Quantum Field Theory I

Foundations and Abelian and Non-Abelian Gauge Theories

Author: Edouard B. Manoukian

Publisher: Springer

ISBN: 3319309390

Category: Science

Page: 586

View: 3813

This textbook covers a broad spectrum of developments in QFT, emphasizing those aspects that are now well consolidated and for which satisfactory theoretical descriptions have been provided. The book is unique in that it offers a new approach to the subject and explores many topics merely touched upon, if covered at all, in standard reference works. A detailed and largely non-technical introductory chapter traces the development of QFT from its inception in 1926. The elegant functional differential approach put forward by Schwinger, referred to as the quantum dynamical (action) principle, and its underlying theory are used systematically in order to generate the so-called vacuum-to-vacuum transition amplitude of both abelian and non-abelian gauge theories, in addition to Feynman’s well-known functional integral approach, referred to as the path-integral approach. Given the wealth of information also to be found in the abelian case, equal importance is put on both abelian and non-abelian gauge theories. Particular emphasis is placed on the concept of a quantum field and its particle content to provide an appropriate description of physical processes at high energies, where relativity becomes indispensable. Moreover, quantum mechanics implies that a wave function renormalization arises in the QFT field independent of any perturbation theory - a point not sufficiently emphasized in the literature. The book provides an overview of all the fields encountered in present high-energy physics, together with the details of the underlying derivations. Further, it presents “deep inelastic” experiments as a fundamental application of quantum chromodynamics. Though the author makes a point of deriving points in detail, the book still requires good background knowledge of quantum mechanics, including the Dirac Theory, as well as elements of the Klein-Gordon equation. The present volume sets the language, the notation and provides additional background for reading Quantum Field Theory II - Introduction to Quantum Gravity, Supersymmetry and String Theory, by the same author. Students in this field might benefit from first reading the book Quantum Theory: A Wide Spectrum (Springer, 2006), by the same author.

Classical Field Theory

On Electrodynamics, Non-Abelian Gauge Theories and Gravitation

Author: Florian Scheck

Publisher: Springer

ISBN: 3662555794

Category: Science

Page: 464

View: 3579

Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

Gauge Theories in Particle Physics, Volume II

QCD and the Electroweak Theory, Third Edition

Author: I.J.R. Aitchison,A.J.G. Hey

Publisher: CRC Press

ISBN: 9780849387760

Category: Science

Page: 466

View: 5696

This is the second volume of the third edition of a successful text, now substantially enlarged and updated to reflect developments over the last decade in the curricula of university courses and in particle physics research. Volume I covered relativistic quantum mechanics, electromagnetism as a gauge theory, and introductory quantum field theory, and ended with the formulation and application of quantum electrodynamics (QED), including renormalization. Building on these foundations, this second volume provides a complete, accessible, and self-contained introduction to the remaining two gauge theories of the standard model of particle physics: quantum chromodynamics (QCD) and the electroweak theory. The treatment significantly extends that of the second edition in several important respects. Simple ideas of group theory are now incorporated into the discussion of non-Abelian symmetries. Two new chapters have been added on QCD, one devoted to the renormalization group and scaling violations in deep inelastic scattering and the other to non-perturbative aspects of QCD using the lattice (path-integral) formulation of quantum field theory; the latter is also used to illuminate various aspects of renormalization theory, via analogies with condensed matter systems. Three chapters treat the fundamental topic of spontaneous symmetry breaking: the (Bogoliubov) superfluid and the (BCS) superconductor are studied in some detail; one chapter is devoted to the implications of global chiral symmetry breaking in QCD; and one to the breaking of local SU(2)xU(1) symmetry in the electroweak theory. Weak interaction phenomenology is extended to include discussion of discrete symmetries and of the possibility that neutrinos are Majorana (rather than Dirac) particles. Most of these topics are normally found only in more advanced texts, and this is the first book to treat them in a manner accessible to the wide readership that the previous editions have attracted.

Classical Solutions in Quantum Field Theory

Solitons and Instantons in High Energy Physics

Author: Erick J. Weinberg

Publisher: Cambridge University Press

ISBN: 1139576372

Category: Science

Page: N.A

View: 8717

Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important nonperturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions.

Gauge Theories in Particle Physics

QCD and the Electroweak Theory, Third Edition

Author: I.J.R. Aitchison,A.J.G. Hey

Publisher: CRC Press

ISBN: 9780750309509

Category: Science

Page: 466

View: 1725

This is the second volume of the third edition of a successful text, now substantially enlarged and updated to reflect developments over the last decade in the curricula of university courses and in particle physics research. Volume I covered relativistic quantum mechanics, electromagnetism as a gauge theory, and introductory quantum field theory, and ended with the formulation and application of quantum electrodynamics (QED), including renormalization. Building on these foundations, this second volume provides a complete, accessible, and self-contained introduction to the remaining two gauge theories of the standard model of particle physics: quantum chromodynamics (QCD) and the electroweak theory. The treatment significantly extends that of the second edition in several important respects. Simple ideas of group theory are now incorporated into the discussion of non-Abelian symmetries. Two new chapters have been added on QCD, one devoted to the renormalization group and scaling violations in deep inelastic scattering and the other to non-perturbative aspects of QCD using the lattice (path-integral) formulation of quantum field theory; the latter is also used to illuminate various aspects of renormalization theory, via analogies with condensed matter systems. Three chapters treat the fundamental topic of spontaneous symmetry breaking: the (Bogoliubov) superfluid and the (BCS) superconductor are studied in some detail; one chapter is devoted to the implications of global chiral symmetry breaking in QCD; and one to the breaking of local SU(2)xU(1) symmetry in the electroweak theory. Weak interaction phenomenology is extended to include discussion of discrete symmetries and of the possibility that neutrinos are Majorana (rather than Dirac) particles. Most of these topics are normally found only in more advanced texts, and this is the first book to treat them in a manner accessible to the wide readership that the previous editions have attracted.

Mechanik

Von den Newtonschen Gesetzen zum deterministischen Chaos

Author: Florian Scheck

Publisher: Springer-Verlag

ISBN: 3662085933

Category: Science

Page: 431

View: 1062

Die vierte Auflage der Mechanik wurde in einigen Abschnitten ergänzt (z.B. zur Hamiltonschen Prinzipialfunktion und zum Aufstehkreisel) und auf Fehler durchgesehen, zudem wurden die Aufgaben überarbeitet, wobei nun alle vollständigen Lösungen mit aufgenommen wurden. Das wird all jenen zugute kommen, die diese umfassende Einführung in die Mechanik vorlesungsbegleitend oder zum Selbststudium verwenden wollen. Am Grundaufbau des Buches wurde nichts geändert: von elementarer Newtonscher Mechanik bis zur Diskussion von deterministischem Chaos und kontinuierlichen Systemen. Ein mathematischer Anhang und ein Wegweiser durch die Literatur runden das Buch ab.

Selfdual Gauge Field Vortices

An Analytical Approach

Author: Gabriella Tarantello

Publisher: Springer Science & Business Media

ISBN: 9780817646080

Category: Science

Page: 325

View: 3395

This monograph discusses specific examples of selfdual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern–Simons–Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices.

Lectures on Quantum Chromodynamics

Author: A. V. Smilga

Publisher: World Scientific

ISBN: 9789812810595

Category: Science

Page: 352

View: 1090

Quantum chromodynamics is the fundamental theory of strong interactions. It is a physical theory describing Nature. Lectures on Quantum Chromodynamics concentrates, however, not on the phenomenological aspect of QCD; books with comprehensive coverage of phenomenological issues have been written. What the reader will find in this book is a profound discussion on the theoretical foundations of QCD with emphasis on the nonperturbative formulation of the theory: What is gauge symmetry on the classical and on the quantum level? What is the path integral in field theory? How to define the path integral on the lattice, keeping intact as many symmetries of the continuum theory as possible? What is the QCD vacuum state? What is the effective low energy dynamics of QCD? How do the ITEP sum rules work? What happens if we heat and/or squeeze hadronic matter? Perturbative issues are also discussed: How to calculate Feynman graphs? What is the BRST symmetry? What is the meaning of the renormalization procedure? How to resum infrared and collinear singularities? And so on. The book is an outgrowth of the course of lectures given by the author for graduate students at ITEP in Moscow. Much extra material has been added. Sample Chapter(s). Introduction: Some History (331 KB). Lecture 1.1: Path Ordered Exponentials. Invariant Actions (624 KB). Lecture 1.2: Classical Solutions (266 KB). Lecture 2.1: Topological Charge (329 KB). Lecture 2.2: Explicit Solutions (338 KB). Lecture 3.1: Conventional Approach (330 KB). Lecture 3.2: Euclidean Path Integral (150 KB). Lecture 3.3: Holomorphic Representation (177 KB). Lecture 3.4: Grassmann Dynamic Variables (340 KB). Lecture 4.1: Dirac Quantization Procedure 782 KB). Lecture 4.2: Path Integral on the Lattice (330 KB). Lecture 5.1: Quantum Pendulum (534 KB). Lecture 5.2: Large Gauge Transformations in Non-Abelian Theory (395 KB). Contents: Foundations: YangOCoMills Field; Instantons; Path Integral in Quantum Mechanics; Quantization of Gauge Theories; Perturbation Theory: Diagram Technique in Simple and Complicated Theories; When the Gauge is Fixed OC Regularization and Renormalization; Running Coupling Constant; Weathering Infrared Storms; Collinear Singularities: Theory and Phenomenology; Nonperturbative QCD: Symmetries: Anomalous and Not; Quarks on Euclidean Lattice; Aspects of Chiral Symmetry; Mesoscopic QCD; Fairy QCD; ITEP Sum Rules: The Duality Festival; Hot and Dense QCD; Confinement. Readership: High energy physicists and advanced level graduate students in high energy physics."

Distributionen Und Hilbertraumoperatoren

Mathematische Methoden Der Physik

Author: Philippe Blanchard,Erwin Brüning

Publisher: Springer

ISBN: 9783211825075

Category: Science

Page: 375

View: 7797

Das Buch bietet eine Einführung in die zum Studium der Theoretischen Physik notwendigen mathematischen Grundlagen. Der erste Teil des Buches beschäftigt sich mit der Theorie der Distributionen und vermittelt daneben einige Grundbegriffe der linearen Funktionalanalysis. Der zweite Teil baut darauf auf und gibt eine auf das Wesentliche beschränkte Einführung in die Theorie der linearen Operatoren in Hilbert-Räumen. Beide Teile werden von je einer Übersicht begleitet, die die zentralen Ideen und Begriffe knapp erläutert und den Inhalt kurz beschreibt. In den Anhängen werden einige grundlegende Konstruktionen und Konzepte der Funktionalanalysis dargestellt und wichtige Konsequenzen entwickelt.

Relativistische Quantenmechanik

Author: Armin Wachter

Publisher: Springer-Verlag

ISBN: 3540274847

Category: Science

Page: 390

View: 2627

- Welche Probleme tauchen in relativistischen Erweiterungen der Schrödinger-Theorie auf, insbesondere wenn man an der gewohnten Ein-Teilchen-Wahrscheinlichkeitsinterpretation festhält? - Inwieweit können diese Schwierigkeiten überwunden werden? - Worin besteht die physikalische Notwendigkeit von Quantenfeldtheorien? Viele Bücher geben auf solch fundamentale Verständnisfragen nur unzureichend Antwort, indem sie das relativistisch-quantenmechanische Ein-Teilchenkonzept zugunsten einer möglichst frühen Einführung der Feldquantisierung relativ schnell abhandeln oder ganz weglassen. Im Gegensatz dazu betont das vorliegende Lehrbuch gerade diesen Ein-Teilchenaspekt (relativistische Quantenmechanik ‚im engeren Sinne’), diskutiert die damit einhergehenden Probleme und motiviert somit auf physikalisch verständliche Weise die Notwendigkeit quantisierter Felder. Die ersten beiden Kapitel beschäftigen sich mit der ausführlichen Darlegung und Gegenüberstellung der Klein-Gordon- und Dirac-Theorie - immer mit Blick auf die nichtrelativistische Theorie. Im dritten Kapitel werden relativistische Streuprozesse behandelt und die Feynman-Regeln aus Propagatorverfahren heraus entwickelt. Dabei wird auch hier deutlich, warum man letztlich um eine quantenfeldtheoretische Begründung nicht herumkommt. Dieses Lehrbuch wendet sich an alle Studierenden der Physik, die an einer übersichtlich geordneten Darstellung der relativistischen Quantenmechanik ‚im engeren Sinne’ und deren Abgrenzung zu Quantenfeldtheorien interessiert sind.

Courses of Study

Author: Cornell University

Publisher: N.A

ISBN: N.A

Category: Education

Page: N.A

View: 7567

American Scientist

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Greek letter societies

Page: N.A

View: 9409

The Geometric Phase in Quantum Systems

Foundations, Mathematical Concepts, and Applications in Molecular and Condensed Matter Physics

Author: Arno Bohm,Ali Mostafazadeh,Hiroyasu Koizumi,Qian Niu,Josef Zwanziger

Publisher: Springer Science & Business Media

ISBN: 3662103338

Category: Science

Page: 427

View: 6283

From the reviews: "...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).

Quantenmechanik (QM I)

Eine Einführung

Author: Franz Schwabl

Publisher: Springer-Verlag

ISBN: 3540736751

Category: Science

Page: 430

View: 1430

Das bewährte Standardlehrbuch in umfassend überarbeiteter und ergänzter 7. Auflage mit zahlreichen neu gestalteten Abbildungen, neuen Kapiteln zur supersymmetrischen Quantenmechanik und Theorie des Messprozesses sowie über 100 Aufgaben. Neben den Grundlagen und vielen Anwendungen erörtert der Autor neue Aspekte der Quantentheorie und ihrer experimentellen Überprüfung. Die explizite Ausführung aller Zwischenrechnungen hilft Studierenden, Quantenmechanik schneller und leichter zu verstehen. Die optimale Vorbereitung auf "Quantenmechanik für Fortgeschrittene (QM II)" desselben Autors. Im Anhang: mathematische Hilfsmittel und ergänzende Formeln.

Differentialgeometrie, Topologie und Physik

Author: Mikio Nakahara

Publisher: Springer-Verlag

ISBN: 3662453002

Category: Science

Page: 597

View: 374

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.

The Theory and Applications of Instanton Calculations

Author: Manu Paranjape

Publisher: Cambridge University Press

ISBN: 1107155479

Category: Science

Page: 326

View: 5947

This book explains in detail the key concepts, calculations and applications elucidating quantum tunnelling mediated by instantons, using the Feynman path integral.

Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1250