Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition
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Calabi Yau Manifolds
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Author : Tristan Hbsch
language : en
Publisher: World Scientific
Release Date : 1994
Calabi Yau Manifolds written by Tristan Hbsch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or equivalently, with trivial canonical bundle (canonical class). They are used to construct possibly realistic (super)string models and are thus being studied vigorously in the recent physics literature.In the main part of the Book, collected and reviewed are relevant results on (1) several major techniques of constructing such spaces and (2) computation of physically relevant quantities such as massless field spectra and their Yukawa interactions. Issues of (3) stringy corrections and (4) moduli space and its geometry are still in the stage of rapid and continuing development, whence there is more emphasis on open problems here. Also is included a preliminary discussion of the conjectured universal moduli space and related open problems. Finally, several detailed models and sample computations are included throughout the Book to exemplify the techniques and the general discussion.The Book also contains a Lexicon (28 pages) of 150 assorted terms, key-words and main results and theorems, well suited for a handy reference. Although cross-referenced with the main part of the Book, the Lexicon can also be used independently.The level of mathematics is guided and developed between that of the popular Physics Reports of Eguchi, Gilkey and Hanson and the book Superstrings (Vol. 2) by Green, Schwarz and Witten on one end and Principles of Algebraic Geometry of Griffiths and Harris on the other.This is the first systematic exposition in book form of the material on Calabi-Yau spaces, related mathematics and the physics application, otherwise scattered through research articles in journals and conference proceedings.
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition
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Author : Tristan Hubsch
language : en
Publisher: World Scientific
Release Date : 2024-12-17
Calabi Yau Manifolds A Bestiary For Physicists 2nd Edition written by Tristan Hubsch and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-17 with Science categories.
Calabi-Yau spaces are complex spaces with a vanishing first Chern class, or, equivalently, with a trivial canonical bundle (sheaf), so they admit a Ricci-flat Kähler metric that satisfies the vacuum Einstein equations. Used to construct possibly realistic (super)string models, they are being studied vigorously by physicists and mathematicians alike. Calabi-Yau spaces have also turned up in computations of probability amplitudes in quantum field theory. This book collects and reviews relevant results on several major techniques of (1) constructing such spaces and (2) computing physically relevant quantities such as spectra of massless fields and their Yukawa interactions. These are amended by (3) stringy corrections and (4) results about the moduli space and its geometry, including a preliminary discussion of the still conjectural universal deformation space. It also contains a lexicon of assorted terms and important results and theorems, which can be used independently.The first edition of Calabi-Yau Manifolds: A Bestiary for Physicists was the first systematic book covering Calabi-Yau spaces, related mathematics, and their application in physics. Thirty years on, this new edition explores the intense development in the field since 1992, providing an additional 400 references. It also addresses advances in machine learning and other computer-aided methods that have recently made physically relevant computations feasible, opened new avenues in the field, and begun to deliver concretely on the now 40-year-old promise of string theory. The presentation of ideas, results, and computational methods is complemented by detailed models and sample computations throughout. This second edition also contains a new closing section, outlining the staggering advances of the past three decades and providing suggestions for future reading.
Mathematical Tools For Physicists
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Author : George L. Trigg
language : en
Publisher: John Wiley & Sons
Release Date : 2006-08-21
Mathematical Tools For Physicists written by George L. Trigg and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Science categories.
Mathematical Tools for Physicists is a unique collection of 18 carefully reviewed articles, each one written by a renowned expert working in the relevant field. The result is beneficial to both advanced students as well as scientists at work; the former will appreciate it as a comprehensive introduction, while the latter will use it as a ready reference. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic/ analytic / geometric methods - Symmetries and conservation laws - Mathematical modeling - Quantum computation The emphasis throughout is ensuring quick access to the information sought, and each article features: - an abstract - a detailed table of contents - continuous cross-referencing - references to the most relevant publications in the field, and - suggestions for further reading, both introductory as well as highly specialized. In addition, a comprehensive index provides easy access to the vast number of key words extending beyond the range of the headlines.
The Calabi Yau Landscape
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Author : Yang-Hui He
language : en
Publisher: Springer Nature
Release Date : 2021-07-31
The Calabi Yau Landscape written by Yang-Hui He and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-31 with Mathematics categories.
Can artificial intelligence learn mathematics? The question is at the heart of this original monograph bringing together theoretical physics, modern geometry, and data science. The study of Calabi–Yau manifolds lies at an exciting intersection between physics and mathematics. Recently, there has been much activity in applying machine learning to solve otherwise intractable problems, to conjecture new formulae, or to understand the underlying structure of mathematics. In this book, insights from string and quantum field theory are combined with powerful techniques from complex and algebraic geometry, then translated into algorithms with the ultimate aim of deriving new information about Calabi–Yau manifolds. While the motivation comes from mathematical physics, the techniques are purely mathematical and the theme is that of explicit calculations. The reader is guided through the theory and provided with explicit computer code in standard software such as SageMath, Python and Mathematica to gain hands-on experience in applications of artificial intelligence to geometry. Driven by data and written in an informal style, The Calabi–Yau Landscape makes cutting-edge topics in mathematical physics, geometry and machine learning readily accessible to graduate students and beyond. The overriding ambition is to introduce some modern mathematics to the physicist, some modern physics to the mathematician, and machine learning to both.
String Theory In A Nutshell
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Author : Elias Kiritsis
language : en
Publisher: Princeton University Press
Release Date : 2019-04-16
String Theory In A Nutshell written by Elias Kiritsis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-16 with Science categories.
The essential introduction to modern string theory—now fully expanded and revised String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world’s leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature. This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly. The essential one-volume reference for students and researchers in theoretical high-energy physics Now fully expanded and revised Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems An online illustration package is available to professors
The Physics Of Reality
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Author : Richard L. Amoroso
language : en
Publisher: World Scientific
Release Date : 2013
The Physics Of Reality written by Richard L. Amoroso and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematical physics categories.
A truly Galilean-class volume, this book introduces a new method in theory formation, completing the tools of epistemology. It covers a broad spectrum of theoretical and mathematical physics by researchers from over 20 nations from four continents. Like Vigier himself, the Vigier symposia are noted for addressing avant-garde, cutting-edge topics in contemporary physics. Among the six proceedings honoring J.-P. Vigier, this is perhaps the most exciting one as several important breakthroughs are introduced for the first time. The most interesting breakthrough in view of the recent NIST experimental violations of QED is a continuation of the pioneering work by Vigier on tight bound states in hydrogen. The new experimental protocol described not only promises empirical proof of large-scale extra dimensions in conjunction with avenues for testing string theory, but also implies the birth of the field of unified field mechanics, ushering in a new age of discovery. Work on quantum computing redefines the qubit in a manner that the uncertainty principle may be routinely violated. Other breakthroughs occur in the utility of quaternion algebra in extending our understanding of the nature of the fermionic singularity or point particle. There are several other discoveries of equal magnitude, making this volume a must-have acquisition for the library of any serious forward-looking researchers.
Intersection Spaces Spatial Homology Truncation And String Theory
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Author : Markus Banagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-08
Intersection Spaces Spatial Homology Truncation And String Theory written by Markus Banagl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-08 with Mathematics categories.
The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality.
Complex Algebraic Geometry
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Author : János Kollár
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Complex Algebraic Geometry written by János Kollár and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Lecture notes from the Third Summer Session of the Regional Geometry Institute, held in Park City, Utah, in 1993.
Riemannian Holonomy Groups And Calibrated Geometry
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Author : Dominic D. Joyce
language : en
Publisher: Oxford University Press
Release Date : 2007
Riemannian Holonomy Groups And Calibrated Geometry written by Dominic D. Joyce and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Riemannian Holonomy Groups and Calibrated Geometry covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
Gravity And Strings
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Author : Tomás Ortín
language : en
Publisher: Cambridge University Press
Release Date : 2015-03-26
Gravity And Strings written by Tomás Ortín and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-26 with Science categories.
Self-contained and comprehensive, this definitive new edition provides a complete overview of the intersection of gravity, supergravity, and superstrings.