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General relativity (Physics) --- Mathematics

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This book, first published in 2007, is an introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.

Quantum field theory --- Quantum gravity --- Gravity --- Théorie quantique des champs --- Gravité quantique --- Gravité --- Gravity. --- Quantum field theory. --- Quantum gravity. --- Théorie quantique des champs --- Gravité quantique --- Gravité --- Geophysics --- Mechanics --- Pendulum --- Gravity, Quantum --- General relativity (Physics) --- Gravitation --- Quantum theory --- Relativistic quantum field theory --- Field theory (Physics) --- Relativity (Physics)

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Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas.

General relativity (Physics) --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics --- Relativity (Physics) --- Mathematics. --- Global differential geometry. --- Astronomy. --- Classical and Quantum Gravitation, Relativity Theory. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Differential Geometry. --- Astronomy, Astrophysics and Cosmology. --- Geometry, Differential --- Math --- Science --- Gravitation. --- Applied mathematics. --- Engineering mathematics. --- Mathematical physics. --- Differential geometry. --- Astrophysics. --- Astronomical physics --- Astronomy --- Cosmic physics --- Differential geometry --- Physical mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Mathematics --- Properties

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The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas which evolved while developing a theory of quantum gravity require highly advanced mathematical methods. This book presents different mathematical approaches to formulate a theory of quantum gravity. It represents a carefully selected cross-section of lively discussions about the issue of quantum gravity which took place at the second workshop "Mathematical and Physical Aspects of Quantum Gravity" in Blaubeuren, Germany. This collection covers in a unique way aspects of various competing approaches. A unique feature of the book is the presentation of different approaches to quantum gravity making comparison feasible. This feature is supported by an extensive index. The book is mainly addressed to mathematicians and physicists who are interested in questions related to mathematical physics. It allows the reader to obtain a broad and up-to-date overview on a fascinating active research area. .

Quantum gravity --- Mathematical models --- Gravity, Quantum --- General relativity (Physics) --- Gravitation --- Quantum theory --- Quantum theory. --- Mathematical physics. --- Mathematics. --- Astronomy. --- Classical and Quantum Gravitation, Relativity Theory. --- Elementary Particles, Quantum Field Theory. --- Mathematical Methods in Physics. --- Applications of Mathematics. --- Quantum Physics. --- Astronomy, Astrophysics and Cosmology. --- Math --- Science --- Physical mathematics --- Physics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics --- Gravitation. --- Elementary particles (Physics). --- Quantum field theory. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Quantum physics. --- Astrophysics. --- Astronomical physics --- Astronomy --- Cosmic physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Relativistic quantum field theory --- Field theory (Physics) --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Nuclear physics --- Matter --- Antigravity --- Centrifugal force --- Properties

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This four-volume work represents the most comprehensive documentation and study of the creation of general relativity; one of the fundamental physical theories of the 20th century. It comprises key sources from Einstein and others who from the late 19th to the early 20th century contributed to this monumental development. Some of these sources are presented here in translation for the first time. Einstein’s famous Zurich notebook, which documents the pivotal steps toward general relativity, is reproduced here for the first time and transcribed in its entirety. The volumes offer detailed commentaries and analyses of these sources that are based on a close reading of these documents supplemented by interpretations by the leading historians of relativity. All in all, the facets of this work, based on more than a decade of research, combine to constitute one of the most in-depth studies of a scientific revolution ever written.

kennisleer --- Pure sciences. Natural sciences (general) --- Theory of knowledge --- filosofie --- epistomologie --- Philosophy of nature --- Philosophy of science --- wetenschapsgeschiedenis --- epistemologists --- Philosophy --- General relativity (Physics) --- Relativity (Physics) --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Relativistic theory of gravitation --- Relativity theory, General --- Physics --- Einstein, Albert --- Einstein, Albert, --- General relativity (Physics). --- Relativity (Physics). --- Philosophy (General). --- History. --- Genetic epistemology. --- Philosophy of nature. --- Science --- Classical and Quantum Gravitation, Relativity Theory. --- Philosophy, general. --- History of Science. --- Epistemology. --- Philosophy of Nature. --- Philosophy of Science. --- Philosophy. --- Normal science --- Nature --- Nature, Philosophy of --- Natural theology --- Developmental psychology --- Knowledge, Theory of --- Annals --- Auxiliary sciences of history --- Gravitation. --- Philosophy and science. --- Science and philosophy --- Epistemology --- Psychology --- Mental philosophy --- Humanities --- Field theory (Physics) --- Matter --- Antigravity --- Centrifugal force --- Properties --- Aiyinsitan, Abote, --- Aĭnshtaĭn, Albert, --- Ainshutain, A, --- Ain̲sṭain̲, Ālparṭ, --- Ainsṭāina, Albarṭa, --- Ajnštajn, Albert, --- Āynishtayn, --- Aynshtayn, Albert, --- Eĭnshteĭn, Alʹbert, --- אינשטין, אלברט, --- איינשטיין --- איינשטיין, אלבערט, --- איינשטיין, אלברט --- איינשטיין, אלברט, --- Aynştayn, Elbêrt, --- Īnshtīn, --- Aynîştayn, --- Aiyinsitan, --- 愛因斯坦, --- 爱因斯坦,