Quantum Triangulations

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

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, Quantum Theory
Cover of the book Quantum Triangulations by Mauro Carfora, Annalisa Marzuoli, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Mauro Carfora, Annalisa Marzuoli ISBN: 9783319679372
Publisher: Springer International Publishing Publication: November 27, 2017
Imprint: Springer Language: English
Author: Mauro Carfora, Annalisa Marzuoli
ISBN: 9783319679372
Publisher: Springer International Publishing
Publication: November 27, 2017
Imprint: Springer
Language: English

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 reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear.

This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative.

This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear.

This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative.

This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.

More books from Springer International Publishing

Cover of the book The Semantic Web by Mauro Carfora, Annalisa Marzuoli
Cover of the book Scalable Uncertainty Management by Mauro Carfora, Annalisa Marzuoli
Cover of the book Multi-Stage and Multi-Time Scale Feedback Control of Linear Systems with Applications to Fuel Cells by Mauro Carfora, Annalisa Marzuoli
Cover of the book Contracting International Employee Participation by Mauro Carfora, Annalisa Marzuoli
Cover of the book Granite Skyscrapers by Mauro Carfora, Annalisa Marzuoli
Cover of the book Violent Non-state Actors and the Syrian Civil War by Mauro Carfora, Annalisa Marzuoli
Cover of the book Transnational Contexts of Development History, Sociality, and Society of Play by Mauro Carfora, Annalisa Marzuoli
Cover of the book Introduction to Translational Cardiovascular Research by Mauro Carfora, Annalisa Marzuoli
Cover of the book Energy Technology 2018 by Mauro Carfora, Annalisa Marzuoli
Cover of the book Street Art of Resistance by Mauro Carfora, Annalisa Marzuoli
Cover of the book Future Directions in Well-Being by Mauro Carfora, Annalisa Marzuoli
Cover of the book Geometric Inequalities by Mauro Carfora, Annalisa Marzuoli
Cover of the book Software Process Improvement and Capability Determination by Mauro Carfora, Annalisa Marzuoli
Cover of the book Bioethical Insights into Values and Policy by Mauro Carfora, Annalisa Marzuoli
Cover of the book Covenants and Third-Party Creditors by Mauro Carfora, Annalisa Marzuoli
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy