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

by Mathieu Anel (Editor), Gabriel Catren (Editor)

Overview

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.

Product Details

ISBN-13:	9781108490627
Publisher:	Cambridge University Press
Publication date:	04/01/2021
Pages:	436
Product dimensions:	6.18(w) x 9.25(h) x 1.14(d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

'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

From the Publisher