## New Spaces in Physics: Formal and Conceptual Reflections"Mathematicians have long known that geometry is not absolute. Our understanding of what constitutes a "space" has driven, and been driven by, significant applications inside and outside of mathematics. The workshop "New Spaces in Mathematics and Physics," held in 2015 at the Institut Henri Poincaré, brought together many researchers to discuss various new notions of space in mathematics and theoretical physics, with particular attention given to often overlooked aspects of their subjects, conceptual reflections and historical perspectives. This volume and its companion New Spaces in Physics arise from their lectures and discussions. This volume covers a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry. Mathieu Anel is Assistant Professor at Carnegie Mellon University. His research interests include higher category theory, topos theory, and symplectic geometry. Gabriel Catren is Permanent Researcher at the French National Centre for Scientific Research (CNRS). His main areas of research are the foundations of classical and quantum mechanics, and the foundations of gauge theories (general relativity and Yang-Mills theories)"-- |

### Što ljudi govore - Napišite recenziju

Na uobičajenim mjestima nismo pronašli nikakve recenzije.

### Sadržaj

New Spaces in Physics | 5 |

Contents for New Spaces in Mathematics | 9 |

Contents for New Spaces in Mathematics page vii | 15 |

Acknowledgments | 18 |

DIFFERENTIAL GEOMETRY | 29 |

An Introduction to Diffeology 31 | 61 |

Synthetic Differential Geometry | 83 |

The Logic of Quantum Mechanics Revisited | 85 |

Derived Stacks in Symplectic Geometry | 155 |

Higher Prequantum Geometry | 202 |

Spaces as InfinityGroupoids | 258 |

Struggles with the Continuum | 281 |

The Logic of Space | 322 |

7 | 327 |

Muxin | 373 |

Marcos Mariño | 407 |

### Ostala izdanja - Prikaži sve

New Spaces in Physics: Formal and Conceptual Reflections Mathieu Anel,Gabriel Catren Ograničeni pregled - 2021 |

New Spaces in Physics: Volume 2: Formal and Conceptual Reflections Mathieu Anel,Gabriel Catren Ograničeni pregled - 2021 |

### Uobičajeni izrazi i fraze

action algebra approach associated bundle called charge classical closed cohomology commutative compact complex condition connection Connes consider construction corresponding curvature cyclic defined definition derived described differential dimension direct duality element energy equations equivalent Example extension fact field theory finite force formalism formula functions fundamental gauge geometry given gives global gravity groupoid hence higher Hilbert homotopy implies integral intersection invariant isomorphism Lagrangian lattice limit locally logic manifold Math Mathematics means mechanics morphism natural noncommutative Note objects obtained operator pair particles particular phase Phys physics positive prequantum problem projective provides quantization quantum quantum mechanics refer relation relativity result sense singularity smooth space spacetime spectral spectrum stack structure symmetry symplectic theorem topological transformations twistor University vector ÝÑ ÞÑ