Algebraic Structure of String Field Theory
Algebraic Structure of String Field Theory

Author: Martin Doubek

Publisher: Springer Nature

Published: 2020-11-22

Total Pages: 223

ISBN-13: 3030530566

DOWNLOAD EBOOK

This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.

Introduction To String Field Theory
Introduction To String Field Theory

Author: Warren Siegel

Publisher: World Scientific

Published: 1988-09-01

Total Pages: 256

ISBN-13: 9814507458

DOWNLOAD EBOOK

This volume covers the most up-to-date findings on string field theory. It is presented in a new approach as a result of insights gained from the theory. This includes the use of a universal method for treating free field theories, which allows the derivation of a single, simple, free, local, Poincare-invariant, gauge-invariant action that can be applied directly to any fields.

Advances in Algebraic Quantum Field Theory
Advances in Algebraic Quantum Field Theory

Author: Romeo Brunetti

Publisher: Springer

Published: 2015-09-04

Total Pages: 460

ISBN-13: 3319213539

DOWNLOAD EBOOK

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Strings and Geometry
Strings and Geometry

Author: Clay Mathematics Institute. Summer School

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 396

ISBN-13: 9780821837153

DOWNLOAD EBOOK

Contains selection of expository and research article by lecturers at the school. Highlights current interests of researchers working at the interface between string theory and algebraic supergravity, supersymmetry, D-branes, the McKay correspondence andFourer-Mukai transform.

Perturbative Algebraic Quantum Field Theory
Perturbative Algebraic Quantum Field Theory

Author: Kasia Rejzner

Publisher: Springer

Published: 2016-03-16

Total Pages: 186

ISBN-13: 3319259016

DOWNLOAD EBOOK

Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.

Quantum Fields and Strings: A Course for Mathematicians
Quantum Fields and Strings: A Course for Mathematicians

Author: Pierre Deligne

Publisher: American Mathematical Society

Published: 1999-10-25

Total Pages: 801

ISBN-13: 0821820133

DOWNLOAD EBOOK

A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Mathematical Foundations of Quantum Field Theory and Perturbative String Theory
Mathematical Foundations of Quantum Field Theory and Perturbative String Theory

Author: Hisham Sati

Publisher: American Mathematical Soc.

Published: 2011-12-07

Total Pages: 370

ISBN-13: 0821851950

DOWNLOAD EBOOK

Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organized under three main chapters: Foundations for Quantum Field Theory, Quantization of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.

Lectures on Field Theory and Topology
Lectures on Field Theory and Topology

Author: Daniel S. Freed

Publisher: American Mathematical Soc.

Published: 2019-08-23

Total Pages: 202

ISBN-13: 1470452065

DOWNLOAD EBOOK

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Factorization Algebras in Quantum Field Theory
Factorization Algebras in Quantum Field Theory

Author: Kevin Costello

Publisher: Cambridge University Press

Published: 2017

Total Pages: 399

ISBN-13: 1107163102

DOWNLOAD EBOOK

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.

Geometry and Quantum Field Theory
Geometry and Quantum Field Theory

Author: Daniel S. Freed

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 476

ISBN-13: 9780821886830

DOWNLOAD EBOOK

The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.