New Spaces in Physics: Volume 2

New Spaces in Physics: Volume 2 PDF

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 438

ISBN-13: 1108848206

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After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.

New Spaces in Physics

New Spaces in Physics PDF

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04

Total Pages: 437

ISBN-13: 110849062X

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In this graduate-level book, leading researchers explore various new notions of 'space' in mathematical physics.

New Spaces in Mathematics: Volume 1

New Spaces in Mathematics: Volume 1 PDF

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04-01

Total Pages: 602

ISBN-13: 1108848214

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After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. The chapters in this volume cover a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. It is addressed primarily to mathematicians and mathematical physicists, but also to historians and philosophers of these disciplines.

New Foundations for Physical Geometry

New Foundations for Physical Geometry PDF

Author: Tim Maudlin

Publisher: Oxford University Press

Published: 2014-02

Total Pages: 374

ISBN-13: 0198701306

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Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

Mathematics of Classical and Quantum Physics

Mathematics of Classical and Quantum Physics PDF

Author: Frederick W. Byron

Publisher: Courier Corporation

Published: 2012-04-26

Total Pages: 674

ISBN-13: 0486135063

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Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.

Quantum Fields in Curved Space

Quantum Fields in Curved Space PDF

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.

A Course in Modern Mathematical Physics

A Course in Modern Mathematical Physics PDF

Author: Peter Szekeres

Publisher: Cambridge University Press

Published: 2004-12-16

Total Pages: 620

ISBN-13: 9780521829601

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This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.

Fashion, Faith, and Fantasy in the New Physics of the Universe

Fashion, Faith, and Fantasy in the New Physics of the Universe PDF

Author: Roger Penrose

Publisher: Princeton University Press

Published: 2016-09-13

Total Pages: 520

ISBN-13: 1400880289

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One of the world's leading physicists questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.

New Spaces in Mathematics

New Spaces in Mathematics PDF

Author: Mathieu Anel

Publisher: Cambridge University Press

Published: 2021-04

Total Pages: 601

ISBN-13: 1108490638

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In this graduate-level book, leading researchers explore various new notions of 'space' in mathematics.