2nd Edition

# Relativistic Quantum Mechanics An Introduction to Relativistic Quantum Fields

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 summarise 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 analysed. 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 and third books in this collection: Electroweak Interactions and An Introduction to Gauge Theories.

**Key Features of the new edition:**

Besides a general revision of text and formulae, three new chapters have been added.

· Chapter 17 introduces and discusses double beta decay processes with and without neutrino emission, the latter being the only process able to determine the Dirac or Majorana nature of the neutrino (discussed in Chapter 13). A discussion of the limits to the Majorana neutrino mass obtained recently in several underground laboratories is included.

· Chapter 18 illustrates the calculation of the mass spectrum of “quarkonia” (mesons composed by a pair of heavy, charm or beauty quarks), in analogy with the positronium spectrum discussed in Chapter 12. This calculation has put into evidence the existence of “unexpected” states and has led to the new field of “exotic hadrons”, presently under active theoretical and experimental scrutiny.

· Chapter 19 illustrates the Born-Oppenheimer approximation, extensively used in the computation of simple molecules, and its application to the physics of exotic hadrons containing a pair of heavy quarks, with application to the recently observed doubly charmed baryons.

Chapter 1: The Symmetries of Space-Time. Chapter 2: The Classical Free Particle. Chapter 3: The Lagrangian Theory of Fields. Chapter 4: The Klein-Gordon Field Quantisation. Chapter 5: Electromagnetic Field Quantisation. Chapter 6: The Dirac Equation. Chapter 7: Quantisation of the Dirac Field. Chapter 8: Free Field Propagators. Chapter 9: Interactions. Chapter 10: Time Evolution of Quantum Systems. Chapter 11: Relativistic Perturbation Theory. Chapter 12: The Discrete Symmetries: P, C, T. Chapter 13: Weyl and Majorana Neutrinos. Chapter 14: Applications: QED. Chapter 15: Applications: Weak Interactions. Chapter 16: Neutrino Oscillations. Chapter 17: Neutrinoless Double-Beta Decay. Chapter 18: A Leap Forward: Charmonium. Chapter 19: The Born-Oppenheimer Approximation for the Doubly Charmed Baryon. Appendix A: Basic Elements of Quantum Mechanics. Appendix B: The Non-relativistic Hydrogen Atom. Bibliography. Index.

### Biography

**Luciano Maiani**, born in 1941, is emeritus professor of theoretical physics

at the University of Rome, \La Sapienza", and author of more than two hundred

scienti_c publications on the theoretical physics of elementary particles.

He, together with S. Glashow and J. Iliopoulos, made the prediction of a new

family of particles, those with \charm", which form an essential part of the

uni_ed theory of the weak and electromagnetic forces. He has been president

of the Italian Institute for Nuclear Physics (INFN), Director-General of

CERN in Geneva and president of the Italian National Council for Research

(CNR). He promoted the development of the Virgo Observatory for gravitational

wave detection, the neutrino beam from CERN to Gran Sasso and at

CERN directed the crucial phases of the construction of the Large Hadron

Collider. He has taught and worked in numerous foreign institutes. He was

head of the theoretical physics department at the University of Rome, \La

Sapienza", from 1976 to 1984 and held the chair of theoretical physics from

1984 to 2011. He is a member of the Italian Lincean Academy and a Fellow

of the American Physical Society.

**Omar Benhar**, born in 1953, is an INFN research director and teaches gauge

theories at the University of Rome, \La Sapienza". He has worked extensively

in the USA as visiting professor, at the University of Illinois and the Old

Dominion University, as well as associate scientist at the Thomas Je_erson

National Accelerator Facility. Since 2013, he has served as an adjunct professor

at the Centre for Neutrino Physics of Virginia Polytechnic Institute and

State University. He is the author of more than a hundred scienti_c papers

on the theory of many-particle systems, the structure of compact stars and

electroweak interactions of nuclei.

Library of Congress Cataloging-in-Publication Data

Names: Maiani, L. (Luciano), author. | Benhar, Omar, author.

Title: Relativistic quantum mechanics / Luciano Maiani and Omar Benhar.

Description: Second edition. | Boca Raton, FL : CRC Press, 2024. | Includes

bibliographical references and index. | Summary: "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 summarise 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 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 analysed. 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"-- Provided by publisher.

Identifiers: LCCN 2024001588 | ISBN 9781032565941 (hbk) | ISBN

9781032559407 (pbk) | ISBN 9781003436263 (ebk)

Subjects: LCSH: Quantum theory.

Classification: LCC QC174.12 .M33 2024 | DDC 530.12--dc23/eng/20240509

LC record available at https://lccn.loc.gov/2024001588