Ettore Majorana: Unpublished Research Notes on Theoretical Physics
The editors of this volume bring to life a major part of Ettore Majorana’s work that up to now was not accessible to the general audience. These are the contents of the Quaderni (notebooks) of Ettore Majorana, edited and translated in English. Ettore Majo
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Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application
Series Editors: GIANCARLO GHIRARDI, University of Trieste, Italy VESSELIN PETKOV, Concordia University, Canada TONY SUDBERY, University of York, UK ALWYN VAN DER MERWE, University of Denver, CO, USA
Volume 159 For other titles published in this series, go to www.springer.com/series/6001
Ettore Majorana: Unpublished Research Notes on Theoretical Physics Edited by
S. Esposito University of Naples “Federico II” Italy E. Recami University of Bergamo Italy A. van der Merwe University of Denver Colorado, USA R. Battiston University of Perugia Italy
Editors Salvatore Esposito Università di Napoli “Federico II” Dipartimento di Scienze Fisiche Complesso Universitario di Monte S. Angelo Via Cinthia 80126 Napoli Italy Erasmo Recami Università di Bergamo Facoltà di Ingegneria 24044 Dalmine (BG) Italy
Alwyn van der Merwe University of Denver Department of Physics and Astronomy Denver, CO 80208 USA
Roberto Battiston Università di Perugia Dipartimento di Fisica Via A. Pascoli 06123 Perugia Italy
Back cover photo of E. Majorana: Copyright by E. Recami & M. Majorana, reproduction of the photo is not allowed (without written permission of the right holders)
ISBN 978-1-4020-9113-1
e-ISBN 978-1-4020-9114-8
Library of Congress Control Number: 2008935622 c 2009 Springer Science + Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without the written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for the exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
“But, then, there are geniuses like Galileo and Newton. Well, Ettore Majorana was one of them...” Enrico Fermi (1938)
CONTENTS
Preface
xiii
Bibliography
xxxvii
Table of contents of the complete set of Majorana’s Quaderni (ca. 1927-1933) xliii
CONTENTS OF THE SELECTED MATERIAL Part I 3
Dirac Theory 1.1 1.2 1.3 1.4
1.5 1.6
Vibrating string [Q02p038] A semiclassical theory for the electron [Q02p039] 1.2.1 Relativistic dynamics 1.2.2 Field equations Quantization of the Dirac field [Q01p133] Interacting Dirac fields [Q02p137] 1.4.1 Dirac equation 1.4.2 Maxwell equations 1.4.3 Maxwell-Dirac theory 1.4.3.1 Normal mode decomposition 1.4.3.2 Particular representations of Dirac operators Symmetrization [Q02p146] Preliminaries for a Dirac equation in real terms [Q13p003] 1.6.1 First formalism 1.6.2 Second formalism 1.6.3 Angular momentum 1.6.4 Plane-wave expansion 1.6.5 Real fields 1.6.6 Interaction with an electromagnetic field
vii
3 4 4 7 22 25 25 27 29 31 32 35 35 36 38 40 44 45 45
viii
E. MAJORANA: RESEARCH NOTES ON THEORETICAL PHYSICS
1.7
Dirac-like equations for particles with spin higher than 1/2 [Q0
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