New Spaces in Physics: Volume 2: Formal and Conceptual Reflections

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Mathieu Anel (Carnegie Mellon University, Pennsylvania) Gabriel Catren (Centre National de la Recherche Scientifique (CNRS), Paris)

New Spaces in Physics

Volume 2: Formal and Conceptual Reflections

Mathieu Anel (Carnegie Mellon University, Pennsylvania), Gabriel Catren (Centre National de la Recherche Scientifique (CNRS), Paris)

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English

Cambridge University Press
01 April 2021

Geometry; Topology; Gravity; Quantum physics (quantum mechanics & quantum field theory); Mathematical physics

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.

Edited by: Mathieu Anel (Carnegie Mellon University Pennsylvania), Gabriel Catren (Centre National de la Recherche Scientifique (CNRS), Paris)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 235mm, Width: 157mm, Spine: 29mm
Weight: 730g
ISBN: 9781108490627
ISBN 10: 110849062X
Pages: 1
Publication Date: 01 April 2021
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Introduction Mathieu Anel and Gabriel Catren; Part I. Noncommutative and supercommutative geometries: 1. Noncommutative geometry, the spectral standpoint Alain Connes; 2. The logic of quantum mechanics (revisited) Klaas Landsman; 3. Supergeometry in mathematics and physics Mikhail Kapranov; Part II. Symplectic geometry: 4. Derived stacks in symplectic geometry Damien Calaque; 5. Higher prequantum geometry Urs Schreiber; Part III. Spacetime: 6. Struggles with the continuum John C. Baez; 7. Twistor theory: a geometric perspective for describing the physical world Roger Penrose; 8. Quantum geometry of space Muxin Han; 9. Stringy geometry and emergent space Marcos Mariño.

Mathieu Anel is a Visiting Assistant Professor at Carnegie Mellon University. His research interests include higher category theory, algebraic topology, and topos theory. Gabriel Catren is Permanent Researcher in philosophy of physics at the French National Centre for Scientific Research (CNRS). His research interests include the foundations of classical and quantum mechanics, and the foundations of gauge theories.

Reviews for New Spaces in Physics: Volume 2: Formal and Conceptual Reflections

'The collection would be of interest to any physicist, mathematician, historian, or philosopher seeking a survey of the approaches to dealing with the modern concept of space in physics … Recommended.' E. Kincanon, Choice Magazine