Integrability, Quantization, and Geometry: I. Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrability, Quantization, and Geometry: I. Integrable Systems write by Sergey Novikov. This book was released on 2021-04-12. Integrability, Quantization, and Geometry: I. Integrable Systems available in PDF, EPUB and Kindle. This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Integrability, Quantization, and Geometry
Integrability, Quantization, and Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrability, Quantization, and Geometry write by Sergeĭ Petrovich Novikov. This book was released on 2021. Integrability, Quantization, and Geometry available in PDF, EPUB and Kindle. This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.The contributions to this collection of papers are split into two parts: ""Integrable Systems"" and ""Quantum Theories and Algebraic Geometry"", reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, i.
Geometry, Integrability and Quantization
Geometry, Integrability and Quantization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometry, Integrability and Quantization write by Ivailo M. Mladenov. This book was released on 2000. Geometry, Integrability and Quantization available in PDF, EPUB and Kindle.
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry
Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry write by Sergey Novikov. This book was released on 2021-04-12. Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry available in PDF, EPUB and Kindle. This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantization, Geometry and Noncommutative Structures in Mathematics and Physics write by Alexander Cardona. This book was released on 2017-10-26. Quantization, Geometry and Noncommutative Structures in Mathematics and Physics available in PDF, EPUB and Kindle. This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
