Search Results: an-introduction-to-riemann-surfaces-algebraic-curves-and-moduli-spaces-theoretical-and-mathematical-physics

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

Author: Martin Schlichenmaier

Publisher: Springer Science & Business Media

ISBN: 3540711759

Category: Science

Page: 217

View: 3066

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.

An Introduction to Families, Deformations and Moduli

Author: T. E. Venkata Balaji

Publisher: Universitätsverlag Göttingen

ISBN: 3941875329

Category: Complex manifolds

Page: 208

View: 7019

Quantum Field Theory I: Basics in Mathematics and Physics

A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 354034764X

Category: Science

Page: 1051

View: 1270

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.

Quantum Field Theory III: Gauge Theory

A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3642224210

Category: Mathematics

Page: 1126

View: 890

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).

Differentialgeometrie, Topologie und Physik

Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 2114

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.

Mathematical Tools for Physicists

Author: George L. Trigg

Publisher: John Wiley & Sons

ISBN: 3527607250

Category: Science

Page: 686

View: 1079

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.

Handbook of Teichmüller Theory

Author: Athanase Papadopoulos

Publisher: European Mathematical Society

ISBN: 9783037191033

Category: Mathematics

Page: 866

View: 1382

Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs

Author: S. M. Natanzon

Publisher: American Mathematical Soc.

ISBN: 9780821889657

Category:

Page: N.A

View: 9565

Riemann Surfaces and Algebraic Curves

Author: Renzo Cavalieri,Eric Miles

Publisher: Cambridge University Press

ISBN: 110714924X

Category: Mathematics

Page: 200

View: 839

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

Computational Approach to Riemann Surfaces

Author: Alexander I. Bobenko

Publisher: Springer Science & Business Media

ISBN: 3642174124

Category: Mathematics

Page: 257

View: 2837

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.

Ueber das Verschwinden der Theta-Functionen

Author: Bernhard Riemann

Publisher: N.A

ISBN: N.A

Category: Functions, Theta

Page: 12

View: 7064

Analysis and Mathematical Physics

Author: Bjorn Gustafsson,Alexander Vasiliev

Publisher: Springer Science & Business Media

ISBN: 9783764399061

Category: Mathematics

Page: 514

View: 6468

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.

The Moduli Space of Curves

Author: Robert H. Dijkgraaf,Carel Faber,Gerard B.M. van der Geer

Publisher: Springer Science & Business Media

ISBN: 1461242649

Category: Mathematics

Page: 563

View: 1989

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.

Encyclopedia of applied physics

Author: American Institute of Physics

Publisher: Wiley-VCH

ISBN: 9783527294756

Category: Science

Page: 591

View: 5447

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.

The Geometry of Moduli Spaces of Sheaves

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: 3125

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.

Moduli Spaces of Curves, Mapping Class Groups and Field Theory

Author: Xavier Buff

Publisher: American Mathematical Soc.

ISBN: 0821831674

Category: Mathematics

Page: 131

View: 3581

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.

Gesammelte Abhandlungen

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

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 751

View: 8277

Einführung in die Geometrie und Topologie

Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 1945

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.

Consistent classical supergravity theories

Author: Martin Müller

Publisher: Springer

ISBN: 9783540514275

Category: Supergravity

Page: 125

View: 4018

Supergravity can be seen as an intermediate step between general relativity and a future quantum theory of gravity. For the reader familiar with the basic concepts, this volume gives a concise presentation of both conformal and Poincaré supergravity. The consistent four-dimensional supergravity theories are classified. For the practitioner in this field the book will be a valuable source, in particular with respect to the rather awkward formulae needed for further modelling, which have been carefully checked by the author. The book will be helpful not only for researchers, but also for advanced students.

Subject Guide to Books in Print

An Index to the Publishers' Trade List Annual

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5135

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