1st Edition

Relativistic Quantum Mechanics An Introduction to Relativistic Quantum Fields

By Luciano Maiani, Omar Benhar Copyright 2016
    328 Pages 21 B/W Illustrations
    by CRC Press

    328 Pages
    by CRC Press

    Written by two of the most prominent leaders in particle physics, Relativistic Quantum Mechanics: An Introduction to Relativistic Quantum Fields provides a classroom-tested introduction to the formal and conceptual foundations of quantum field theory. Designed for advanced undergraduate- and graduate-level physics students, the text only requires previous courses in classical mechanics, relativity, and quantum mechanics.

    The introductory chapters of the book summarize the theory of special relativity and its application to the classical description of the motion of a free particle and a field. The authors then explain the quantum formulation of field theory through the simple example of a scalar field described by the Klein–Gordon equation as well as its extension to the case of spin ½ particles described by the Dirac equation. They also present the elements necessary for constructing the foundational theories of the standard model of electroweak interactions, namely quantum electrodynamics and the Fermi theory of neutron beta decay. Many applications to quantum electrodynamics and weak interaction processes are thoroughly analyzed. The book also explores the timely topic of neutrino oscillations.

    Logically progressing from the fundamentals to recent discoveries, this textbook provides students with the essential foundation to study more advanced theoretical physics and elementary particle physics. It will help them understand the theory of electroweak interactions and gauge theories.

    View the second book in this collection: Electroweak Interactions.

    THE SYMMETRIES OF SPACE-TIME
    THE PRINCIPLE OF RELATIVITY
    PROPER AND ORTHOCHRONOUS LORENTZ TRANSFORMATIONS
    CAUSAL STRUCTURE OF SPACE-TIME
    CONTRAVARIANT AND COVARIANT VECTORS

    THE CLASSICAL FREE PARTICLE
    SPACE-TIME MOTION
    PARTICLE OF ZERO MASS
    ACTION PRINCIPLE FOR THE FREE PARTICLE
    THE MASS-ENERGY RELATION

    THE LAGRANGIAN THEORY OF FIELDS
    THE ACTION PRINCIPLE
    HAMILTONIAN AND CANONICAL FORMALISM
    TRANSFORMATION OF FIELDS
    CONTINUOUS SYMMETRIES
    NOETHER’S THEOREM
    ENERGY-MOMENTUM TENSOR

    KLEIN–GORDON FIELD QUANTISATION
    THE REAL SCALAR FIELD
    GREEN’S FUNCTIONS OF THE SCALAR FIELD
    QUANTISATION OF THE SCALAR FIELD

    ELECTROMAGNETIC FIELD QUANTISATION
    MAXWELL’S EQUATIONS IN COVARIANT FORM
    GREEN’S FUNCTIONS OF THE ELECTROMAGNETIC FIELD
    THE MAXWELL–LORENTZ EQUATIONS
    HAMILTON FORMALISM AND MINIMAL SUBSTITUTION
    QUANTISATION OF THE ELECTROMAGNETIC FIELD IN VACUUM
    THE SPIN OF THE PHOTON

    THE DIRAC EQUATION
    FORM AND PROPERTIES OF THE DIRAC EQUATION
    THE RELATIVISTIC HYDROGEN ATOM
    TRACES OF THE γ MATRICES

    QUANTISATION OF THE DIRAC FIELD
    PARTICLES AND ANTIPARTICLES
    SECOND QUANTISATION: HOW IT WORKS
    CANONICAL QUANTISATION OF THE DIRAC FIELD
    THE REPRESENTATION OF THE LORENTZ GROUP
    MICROCAUSALITY
    THE RELATION BETWEEN SPIN AND STATISTICS

    FREE FIELD PROPAGATORS
    THE TIME-ORDERED PRODUCT
    PROPAGATORS OF THE SCALAR FIELD
    PROPAGATORS OF THE DIRAC FIELD
    THE PHOTON PROPAGATOR

    INTERACTIONS
    QUANTUM ELECTRODYNAMICS
    THE FERMI INTERACTION FOR β DECAY
    STRONG INTERACTIONS
    HADRONS, LEPTONS AND FIELDS OF FORCE

    TIME EVOLUTION OF QUANTUM SYSTEMS
    THE SCHRÖDINGER REPRESENTATION
    THE HEISENBERG REPRESENTATION
    THE INTERACTION REPRESENTATION
    SYMMETRIES AND CONSTANTS OF THE MOTION

    RELATIVISTIC PERTURBATION THEORY
    THE DYSON FORMULA
    CONSERVATION LAWS
    COLLISION CROSS SECTION AND LIFETIME

    THE DISCRETE SYMMETRIES: P, C, T
    PARITY
    CHARGE CONJUGATION
    TIME REVERSAL
    TRANSFORMATION OF THE STATES
    SOME APPLICATIONS
    THE CPT THEOREM

    WEYL AND MAJORANA NEUTRINOS
    THE WEYL NEUTRINO
    THE MAJORANA NEUTRINO
    RELATIONSHIPS BETWEEN WEYL, MAJORANA AND DIRAC NEUTRINOS

    APPLICATIONS: QED
    SCATTERING IN A CLASSICAL COULOMB FIELD
    ELECTROMAGNETIC FORM FACTORS
    THE ROSENBLUTH FORMULA
    COMPTON SCATTERING
    COMPTON SCATTERING ON RELATIVISTIC ELECTRONS
    THE PROCESSES γγ → e+e− and e+e− → γγ
    e+ e− → μ+ μ− ANNIHILATION

    APPLICATIONS: WEAK INTERACTIONS
    NEUTRON DECAY
    MUON DECAY
    UNIVERSALITY, CURRENT × CURRENT THEORY
    TOWARDS A FUNDAMENTAL THEORY

    NEUTRINO OSCILLATIONS
    OSCILLATIONS IN VACUUM
    NATURAL AND ARTIFICIAL NEUTRINOS
    INTERACTION WITH MATTER: THE MSW EFFECT
    ANALYSIS OF THE EXPERIMENTS
    OPEN PROBLEMS

    APPENDIX: BASIC ELEMENTS OF QUANTUM MECHANICS
    THE PRINCIPLE OF SUPERPOSITION
    LINEAR OPERATORS
    OBSERVABLE QUANTITIES AND HERMITIAN OPERATORS
    THE NON-RELATIVISTIC SPIN 0 PARTICLE
    THE NON-RELATIVISTIC HYDROGEN ATOM

    Some end-of-chapter problems are included..

    Biography

    Luciano Maiani is a professor of physics at La Sapienza University of Rome. He was the president of Italy's Institute for Nuclear Physics (INFN), director-general of the European Organization for Nuclear Research (CERN), and president of Italy's National Research Council (CNR). He is the author or coauthor of more than 200 scientific publications on the theory of elementary particles. In 1970, S. Glashow, J. Iliopoulos, and Dr. Maiani put forth the important Glashow-Iliopoulos-Maiani (GIM) mechanism, which predicted charmed particles. Dr. Maiani has also won numerous honors, including the Dirac Medal. Omar Benhar is the research director at INFN and a senior member of the High Energy Theory Group at La Sapienza University of Rome. Dr. Benhar has published more than 100 papers in the areas of astroparticle physics and particle phenomenology.

    "Two prestigious authors, Maiani (physics, La Sapienza Univ. of Rome) and Benhar (research director, Institute for Nuclear Physics, Italy) have collaborated on this excellent work. The authors suggest that the reader must have a background in classical mechanics, quantum mechanics, and relativity prior to delving into this work. The first three chapters give a solid review of relativity, mechanics, and Lagrangian theory. Further chapters discuss the quantization of the electromagnetic fields and provide a thorough treatment of the Dirac equation. Of special interest is the discussion about the relation between spin and statistics, a topic often omitted in similar books. Subsequent chapters deal with propagators and interactions of electromagnetic, weak, and strong forces. After a discussion of perturbation theory, the book considers discrete symmetries, including a subsection on the CPT Theorem. Weyl and Majorana neutrinos, as well as neutrino oscillations, are discussed in some detail in later chapters. The appendix presents a useful review of key aspects of quantum mechanics.
    Summing Up: Highly recommended. Upper-division undergraduates and above."
    —J. F. Burkhart, University of Colorado at Colorado Springs, in the January 2017 issue of CHOICE

    "Recently I had the great pleasure of reading a draft of Luciano Maiani’s book Electroweak Interactions. I praised the primacy of physical principles over formal aspects. The same spirit prevails in the present volume Relativistic Quantum Mechanics, which belongs to the same series. Every concept is introduced as a result of simple physical arguments. By following this book, students will understand the basis of relativistic invariance, that of the relativistic wave equations and the systematics of perturbation theory. They will get everything needed for the study of the gauge theories of particle physics and they will realize that this road points unmistakably to a fully relativistic quantum field theory. I understand that its formal development will be the subject of the third volume in the series. I have fully enjoyed reading the first two books and I am looking forward to the pleasure of reading the third one."
    John Iliopoulos, Ecole Normale Supérieure, Paris

    "The authors masterfully guide the reader through the most direct approaches to constructions of relativistic quantum mechanics and fundamentals of quantum field theory and further to illustrative examples of application to physical processes. The material is presented with exceptional clarity and attention to subtleties of the subject. The book can provide a solid theoretical foundation for students aspiring to become experts in the field of elementary particle physics and can serve as a reference for students and researchers in other sub-fields of physics."
    Mikhail Voloshin, Professor of Physics, University of Minnesota