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

Cambridge University Press, 4/1/2021
EAN 9781108490627, ISBN10: 110849062X

Hardcover, 1 pages, 23.6 x 15.7 x 2.8 cm
Language: English
Originally published in English

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.

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.