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The Dirac Equation in Curved Spacetime

Author: Peter Collas

Publisher:

Published: 2019

Total Pages: 109

ISBN-13: 9783030148263

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.

The Dirac Equation in Curved Spacetime

Author: Peter Collas

Publisher: Springer

Published: 2019-03-21

Total Pages: 109

ISBN-13: 3030148254

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Aspects of Quantum Field Theory in Curved Spacetime

Author: Stephen A. Fulling

Publisher: Cambridge University Press

Published: 1989-08-24

Total Pages: 332

ISBN-13: 9780521377683

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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.

Quantum Fields in Curved Space

Author: N. D. Birrell

Publisher: Cambridge University Press

Published: 1984-02-23

Total Pages: 362

ISBN-13: 1107392810

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This book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Although the treatment is general, special emphasis is given to the Hawking black hole evaporation effect, and to particle creation processes in the early universe. The last decade has witnessed a phenomenal growth in this subject. This is the first attempt to collect and unify the vast literature that has contributed to this development. All the major technical results are presented, and the theory is developed carefully from first principles. Here is everything that students or researchers will need to embark upon calculations involving quantum effects of gravity at the so-called one-loop approximation level.

Quantum Field Theory in Curved Spacetime

Author: Leonard Parker

Publisher: Cambridge University Press

Published: 2009-08-20

Total Pages: 472

ISBN-13: 1139480855

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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.

Quantum Field Theory in Curved Spacetime

Author: Leonard Parker

Publisher: Cambridge University Press

Published: 2009-08-20

Total Pages: 472

ISBN-13: 0521877873

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Suitable for graduate students, this book develops quantum field theory in curved spacetime in a pedagogical style.

Einstein's Unification

Author: Jeroen van Dongen

Publisher: Cambridge University Press

Published: 2010-06-10

Total Pages: 225

ISBN-13: 0521883466

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Shedding new light on Einstein's study of unified field theory, this book will interest physicists, historians and philosophers of science.

Quantum Mechanics in Curved Space-Time

Author: Jurgen Audretsch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 555

ISBN-13: 1461538149

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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.

The Wave Equation on a Curved Space-Time

Author: F. G. Friedlander

Publisher: Cambridge University Press

Published: 1975

Total Pages: 298

ISBN-13: 0521205670

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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.

Supersymmetry in Quantum Mechanics

Author: Fred Cooper

Publisher: World Scientific

Published: 2001

Total Pages: 226

ISBN-13: 9789810246129

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This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by students in advanced undergraduate quantum mechanics courses. Problems have been given at the end of each chapter, along with complete solutions to all the problems. The text also includes material of interest in current research not usually discussed in traditional courses on quantum mechanics, such as the connection between exact solutions to classical solution problems and isospectral quantum Hamiltonians, and the relation to the inverse scattering problem.