Author: Martin Schlichenmaier

Publisher: Springer Science & Business Media

ISBN: 3540711759

Category: Science

Page: 217

View: 490

This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
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A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 354034764X

Category: Science

Page: 1051

View: 8940

This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
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A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3642224210

Category: Mathematics

Page: 1126

View: 4187

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
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Author: George L. Trigg

Publisher: John Wiley & Sons

ISBN: 3527607250

Category: Science

Page: 686

View: 4567

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.
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Author: Oswald Teichmüller,Lars Valerian Ahlfors,Frederick W. Gehring

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 751

View: 5341

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Author: Alexander I. Bobenko,Christian Klein

Publisher: Springer Science & Business Media

ISBN: 3642174124

Category: Mathematics

Page: 257

View: 1555

This volume is a well structured overview of existing computational approaches to Riemann surfaces as well as those under development. It covers the software tools currently available and provides solutions to partial differential equations and surface theory.
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Author: Renzo Cavalieri,Eric Miles

Publisher: Cambridge University Press

ISBN: 110714924X

Category: Mathematics

Page: 200

View: 3414

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
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Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 6522

Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.
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Author: Björn Gustafsson,Alexander Vasil'ev

Publisher: Springer Science & Business Media

ISBN: 9783764399061

Category: Mathematics

Page: 514

View: 4070

Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.
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A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Daniel Huybrechts,Manfred Lehn

Publisher: Vieweg+Teubner Verlag

ISBN: 9783663116257

Category: Technology & Engineering

Page: 270

View: 3489

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.
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Author: S-T Yau

Publisher: World Scientific

ISBN: 9814603783

Category: String models

Page: 664

View: 7514

Contents:Introduction to Quantum Field Theory, Path Integrals and String (B Hatfield)From Polyakov to Moduli (J Polchinski)Geometry of Quantum Strings (E D'Hoker & D H Phong)BRST Quantization and BRST Cohomology (N Marcus & A Sagnotti)Analytic Structure of Two-Dimensional Quantum Field Theories (P Nelson)Geometrical Meaning of Currents in String Theory (O Alvarez & P Windey)String Field Theory and the Geometry of Moduli Space (S Giddings)String Theory Without a Background Spacetime Geometry (G Horowitz)Holomorphic Curves on Manifolds of SU(3) Holonomy (E Witten)Vertex Operator Calculus (I Frenkel et al.)On Determinant Line Bundles (D Freed)h-Invariant and the Index (I Singer)Action Principles and Global Geometry (G Zuckerman)Introduction to Moduli Space of Curves (J Harris)Moduli Space of Punctured Surfaces (R Penner)Geometric Complex Coordinates for Teichmüller Space (A Marden)Asymptotics of the Selberg Zeta Function and the Polyakov Bosonic Integrand (S Wolpert)Super Riemann Surfaces (J Rabin)Divisors on Mg and the Cosmological Constant (M Chang & Z Ran)Severi Problem: A Post-Mortem (?) (Z Ran)Slope of Subvarieties of M15 (6 2/3 ≤ S15 ≤ 6 3/4) (M Chang & Z Ran)Arithmetic Intersections (G Faltings)Deformation Theory for Cohomology of Analytic Vector Bundles on Kähler Manifolds (M Green & R Lazarsfeld)Topology and Geometry in Superstring-Inspired Phenomenology (B Greene et al.)Yukawa Couplings between (2, 1)-Forms (P Candelas)Three-Dimensional Algebraic Maniforlds with C1=0 and x=-6 (G Tian & S T Yau)Hermitian-Yang-Mills Connection on Non-Kähler Manifolds (J Li & S T Yau)Existence of Kähler-Einstein Metrics on Complete Kähler Manifolds (G Tian & S T Yau)Smoothness of the Universal Deformation Space of Compact Calabi-Yau Manifolds and its Peterson-Weil Metric (G Tian)Critical Phenomena (S Shenker) Readership: Mathematical and high energy physicists. Keywords:String Theory;Proceedings;Conference;San Diego/California
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Author: American Institute of Physics

Publisher: Wiley-VCH

ISBN: 9783527294756

Category: Science

Page: 591

View: 7292

The 23-volume Encyclopedia of Applied Physics - EAP - is a monumental first in scope, depth, and usability. It demonstrates the synergy between physics and technological applications. Information is presented according to the following subject areas: * General Aspects; Mathematical and Information Techniques * Measurement Sciences, General Devices and/or Methods * Nuclear and Elementary Particle Physics * Atomic and Molecular Physics * Electricity and Magnetism * Optics (classical and quantum) * Acoustics * Thermodynamics and Properties of Gases * Fluids and Plasma Physics * Condensed Matter: Structure and Mechanical Properties; Thermal, Acoustic, and Quantum Properties ; Electronic Properties ; Magnetic Properties ; Dielectrical and Optical Properties; Surfaces and Interfaces * Materials Science * Physical Chemistry * Energy Research and Environmental Physics * Biophysics and Medical Physics * Geophysics, Meteorology, Space Physics and Aeronautics EAP consists of 20 hardcover volumes arranged alphabetically. A cumulative subject index will be published after every three volumes, with a full index accompanying the complete work.
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Author: Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer

Publisher: Springer Science & Business Media

ISBN: 1461242649

Category: Mathematics

Page: 563

View: 6774

The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
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Author: Xavier Buff

Publisher: American Mathematical Soc.

ISBN: 0821831674

Category: Mathematics

Page: 131

View: 5339

This book grew out of a workshop on the applications of moduli spaces of Riemann surfaces in theoretical physics and number theory and on Grothendieck's dessins d'enfants and their generalizations. Chapter 1 gives an introduction to Teichmuller space that is more concise than the popular textbooks, yet contains full proofs of many useful results which are often difficult to find in the literature. This chapter also contains an introduction to moduli spaces of curves, with a detailed description of the genus zero case, and in particular of the part at infinity. Chapter 2 takes up the subject of the genus zero moduli spaces and gives a complete description of their fundamental groupoids, based at tangential base points neighboring the part at infinity; the description relies on an identification of the structure of these groupoids with that of certain canonical subgroupoids of a free braided tensor category. It concludes with a study of the canonical Galois action on the fundamental groupoids, computed using Grothendieck-Teichmuller theory. Finally, Chapter 3 studies strict ribbon categories, which are closely related to braided tensor categories: here they are used to construct invariants of 3-manifolds which in turn give rise to quantum field theories.
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