Connections In Classical And Quantum Field Theory

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Connections in Classical and Quantum Field Theory

L Mangiarotti,G Sardanashvily
Connections in Classical and Quantum Field Theory Book PDF

Author : L Mangiarotti,G Sardanashvily
Publisher : World Scientific
Page : 516 pages
File Size : 42,8 Mb
Release : 2000-04-28
Category : Science
ISBN : 9789814501408

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Connections in Classical and Quantum Field Theory by L Mangiarotti,G Sardanashvily Pdf

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry. keywords:Lagrangian Field Theory;Hamiltonian Field Theory;Classical Mechanics;BRST Formalism;Topological Field Theories;Non-Commutative Geometry;Theoretical Physics;Mathematical Physics;Fibre Bundle;Connection;Jet Manifold;Gauge Theory;Gravitation;Theory;Quantum Field;Geometric Quantization;Supergeometry;BRST;Theory “this book certainly offers a valuable supplement to the existing literature on the impact of connection theory on theoretical physics.” Mathematical Reviews

Connections in Classical and Quantum Field Theory

L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili
Connections in Classical and Quantum Field Theory Book PDF

Author : L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili
Publisher : World Scientific
Page : 518 pages
File Size : 51,7 Mb
Release : 2000
Category : Science
ISBN : 9812813748

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Connections in Classical and Quantum Field Theory by L. Mangiarotti,Gennadi? Aleksandrovich Sardanashvili Pdf

Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.

From Classical to Quantum Fields

Laurent Baulieu,John Iliopoulos,Roland Seneor,Roland Sénéor
From Classical to Quantum Fields Book PDF

Author : Laurent Baulieu,John Iliopoulos,Roland Seneor,Roland Sénéor
Publisher : Oxford University Press
Page : 951 pages
File Size : 44,7 Mb
Release : 2017
Category : Science
ISBN : 9780198788393

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From Classical to Quantum Fields by Laurent Baulieu,John Iliopoulos,Roland Seneor,Roland Sénéor Pdf

Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.

Lectures on Classical and Quantum Theory of Fields

Henryk Arodz,Leszek Hadasz
Lectures on Classical and Quantum Theory of Fields Book PDF

Author : Henryk Arodz,Leszek Hadasz
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 48,7 Mb
Release : 2010-11-15
Category : Science
ISBN : 9783642156243

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Lectures on Classical and Quantum Theory of Fields by Henryk Arodz,Leszek Hadasz Pdf

This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

Dynamics of Classical and Quantum Fields

Girish S. Setlur
Dynamics of Classical and Quantum Fields Book PDF

Author : Girish S. Setlur
Publisher : Taylor & Francis
Page : 383 pages
File Size : 48,5 Mb
Release : 2013-12-05
Category : Science
ISBN : 9781466556294

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Dynamics of Classical and Quantum Fields by Girish S. Setlur Pdf

Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous probl

From Classical Field Theory to Perturbative Quantum Field Theory

Michael Dütsch
From Classical Field Theory to Perturbative Quantum Field Theory Book PDF

Author : Michael Dütsch
Publisher : Springer
Page : 536 pages
File Size : 52,5 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783030047382

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From Classical Field Theory to Perturbative Quantum Field Theory by Michael Dütsch Pdf

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

Advanced Classical Field Theory

G. Giachetta
Advanced Classical Field Theory Book PDF

Author : G. Giachetta
Publisher : World Scientific
Page : 393 pages
File Size : 47,5 Mb
Release : 2009
Category : Science
ISBN : 9789812838964

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Advanced Classical Field Theory by G. Giachetta Pdf

Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.

Mathematical Aspects of Quantum Field Theory

Edson de Faria,Welington de Melo
Mathematical Aspects of Quantum Field Theory Book PDF

Author : Edson de Faria,Welington de Melo
Publisher : Cambridge University Press
Page : 128 pages
File Size : 46,5 Mb
Release : 2010-08-12
Category : Science
ISBN : 9781139489805

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Mathematical Aspects of Quantum Field Theory by Edson de Faria,Welington de Melo Pdf

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.

Geometric Formulation of Classical and Quantum Mechanics

G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili
Geometric Formulation of Classical and Quantum Mechanics Book PDF

Author : G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili
Publisher : World Scientific
Page : 405 pages
File Size : 44,6 Mb
Release : 2011
Category : Science
ISBN : 9789814313728

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Geometric Formulation of Classical and Quantum Mechanics by G. Giachetta,L. G. Magiaradze,Gennadi? Aleksandrovich Sardanashvili Pdf

The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Relativistic Quantum Mechanics and Introduction to Field Theory

Francisco J. Yndurain
Relativistic Quantum Mechanics and Introduction to Field Theory Book PDF

Author : Francisco J. Yndurain
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2011-10-02
Category : Mathematics
ISBN : 3642646743

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Relativistic Quantum Mechanics and Introduction to Field Theory by Francisco J. Yndurain Pdf

This advanced textbook supplies graduate students with a primer in quantum theory. A variety of processes are discussed with concepts such as potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory, the author emphasizes the deduction of the said potentials or currents. A modern presentation of the subject together with many exercises, unique in its unusual underlying concept of combining relativistic quantum mechanics with basic quantum field theory.

Advanced Quantum Mechanics

Reinhold Blümel
Advanced Quantum Mechanics Book PDF

Author : Reinhold Blümel
Publisher : Jones & Bartlett Learning
Page : 438 pages
File Size : 49,8 Mb
Release : 2011-08-24
Category : Science
ISBN : 9781934015520

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Advanced Quantum Mechanics by Reinhold Blümel Pdf

Physics

Introductory Quantum Mechanics

Paul R. Berman
Introductory Quantum Mechanics Book PDF

Author : Paul R. Berman
Publisher : Springer
Page : 637 pages
File Size : 51,6 Mb
Release : 2017-12-26
Category : Science
ISBN : 9783319685984

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Introductory Quantum Mechanics by Paul R. Berman Pdf

This book presents a basic introduction to quantum mechanics. Depending on the choice of topics, it can be used for a one-semester or two-semester course. An attempt has been made to anticipate the conceptual problems students encounter when they first study quantum mechanics. Wherever possible, examples are given to illustrate the underlying physics associated with the mathematical equations of quantum mechanics. To this end, connections are made with corresponding phenomena in classical mechanics and electromagnetism. The problems at the end of each chapter are intended to help students master the course material and to explore more advanced topics. Many calculations exploit the extraordinary capabilities of computer programs such as Mathematica, MatLab, and Maple. Students are urged to use these programs, just as they had been urged to use calculators in the past. The treatment of various topics is rather complete, in that most steps in derivations are included. Several of the chapters go beyond what is traditionally covered in an introductory course. The goal of the presentation is to provide the students with a solid background in quantum mechanics.

Integrable Systems, Quantum Groups, and Quantum Field Theories

Alberto Ibort,M.A. Rodríguez
Integrable Systems Quantum Groups and Quantum Field Theories Book PDF

Author : Alberto Ibort,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

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Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort,M.A. Rodríguez Pdf

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Classical Double Copy, The: New Connections In Gauge Theory And Gravity

Christopher White
Classical Double Copy The New Connections In Gauge Theory And Gravity Book PDF

Author : Christopher White
Publisher : World Scientific
Page : 251 pages
File Size : 50,6 Mb
Release : 2024-04-22
Category : Science
ISBN : 9781800615472

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Classical Double Copy, The: New Connections In Gauge Theory And Gravity by Christopher White Pdf

Our current understanding of nature is in terms of matter that is acted on by forces. There are four fundamental forces, of which three are described by so-called gauge theories, a type of quantum field theory. The fourth force, gravity, is best described by general relativity, and our traditional ways of thinking about gauge theories and gravity look completely different from each other.In recent years, an exciting new correspondence called the 'double copy' has emerged, which suggests that the above theories may be much more closely related than previously thought. Inspired by previous work in string theory, it originated in the study of how particles interact, but has since been generalised to show that many gravitational quantities can be simply obtained by recycling simpler gauge theory results. This has significant practical applications — such as new calculational tools for astrophysics — but is also of conceptual importance, in suggesting that our current ways of thinking about fundamental physics are hiding a vast underlying structure.This book reviews our current theories of fundamental physics, before describing in detail how the double copy was discovered, how it can be applied to different types of object in gauge or gravity theory, and what its current and future applications are. No prior knowledge of quantum field theory or string theory is assumed, such that the book will be of interest to a broad audience of physicists and mathematicians.

Quantum Field Theory for Economics and Finance

B. E. Baaquie
Quantum Field Theory for Economics and Finance Book PDF

Author : B. E. Baaquie
Publisher : Cambridge University Press
Page : 717 pages
File Size : 53,9 Mb
Release : 2018-08-23
Category : Business & Economics
ISBN : 9781108423151

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Quantum Field Theory for Economics and Finance by B. E. Baaquie Pdf

This book provides an introduction to how the mathematical tools from quantum field theory can be applied to economics and finance. Providing a range of quantum mathematical techniques for designing financial instruments, it demonstrates how a range of topics have quantum mechanical formulations, from asset pricing to interest rates.