New spaces in physics : formal and conceptual reflections

著者

    • Anel, Mathieu
    • Catren, Gabriel

書誌事項

New spaces in physics : formal and conceptual reflections

edited by Mathieu Anel, Gabriel Catren

Cambridge University Press, 2021

  • : hardback

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注記

Includes bibliographical references

内容説明・目次

内容説明

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 Poincare 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.

目次

  • 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 Marino.

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