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Quantum Non-linear Sigma-Models

2013-03-09 Science
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Release : 2013-03-09
Genre : Science
Kind : eBook
Book Rating : 928/5 ( reviews)

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Book Synopsis Quantum Non-linear Sigma-Models by : Sergei V. Ketov

Download or read book Quantum Non-linear Sigma-Models written by Sergei V. Ketov. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive presentation of the quantum non-linear sigma-models. The original papers consider in detail geometrical properties and renormalization of a generic non-linear sigma-model, illustrated by explicit multi-loop calculations in perturbation theory.

Quantum Non-linear Sigma-Models

2000-09-14 Mathematics
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Release : 2000-09-14
Genre : Mathematics
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Book Rating : 610/5 ( reviews)

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Book Synopsis Quantum Non-linear Sigma-Models by : Sergei V. Ketov

Download or read book Quantum Non-linear Sigma-Models written by Sergei V. Ketov. This book was released on 2000-09-14. Available in PDF, EPUB and Kindle. Book excerpt: Offers a systematic presentation of the modern quantum field theory of non-linear sigma-models. These models are very popular in theoretical high energy physics, string theory, and statistical physics. The geometric and quantum renormalization properties of the most general non-linear sigma-models are considered in detail within the framework of quantum perturbation theory. The main applications to be considered in the book can be found in string theory, conformal field theory, and general relativity.

Super Field Theories

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 131/5 ( reviews)

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Book Synopsis Super Field Theories by : H.C. Lee

Download or read book Super Field Theories written by H.C. Lee. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: The Super Field Theory Workshop, held at Simon Fraser University, Vancouver, Canada July 25 - August 5, 1986 was originally intended to be a sequel to the 1983 Chalk River Workshop on Kaluza-Klein Theories and the 1985 Workshop on Quantum Field Theories held at the University of Western Ontario. The scope of the workshop was therefore not to be very big, with a program of about 20 papers, an anticipated 30 to 45 participants, and with much time scheduled for discussion and personal contact. These goals were soon changed in the face of wide interest in the workshop, both for participation and for giving talks, so that the workshop materialized with about 90 participants and 40 talks. This volume contains the texts, some considerably expanded from the oral version, of most of the talks pre sented at the workshop. Not included are a few talks whose manuscripts were not made available to the editors. In the last few years the subject of particle physics and unified field theory has developed in a way not witnessed in the last fifty years: a confluence with mathematics, especially in geometry, topology and algebra at an advanced level. This has vastly expanded the horizon of the disci pline and heightened the expectation that a true understanding of the fun damental laws of physics may soon be within reach. Most aspects of this new development are covered, many in pedagogical detail, by articles in this volume.

Yang–Baxter Deformation of 2D Non-Linear Sigma Models

2021-06-03 Science
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Release : 2021-06-03
Genre : Science
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Book Rating : 031/5 ( reviews)

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Book Synopsis Yang–Baxter Deformation of 2D Non-Linear Sigma Models by : Kentaroh Yoshida

Download or read book Yang–Baxter Deformation of 2D Non-Linear Sigma Models written by Kentaroh Yoshida. This book was released on 2021-06-03. Available in PDF, EPUB and Kindle. Book excerpt: In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.

Quantum Triangulations

2017-11-27 Science
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Release : 2017-11-27
Genre : Science
Kind : eBook
Book Rating : 376/5 ( reviews)

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Book Synopsis Quantum Triangulations by : Mauro Carfora

Download or read book Quantum Triangulations written by Mauro Carfora. This book was released on 2017-11-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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