Quantum Triangulations Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow /

• Main Authors: Carfora, Mauro (Author), Marzuoli, Annalisa (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Lecture Notes in Physics, 942
• Subjects: Physics.; Mathematical physics.; Manifolds (Mathematics).; Complex manifolds.; Gravitation.; Quantum physics.; Quantum Physics.; Mathematical Physics.; Manifolds and Cell Complexes (incl. Diff.Topology).; Classical and Quantum Gravitation, Relativity Theory.; Mathematical Applications in the Physical Sciences.; Numerical and Computational Physics, Simulation.

This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often rev...

Table of Contents:

• Preface
• Acknowledgements
• Triangulated Surfaces and Polyhedral Structures
• Singular Euclidean Structures and Riemann Surfaces
• Polyhedral Surfaces and the Weil-Petersson Form
• The Quantum Geometry of Polyhedral Surfaces: Non–Linear σ Model and Ricci Flow
• The Quantum Geometry of Polyhedral Surfaces: Variations on Strings and All That
• State Sum Models and Observables
• State Sum Models and Observables
• Combinatorial Framework for Topological Quantum Computing
• Appendix A: Riemannian Geometry
• Appendix B: A Capsule of Moduli Space Theory
• Appendix C: Spectral Theory on Polyhedral Surfaces
• Index.