Mathematical Aspects Of Quantum Field Theory And Strings

Mathematical Aspects of Quantum Field Theory and Strings PDF
Author: Sheldon Katz
Publisher:
ISBN: 9780521876445
Size: 16.94 MB
Format: PDF, Mobi
Category :
Languages : en
Pages :
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Book Description:

Mathematical Aspects Of String Theory

Mathematical Aspects of String Theory PDF
Author: S-T Yau
Publisher: World Scientific
ISBN: 9814603783
Size: 24.60 MB
Format: PDF, Kindle
Category : String models
Languages : en
Pages : 664
View: 3926

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Book Description: 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

Non Perturbative Quantum Field Theory Mathematical Aspects And Applications

Non perturbative Quantum Field Theory  Mathematical Aspects And Applications PDF
Author: Jurg Frohlich
Publisher: World Scientific
ISBN: 9814506567
Size: 58.19 MB
Format: PDF, Kindle
Category :
Languages : en
Pages : 854
View: 247

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Book Description: Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

Quantum Field Theory I Basics In Mathematics And Physics

Quantum Field Theory I  Basics in Mathematics and Physics PDF
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 354034764X
Size: 29.44 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 1051
View: 7735

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Book Description: 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.

Aspects Of Quantum Field Theory In Curved Spacetime

Aspects of Quantum Field Theory in Curved Spacetime PDF
Author: Stephen A. Fulling
Publisher: Cambridge University Press
ISBN: 9780521377683
Size: 21.67 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 315
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Book Description: The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.

Mathematical Aspects Of Quantum Field Theory

Mathematical Aspects of Quantum Field Theory PDF
Author: Edson de Faria
Publisher: Cambridge University Press
ISBN: 1139489801
Size: 45.13 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages :
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Book Description: Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Mathematical Aspects Of Quantum Field Theories

Mathematical Aspects of Quantum Field Theories PDF
Author: Damien Calaque
Publisher: Springer
ISBN: 3319099493
Size: 19.18 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 556
View: 6488

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Book Description: Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.

Topological Quantum Field Theory And Four Manifolds

Topological Quantum Field Theory and Four Manifolds PDF
Author: Jose Labastida
Publisher: Springer Science & Business Media
ISBN: 1402031777
Size: 47.15 MB
Format: PDF
Category : Science
Languages : en
Pages : 224
View: 5122

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Book Description: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Quantum Field Theory

Quantum Field Theory PDF
Author: Bertfried Fauser
Publisher: Springer Science & Business Media
ISBN: 376438736X
Size: 39.10 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 436
View: 6818

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Book Description: The present volume emerged from the 3rd `Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics.

Quantum Field Theory Ii

Quantum Field Theory II PDF
Author: Edouard B. Manoukian
Publisher: Springer
ISBN: 3319338528
Size: 59.79 MB
Format: PDF, Kindle
Category : Science
Languages : en
Pages : 364
View: 4449

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Book Description: This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics. The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The quantum aspect of gravitation, as described by the graviton, is introduced and perturbative quantum GR is discussed. The Schwinger-DeWitt formalism is developed to compute the one-loop contribution to the theory and renormalizability aspects of the perturbative theory are also discussed. This follows by introducing only the very basics of a non-perturbative, background-independent, formulation of quantum gravity, referred to as “loop quantum gravity”, which gives rise to a quantization of space. In the second part the author introduces supersymmetry and its consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell’s Theory as well as of Yang-Mills field theory, and of the standard model are worked out. Spontaneous symmetry breaking, improvement of the divergence problem in supersymmetric field theory, and its role in the hierarchy problem are covered. The unification of the fundamental constants in a supersymmetric version of the standard model are then studied. Geometrical aspects necessary to study supergravity are developed culminating in the derivation of its full action. The third part introduces string theory and the analysis of the spectra of the mass (squared) operator associated with the oscillating strings. The properties of the underlying fields, associated with massless particles, encountered in string theory are studied in some detail. Elements of compactification, duality and D-branes are given, as well of the generation of vertices and interactions of strings. In the final sections, the author shows how to recover GR and the Yang-Mills field Theory from string theory.