New Spaces in Physics: Volume 2
Formal and Conceptual Reflections

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

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

9781108490627, Cambridge University Press

Hardback, published 1 April 2021

1 pages, 22 b/w illus. 1 table
23.5 x 15.7 x 2.9 cm, 0.73 kg

'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

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.

Subject Areas: Mathematical physics [PHU], Quantum physics [quantum mechanics & quantum field theory PHQ], Gravity [PHDV], Topology [PBP], Geometry [PBM]