1st Edition

Relativistic Quantum Mechanics
An Introduction to Relativistic Quantum Fields




ISBN 9781498722308
Published December 3, 2015 by CRC Press
328 Pages 21 B/W Illustrations

USD $89.95

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Book Description

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.

Table of Contents

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..

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Author(s)

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.

Reviews

"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