A mathematically coherent quantum gravity

"The development of a successful theory of quantum gravity in the context of the early universe is the key next step in theoretical physics. This book takes that step by describing a coherent mathematical framework for both the evolution of discrete space-time and the quantum graviton in the Planck regime. In doing so it successfully blends developments in both loop quantum gravity and superstring theory with data from the Large Hadron Collider. The result is a coherent mathematical framework that encapsulates newer developments on both the evolution of discrete space-time and the quantum graviton in the early universe. In doing so it addresses a key issue concerning loop quantum gravity raised by Ashtekar: describing conditions for the existence of locally translation-invariant quantum states; a quantum form of the diffeomorphisms of General Relativity." -- Prové de l'editor.

"Version: 20200901"

Conté: Preface : why you should read this book -- 1. Quantum theory -- 1.1. Basic notions -- 1.2. Non-relativistic quantum theory -- 1.3. Exploiting quantum theory embedded in classical gravity -- 1.4. Special relativity -- 1.5. Dirac relativistic spinor theory -- 1.6. von Neumann algebras -- 1.7. A higher level of abstraction : quantum W*-algebras -- 1.8. A brief comparison with the approach of Rovelli and Penrose -- 2. Computational spin networks and quantum paths in space-time -- 2.1. Introduction -- 2.2. The measurement of space and time -- 2.3. Computational spin networks -- 2.4. The homology invariants of space-time -- 2.5. Quantum paths in space-time -- 2.6. Fractal paths in classical space-time -- 2.7. Supersymmetry and the spinor calculus -- 2.8. Irreducible representations of the Poincarâe Lie algebra -- 2.9. Dirac spinors and the spinor calculus -- 3. Particles in algebraic quantum gravity -- 3.1. Introduction -- 3.2. Lie groups, fibre bundles and quantum fields in loop quantum gravity -- 3.3. A remarkable theorem -- 3.4. Properties of the projection onto the base space B of a Stonean fibre bundle K -- 3.5. Quantum connections -- 3.6. The supersymmetric extension of the…