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Relativistic Quantum Mechanics

An Introduction to Relativistic Quantum Fields

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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..*

## 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 ofCHOICE"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 volumeRelativistic 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