly, it provides a deep connection between general relativity, thermodynamics, and quantum field theory. This book develops quantum field theory in curved spacetime in a pedagogical style, suitable for graduate students. The authors present detailed, physically motivated, derivations of cosmological and black hole processes in which curved spacetime plays a key role. They explain how such processes in the rapidly expanding early universe leave observable consequences today, and how in the context of evaporating black holes, these processes uncover deep connections between gravitation and elementary particles. The authors also lucidly describe many other aspects of free and interacting quantized fields in curved spacetime.
Author: Christian Bär
Publisher: European Mathematical Society
Published: 2007
Total Pages: 208
ISBN-13: 9783037190371
DOWNLOAD EBOOK →This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter, one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third chapter establishes the existence and uniqueness of global fundamental solutions on globally hyperbolic spacetimes and discusses Green's operators and well-posedness of the Cauchy problem. The last chapter is devoted to field quantization in the sense of algebraic quantum field theory. The necessary basics on $C^*$-algebras and CCR-representations are developed in full detail. The text provides a self-contained introduction to these topics addressed to graduate students in mathematics and physics. At the same time, it is intended as a reference for researchers in global analysis, general relativity, and quantum field theory.
Author: Sean M. Carroll
Publisher: Cambridge University Press
Published: 2019-08-08
Total Pages: 529
ISBN-13: 1108488390
DOWNLOAD EBOOK →An accessible introductory textbook on general relativity, covering the theory's foundations, mathematical formalism and major applications.
Author: George Francis Rayner Ellis
Publisher: Clarendon Press
Published: 2000
Total Pages: 394
ISBN-13: 9780198506560
DOWNLOAD EBOOK →This text explains special relativity and the basics of general relativity from a geometric viewpoint. Space-time geometry is emphasised throughout, and up-to-date information is provided on black holes, gravitational collapse, and cosmology.
