Ettore Majorana

Unpublished Research Notes on Theoretical Physics

By: Salvatore Esposito (Editor), E. Recami (Editor), Alwyn van der Merwe (Editor)

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Hardcover | 15 October 2008

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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 Majorana had an astounding talent for Physics that made an impression on all the colleagues who had the opportunity to know him. Enrico Fermi, who took him in his group when he was a student, ranked him with Galilei and Newton. Ettore Majorana's career was cut short in 1938, as he mysteriously disappeared at the age of 32, leaving many unpublished works.

This book reveals an interesting perspective over the points of view, the interests, the approach to physical problems of this great physicist and it shows that he had advanced his comprehension of physics to levels that were only reached by other physicists ten years after, or even later. The editors have inserted minimal text, in order to leave the original calculations by Majorana intact, and at the same time help the reader when the formalism had been left unexplained. The preface to this book provides fascinating reflections on the life and pioneering work of this exceptional physicist, placing it in the context of the physical discoveries of the following years. This book will have considerable interests to all those interested in the development of the history of Physics.

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"The topics covered in the Quaderni range from classical physics to quantum field theory. ... The editors inserted a minimal number of words to facilitate the reading of the calculations. I find this book extremely useful, because it signifies the importance of mathematics as a unifying tool for science as a whole. Even research physicists working in elementary particle physics will find this book of value in their pursuits." (Gert Roepstorff, Zentralblatt MATH, Vol. 1194, 2010)

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Published: 28th October 2010

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Preface	p. xiii
Bibliography	p. xxxvii
Table of contents of the complete set of Majorana's Quaderni (ca. 1927-1933)	p. xliii
Contents Of The Selected Material

Dirac Theory	p. 3
Vibrating string [Q02p038]	p. 3
A semiclassical theory for the electron [Q02p039]	p. 4
Relativistic dynamics	p. 4
Field equations	p. 7
Quantization of the Dirac field [Q01p133]	p. 22
Interacting Dirac fields [Q02p137]	p. 25
Dirac equation	p. 25
Maxwell equations	p. 27
Maxwell-Dirac theory	p. 29
Normal mode decomposition	p. 31
Particular representations of Dirac operators	p. 32
Symmetrization [Q02p146]	p. 35
Preliminaries for a Dirac equation in real terms [Q13p003]	p. 35
First formalism	p. 36
Second formalism	p. 38
Angular momentum	p. 40
Plane-wave expansion	p. 44
Real fields	p. 45
Interaction with an electromagnetic field	p. 45
Dirac-like equations for particles with spin higher than 1/2 [Q04p154]	p. 47
Spin-1/2 particles (4-component spinors)	p. 47
Spin-7/2 particles (16-component spinors)	p. 48
Spin-1 particles (6-component spinors)	p. 48
5-component spinors	p. 55
Quantum Electrodynamics	p. 57
Basic lagrangian and hamiltonian formalism for the electromagnetic field [Q01p066]	p. 57
Analogy between the electromagnetic field and the Dirac field [Q02a101]	p. 59
Electromagnetic field: plane wave operators [Q01p068]	p. 64
Dirac formalism	p. 68
Quantization of the electromagnetic field [Q03p061]	p. 71
Continuation I: angular momentum [Q03p155]	p. 78
Continuation II: including the matter fields [Q03p067]	p. 82
Quantum dynamics of electrons interacting with an electromagnetic field [Q02p102]	p. 84
Continuation [Q02p037]	p. 94
Quantized radiation field [Q17p129b]	p. 95
Wave equation of light quanta [Q17p142]	p. 100
Continuation [Q17p151]	p. 101
Free electron scattering [Q17p133]	p. 104
Bound electron scattering [Q17p142]	p. 112
Retarded fields [Q05p065]	p. 116
Time delay	p. 118
Magnetic charges [Q03p163]	p. 119
Appendix: Potential experienced by an electric charge [Q02p101]	p. 121

Atomic Physics	p. 125
Ground state energy of a two-electron atom [Q12p058]	p. 125
Perturbation method	p. 125
Variational method	p. 128
First case	p. 129
Second case	p. 130
Third case	p. 131
Wavefunctions of a two-electron atom [Q17p152]	p. 133
Continuation: wavefunctions for the helium atom [Q05p156]	p. 136
Self-consistent field in two-electron atoms [Q16p100]	p. 141
2s terms for two-electron atoms [Q16p157b]	p. 144
Energy levels for two-electron atoms [Q07p004]	p. 144
Preliminaries for the X and Y terms	p. 148
Simple terms	p. 151
Electrostatic energy of the 2s2p term	p. 155
Perturbation theory for s terms	p. 157
2s2p ³P term	p. 158
X term	p. 159
2s2s ¹S and 2p2p ¹S terms	p. 169
1s1s term	p. 170
1s2s term	p. 174
Continuation	p. 175
Other terms	p. 176
Ground state of three-electron atoms [Q16p157a]	p. 183
Ground state of the lithium atom [Q16p098]	p. 184
Electrostatic potential	p. 184
Ground state	p. 185
Asymptotic behavior for the s terms in alkali [Q16p158]	p. 190
First method	p. 191
Second method	p. 195
Atomic eigenfunctions I [Q02p130]	p. 197
Atomic eigenfunctions II [Q17p161]	p. 201
Atomic energy tables [Q06p026]	p. 204
Polarization forces in alkalies [Q16p049]	p. 205
Complex spectra and hyperfine structures [Q05p051]	p. 211
Calculations about complex spectra [Q05p131]	p. 219
Resonance between a <$>p (ell = 1)<$> electron and an electron with azimuthal quantum number <$>ell^{prime}<$> [Q07p117]	p. 223
Resonance between a d electron and a p shell I	p. 224
Eigenfunctions of <$>dfrac{5}{2}<$>, <$>dfrac{3}{2}<$>, <$>pfrac{3}{2}<$> and <$>pfrac{1}{2}<$> electrons	p. 225
Resonance between a d electron and a p shell II	p. 227
Magnetic moment and diamagnetic susceptibility for a one-electron atom (relativistic calculation) [Q17p036]	p. 229
Theory of incomplete P' triplets [Q07p061]	p. 233
Spin-orbit couplings and energy levels	p. 233
Spectral lines for Mg and Zn	p. 237
Spectral lines for Zn, Cd and Hg	p. 238
Hyperfine structure: relativistic Rydberg corrections [Q04p143]	p. 239
Non-relativistic approximation of Dirac equation for a two-particle system [Q04p149]	p. 242
Non-relativistic decomposition	p. 243
Electromagnetic interaction between two charged particles	p. 244
Radial equations	p. 245
Hyperfine structures and magnetic moments: formulae and tables [Q04p165]	p. 246
Hyperfine structures and magnetic moments: calculations [Q04p169]	p. 251
First method	p. 251
Second method	p. 254
Molecular Physics	p. 261
The helium molecule [Q16p001]	p. 261
The equation for cr-electrons in elliptic coordinates	p. 261
Evaluation of P₂ for s-electrons: relation between W and	p. 263
Evaluation of P₁	p. 275
Vibration modes in molecules [Q06p031]	p. 275
The acetylene molecule	p. 278
Reduction of a three-fermion to a two-particle system [Q03p176]	p. 282
Statistical Mechanics	p. 287
Degenerate gas [Q17p097]	p. 287
Pauli paramagnetism [Q18p157]	p. 288
Ferromagnetism [Q08p014]	p. 289
Ferromagnetism: applications [Q08p046]	p. 300
Again on ferromagnetism [Q06p008]	p. 307

The Theory of Scattering	p. 311
Scattering from a potential well [Q06p015]	p. 311
Simple perturbation method [Q06p024]	p. 316
The Dirac method [Q01p106]	p. 317
Coulomb field	p. 318
The Born method [Q01p109]	p. 319
Coulomb scattering [Q01p010]	p. 321
Quasi coulombian scattering of particles [Q01p001]	p. 324
Method of the particular solutions	p. 327
Coulomb scattering: another regularization method [Q01p008]	p. 328
Two-electron scattering [Q03p029]	p. 330
Compton effect [Q03p041]	p. 331
Quasi-stationary states [Q03p103]	p. 332
Appendix: Transforming a differential equation [Q03p035]	p. 337
Nuclear Physics	p. 339
Wave equation for the neutron [Q17p129]	p. 339
Radioactivity [Q17p005]	p. 339
Nuclear potential [Q17p006]	p. 340
Mean nucleon potential	p. 340
Computation of the interaction potential between nucleons	p. 342
Nucleon density	p. 345
Nucleon interaction I	p. 347
Zeroth approximation	p. 351
Nucleon interaction II	p. 352
Evaluation of some integrals	p. 355
Zeroth approximation	p. 358
Simple nuclei I	p. 363
Simple nuclei II	p. 365
Kinematics of two a particles (statistics)	p. 367
Thomson formula for ß particles in a medium [Q16p083]	p. 368
Systems with two fermions and one boson [Q17p090]	p. 370
Scalar field theory for nuclei? [Q02p086]	p. 370

Classical Physics	p. 385
Surface waves in a liquid [Q12p054]	p. 385
Thomson's method for the determination of e/m [Q09p044[	p. 387
Wien's method for the determination of e/m (positive charges) [Q09p048b]	p. 388
Determination of the electron charge [Q09p028]	p. 390
Townsend effect	p. 390
Ion recombination	p. 390
Ion diffusion	p. 392
Velocity in the electric field	p. 393
Charge of an ion	p. 393
Method of the electrolysis (Townsend)	p. 394
Zaliny's method for the ratio of the mobility coefficients	p. 394
Thomson's method	p. 395
Wilson's method	p. 396
Millikan's method	p. 396
Electromagnetic and electrostatic mass of the electron [Q09p048]	p. 397
Thermionic effect [Q09p053]	p. 397
Langmuir Experiment on the effect of the electron cloud	p. 399
Mathematical Physics	p. 403
Linear partial differential equations. Complete systems [Q11p087]	p. 403
Linear operators	p. 404
Integrals of an ordinary differential system and the partial differential equation which determines them	p. 405
Integrals of a total differential system and the associated system of partial differential equation that determines them	p. 406
Algebraic foundations of the tensor calculus [Q11p093]	p. 409
Covariant and contravariant vectors	p. 409
Geometrical introduction to the theory of differential quadratic forms I [Q11p094]	p. 409
The symbolic equation of parallelism	p. 409
Intrinsic equations of parallelism	p. 409
Christoffel's symbols	p. 411
Equations of parallelism in terms of covariant components	p. 412
Some analytical verifications	p. 413
Permutability	p. 414
Line elements	p. 414
Euclidean manifolds. any V_n can always be considered as immersed in a Euclidean space	p. 415
Angular metric	p. 416
Coordinate lines	p. 417
Differential equations of geodesics	p. 418
Application	p. 420
Geometrical introduction to the theory of differential quadratic forms II [Q11p113]	p. 422
Geodesic curvature	p. 422
Vector displacement	p. 422
Autoparallelism of geodesics	p. 424
Associated vectors	p. 424
Remarks on the case of an indefinite ds²	p. 425
Covariant differentiation. Invariants and differential parameters. Locally geodesic coordinates [Q11p119]	p. 425
Geodesic coordinates	p. 425
Applications	p. 427
Particular cases	p. 429
Applications	p. 430
Divergence of a vector	p. 431
Divergence of a double (contravariant) tensor	p. 432
Some laws of transformation	p. 433
systems	p. 434
Vector product	p. 435
Extension of a field	p. 435
Curl of a vector in three dimensions	p. 436
Sections of a manifold. Geodesic manifolds	p. 436
Geodesic coordinates along a given line	p. 437
Riemann's symbols and properties relating to curvature [Q11p138]	p. 441
Cyclic displacement round an elementary parallelogram	p. 441
Fundamental properties of Riemann's symbols of the second kind	p. 443
Fundamental properties and number of Riemann's symbols of the first kind	p. 444
Bianchi identity and Ricci lemma	p. 447
Tangent geodesic coordinates around the point P₀	p. 447
Index	p. 449
Table of Contents provided by Publisher. All Rights Reserved.

Ettore Majorana

Unpublished Research Notes on Theoretical Physics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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