Lecture Notes of the Les Houches Summer School: Volume 106, June 2016
ISBN : 9780198828150
608 ページ
Hardcover
171 x 246 mm
2019年07月
This volume, 106 of the Les Houches Summer School series, brings together applications of integrability to supersymmetric gauge and string theory.
The book focuses on the application of integrability and problems in quantum field theory. Particular emphasis is given to the exact solution of planar N=4 super-Yang-Mills theory and its relation with string theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other; links with other domains are also explored.
The purpose of the Les Houches Summer School was to bring together young researchers and specialists from statistical physics, condensed matter physics, gauge and string theory, and mathematics, to stimulate discussion across these different research areas.
1. Jesper Lykke Jacobsen: Integrability in statistical systems and quantum spin chains
2 Jorg Teschner: A guide to two-dimensional conformal field theory
3 Gordon W. Semenoff: Lectures on the holographic duality of gauge fields and strings
4 David Kosower: Introduction to Scattering Amplitudes
5 Konstantin Zarembo: Integrability in Sigma-Models
6 Sergei L. Lukyanov and Alexander B. Zamolodchikov: Integrability in 2D fields theory/sigma models
7 Fabian H. L. Essler: Applications of Integrable Models in Condensed Matter and Cold Atom Physics
8 Marius de Leeuw, Asger C. Ipsen, Charlotte Kristjansen, and Matthias Wilhelm: Introduction to Integrability and One-point Functions in N = 4 SYM and its Defect Cousin
9 Nikolay Gromov: Spectrum of N=4 SYM and the Quantum Spectral Curve
10 Shota Komatsu: Three-point Functions in N = 4 Supersymmetric Yang-Mills Theory
11 Vesily Pestun: Localization and N=2 supersymmetric field theory
ISBN : 9780198739623
320 ページ
Hardcover
156 x 234 mm
2019年09月
Oxford Graduate Texts in Mathematics
Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and
complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding.
Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.
0 Basics
1 Monoidal categories
2 Linear structure
3 Dual objects
4 Monoids and comonoids
5 Frobenius structure
6 Complementarity
7 Complete positivity
8 Monoidal 2-categories
ISBN : 9780198835172
480 ページ
Hardcover
156 x 234 mm
2019年
In this modern treatment of the topic, Rolland Trapp presents an accessible introduction to the topic of multivariable calculus, supplemented by the use of fully interactive three-dimensional graphics throughout the text.
Multivariable Calculus opens with an introduction to points, curves and surfaces, easing student transitions from two- to three-dimensions, and concludes with the main theorems of vector calculus. All standard topics of multivariable calculus are covered in between, including a variety of applications within the physical sciences.
The exposition combines rigor and intuition, resulting in a well-rounded resource for students of the subject. In addition, the interactive three-dimensional graphics, accessible through the electronic text or via the companion website, enhance student understanding while improving their acuity.
The style of composition, sequencing of subjects, and interactive graphics combine to form a useful text that appeals to a broad audience: students in the sciences, technology, engineering, and mathematics alike.
1 Introduction to three dimensions
2 Introduction to vectors
3 Differentiation
4 Integration
5 Vector Analysis
ISBN : 9780198847144
112 ページ
Hardcover
156 x 234 mm
Recent groundbreaking discoveries in physics, including the discovery of the Higgs Boson and gravitational waves, have relied on chi-squared analysis and model testing, a data analysis method.
This is the first book to make chi-squared model testing accessible to students in introductory physics lab courses and others who need to learn this method, such as beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences. For over a decade, Harvard University's introductory physics lab sequence has made chi-squared model testing its central theme. Written by two faculty members, the book is based on years of experience teaching students learn how to think like scientists by testing their models using chi-squared analysis.
By including uncertainties in the curve fitting technique, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method.
A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material.
The presentation of one and two parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments.
More challenging topics requiring calculus are addressed in an advanced topic chapter.
This self-contained and student-friendly introduction includes a glossary, end of chapter problems with complete solutions, and software scripts available in several popular programming languages that the reader can use for chi-squared model testing.
1 Introduction
2 Statistical Toolkit
3 One Parameter Chi-squared Analysis
4 Two Parameter Chi-Squared Analysis
5 Case Study 1: Falling Chains
6 Case Study 2: Modeling Air Resistance on Falling Coffee Filters
7 Advanced Topics
Hardcover 2017 ISBN9780691167671 624 pp. 6 1/8 x 9 1/4 222 halftones. 8 line illus. 17 tables.
Paperback 2019 ISBN9780691192291 640 pp. 6 1/8 x 9 1/4 230 b/w illus. 17 tables.
In 1953, a man was found dead from cyanide poisoning near the Philadelphia airport with a picture of a Nazi aircraft in his wallet. Taped to his abdomen was an enciphered message. In 1912, a book dealer named Wilfrid Voynich came into possession of an illuminated cipher manuscript once belonging to Emperor Rudolf II, who was obsessed with alchemy and the occult. Wartime codebreakers tried?and failed?to unlock the book's secrets, and it remains an enigma to this day. In this lively and entertaining book, Craig Bauer examines these and other vexing ciphers yet to be cracked. Some may reveal the identity of a spy or serial killer, provide the location of buried treasure, or expose a secret society?while others may be elaborate hoaxes.
Unsolved! begins by explaining the basics of cryptology, and then explores the history behind an array of unsolved ciphers. It looks at ancient ciphers, ciphers created by artists and composers, ciphers left by killers and victims, Cold War ciphers, and many others. Some are infamous, like the ciphers in the Zodiac letters, while others were created purely as intellectual challenges by figures such as Nobel Prize?winning physicist Richard P. Feynman. Bauer lays out the evidence surrounding each cipher, describes the efforts of geniuses and eccentrics?in some cases both?to decipher it, and invites readers to try their hand at puzzles that have stymied so many others.
Unsolved! takes readers from the ancient world to the digital age, providing an amazing tour of many of history's greatest unsolved ciphers.
Craig P. Bauer is professor of mathematics at York College of Pennsylvania. He is editor in chief of the journal Cryptologia, has served as a scholar in residence at the NSA's Center for Cryptologic History, and is the author of Secret History: The Story of Cryptology. He lives in York, Pennsylvania.
Hardcover 2016 c 2017 ISBN9780691166148 320 pp. 6 1/8 x 9 1/4 164 color illus. 9 line illus. 43 tables.
Paperback 2019 c 2017 ISBN9780691192321 320 pp. 6 1/8 x 9 1/4 164 color + 9 b/w illus. 43 tables.
Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is "yes," then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book?all you need is a sense of curiosity and adventure!
Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same?or different?on all the cards. SET’s strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions?playing this game has generated new mathematics, and the math has led to new questions about the game itself.
The first book devoted to the mathematics of one of today’s most popular card games, The Joy of SET will entertain and enlighten the game enthusiast in all of us.
Liz McMahon and Gary Gordon are professors of mathematics at Lafayette College. Hannah Gordon is a SET Grand Master and currently works for the New York City Department of Education. Rebecca Gordon teaches upper-level math at Sonoma Academy in Santa Rosa, California. As a family, the coauthors have played SET together for more than twenty years.