Wolfgang Hollik - Introduction To Quantum Field Theory And The Standard Model

_______INTRODUCTION TO_______

Quantum Field Theory
and the Standard Model

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________INTRODUCTION TO_________

Quantum Field Theory
and the Standard Model

Wolfgang Hollik

Max Planck Institute for Physics, Germany

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Library of Congress Cataloging-in-Publication Data

Names: Hollik, W. (Wolfgang), 1951author.

Title: Introduction to quantum field theory and the standard model / Wolfgang Hollik, Max Planck Institute for Physics, Germany.

Description: New Jersey : World Scientific, [2022] | Includes bibliographical references and index.

Identifiers: LCCN 2021050559 (print) | LCCN 2021050560 (ebook) | ISBN 9789811242175 (hardcover) | ISBN 9789811242182 (ebook) | ISBN 9789811242199 (ebook other)

Subjects: LCSH: Quantum field theory.

Classification: LCC QC174.45 .H647 2022 (print) | LCC QC174.45 (ebook) | DDC 530.14/3--dc23/eng/20211201

LC record available at https://lccn.loc.gov/2021050559

LC ebook record available at https://lccn.loc.gov/2021050560

British Library Cataloguing-in-Publication Data

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Copyright 2022 by World Scientific Publishing Co. Pte. Ltd.

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Preface

These lecture notes are based on material presented during courses at the Technical University Munich (TUM) to physics students with interest in particle physics and its theoretical foundation. This material has been elaborated and expanded, to provide both the conceptual ideas regarding the Standard Model of particle physics and some technical details on the formulation within the context of gauge theories. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as an example of a successful theory of a fundamental interaction, and is further extended towards quantum chromo-dynamics for the strong interaction and to the electroweak Standard Model for the unified electromagnetic and weak interactions, which could celebrate an enormous success by the 2012 discovery of a new spin-0 particle showing the properties of the predicted Higgs boson.

Quantum field theory is the primary theoretical tool for the description of the microscopic dynamics of the strong and electroweak interactions. It is thus necessary to provide an introduction to the basic concepts of relativistic quantum field theory, perturbation theory, Feynman graphs, before advancing to Abelian and non-Abelian gauge theories and their application to the fundamental forces and the resulting phenomenological implications with their experimental tests. The success of perturbative QCD at high energies goes with the basic features of asymptotic freedom and the parton model, displayed in the chapter on QCD. Phenomenology of W and Z bosons as well as Higgs bosons is part of the electroweak chapter including recent experimental results, precision tests and current status of the Standard Model.

The style is elementary and pedagogical. The text is at a level appropriate for students who had already a course in quantum mechanics and are familiar with classical electrodynamics and the basics of special relativity. Special relativity in the first chapter is a compact recapitulation serving as a summary and for setting the language and notations. The formalism of quantum field theory is kept at a minimum. Especially the Feynman rules are not derived in a systematic way; instead, the method is elucidated on the basis of examples to convey a more intuitive understanding that is thought to be more helpful for an early overview rather than proofs and advanced technical effort. Explicit calculations are performed for selected examples so that the reader becomes acquainted with practical calculations in particular for scattering amplidudes, cross sections and decay rates at lowest order. Extra material on specific theoretical issues is included in various places for the interested student; it can be skipped during a first reading.

The lecture notes provide a compact introduction, convenient for students dealing with particle physics and related areas to get first information before specializing towards experimental or theoretical topics. They may also serve as a basis to study elaborate textbooks, like Michael Peskin and Daniel Schroeders An Introduction to Quantum Field Theory (Westview Press, 1995), Matthew Schwartzs Quantum Field Theory and the Standard Model (Cambridge University Press, 2014), or Steven Weinbergs The Quantum Theory of Fields (Cambridge University Press, 1995).

It is my special concern to thank my colleagues from the Physics Department at TUM, Peter Fierlinger, Lothar Oberauer, Stephan Paul, and Stefan Schnert, for the pleasant cooperation during various lecture courses covering both experimental and theoretical aspects, over many years of teaching.

Wolfgang Hollik

Contents

Chapter 1

Special Relativity

It is a assumed that the reader is already familiar with special relativity, e.g. at the level of a first course on electrodynamics. Thus, this chapter serves essentially as a summary of the relevant theoretical ingredients, to introduce notations and conventions, and to provide the classical basis for advancing to quantum theory in the subseqent chapters.

The Special Theory of Relativity is based on the following two fundamental principles.

(1)Principle of relativity
The laws of nature are in all inertial frames of the same form.

(2)Invariance of light propagation
The propagation of light is independent of the inertial frame. For a pointlike source at a space point