Foundations of Quantum Field Theory. Klaus D Rothe
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Название: Foundations of Quantum Field Theory

Автор: Klaus D Rothe

Издательство: Ingram

Жанр: Физика

Серия: World Scientific Lecture Notes In Physics

isbn: 9789811221941

isbn:

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       Foundations of Quantum Field Theory

       World Scientific Lecture Notes in Physics

      ISSN: 1793-1436

       Published titles*

Vol. 67:Quantum Scaling in Many-Body SystemsM A Continentino
Vol. 69:Deparametrization and Path Integral Quantization of Cosmological ModelsC Simeone
Vol. 70:Noise Sustained Patterns: Fluctuations and NonlinearitiesMarkus Loecher
Vol. 71:The QCD Vacuum, Hadrons and Superdense Matter (2nd ed.)Edward V Shuryak
Vol. 72:Massive Neutrinos in Physics and Astrophysics (3rd ed.)R Mohapatra and P B Pal
Vol. 73:The Elementary Process of BremsstrahlungW Nakel and E Haug
Vol. 74:Lattice Gauge Theories: An Introduction (3rd ed.)H J Rothe
Vol. 75:Field Theory: A Path Integral Approach (2nd ed.)A Das
Vol. 76:Effective Field Approach to Phase Transitions and Some Applications to Ferroelectrics (2nd ed.)J A Gonzalo
Vol. 77:Principles of Phase Structures in Particle PhysicsH Meyer-Ortmanns and T Reisz
Vol. 78:Foundations of Quantum Chromodynamics: An Introduction to Perturbation Methods in Gauge Theories (3rd ed.)T Muta
Vol. 79:Geometry and Phase Transitions in Colloids and PolymersW Kung
Vol. 80:Introduction to Supersymmetry (2nd ed.)H J W Müller-Kirsten and A Wiedemann
Vol. 81:Classical and Quantum Dynamics of Constrained Hamiltonian SystemsH J Rothe and K D Rothe
Vol. 82:Lattice Gauge Theories: An Introduction (4th ed.)H J Rothe
Vol. 83:Field Theory: A Path Integral Approach (3rd ed.)Ashok Das
Vol. 84:Foundations of Quantum Field TheoryKlaus Dieter Rothe

      *For the complete list of published titles, please visit http://www.worldscientific.com/series/wslnp

      World Scientific Lecture Notes in Physics – Vol. 84

       Foundations of Quantum Field Theory

       Klaus D Rothe

      University of Heidelberg, Germany

       Published by

      World Scientific Publishing Co. Pte. Ltd.

      5 Toh Tuck Link, Singapore 596224

      USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

      UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

      Library of Congress Control Number: 2020037035

       British Library Cataloguing-in-Publication Data

      A catalogue record for this book is available from the British Library.

       World Scientific Lecture Notes in Physics — Vol. 84

       FOUNDATIONS OF QUANTUM FIELD THEORY

      Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd.

      All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher.

      For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

      ISBN 978-981-122-192-7 (hardcover)

      ISBN 978-981-122-300-6 (paperback)

      ISBN 978-981-122-193-4 (ebook for institutions)

      ISBN 978-981-122-194-1 (ebook for individuals)

      For any available supplementary material, please visit

       https://www.worldscientific.com/worldscibooks/10.1142/11873#t=suppl

      Printed in Singapore

      To my wife, Neusa Maria, and my son, Thomas

      Quantum Field Theory (QFT) emerged in the 1930’s as a natural extension of Quantum Mechanics to include Special Relativity and particle creation in its second quantized formulation.

      Over the years QFT has gone through an extensive evolution with regard to the role of the quantum fields involved, the range of applicability (elementary particles, phase transitions in solid state physics), the treatment of infinities (renormalization) resulting from its local structure (microcausality), the asymptotic behaviour of Green functions (Callan–Symanzik equation, asymptotic freedom), and the analyticity property of transition amplitudes (S-matrix theory).

      In particular one has learned why Quantum Electrodynamics (QED) is so successful at low energies, whereas perturbative Quantum Chromodynamics (QCD), the theory of the strong interactions, is successful at high energies (asymptotic freedom, deep inelastic scattering). One has further learned that phenomena such as spontaneous symmetry breaking observed in solid state physics (ferromagnet) also plays a role in the theory of weak interactions in particle physics, where it is referred to as “Higgs mechanism”.

      The present lectures essentially represent the content of a two-semester course held by the author at the University of Heidelberg, and thus provides an adequate time-frame for the lecturer and student. As such it was intended to be a compact book providing a bird’s eye view of the very basic foundations of QFT, including the traditional operator, as well as the more modern path integral approach, and should serve as a good basis for post-graduate students, and as orientation for lecturers. Very extensive treatises of the subject can be found in the still excellent book of Bjorken and Drell, as well as in more up-to-date books, such as by C. Itzykson and J.-B. Zuber, E. Peskin and D.V. Schroeder, Lewis H. Ryder and S. Weinberg, which have also served as a basis for these lectures.1 Aside from the author’s point of view in presenting, choosing and arranging the material, most of it can be found in some or other way in the existing literature. We have tried to present the material in reasonable detail, with emphasis on transparency and repeated cross references, at the expense of being sometimes pedantic. We therefore believe that the reader will be able to follow the material without engaging in detailed calculations, which are cumbersome at times. Though we have exemplified various regularization procedures (Pauli–Villars, Dimensional, Taylor-subtraction), we have dominantly used the traditional Pauli–Villars regularization as being the most intuitive one.

      We paid much attention in Chapter 2 to the Lorentz group and its representations in Hilbert-space, since they play a fundamental role in Chapters СКАЧАТЬ