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Theoretical and Mathematical Physics

By: Armin Wachter

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Hardcover | 6 October 2010

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Hardcover
388 Pages

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24.2 x 16.6 x 2.7

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* Which problems do arise within relativistic enhancements of the Schroedinger theory, especially if one adheres to the usual one-particle interpretation? * To what extent can these problems be overcome? * What is the physical necessity of quantum field theories? In many textbooks, only insufficient answers to these fundamental questions are provided by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this book emphasizes particularly this point of view (relativistic quantum mechanics in the ''narrow sense''): it extensively discusses the relativistic one-particle view and reveals its problems and limitations, therefore illustrating the necessity of quantized fields in a physically comprehensible way. The first two chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always with a view to the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the Feynman rules from propagator techniques. This is where the indispensability of quantum field theory reasoning becomes apparent and basic quantum field theory concepts are introduced. This textbook addresses undergraduate and graduate Physics students who are interested in a clearly arranged and structured presentation of relativistic quantum mechanics in the "narrow sense" and its connection to quantum field theories. Each section contains a short summary and exercises with solutions. A mathematical appendix rounds out this excellent textbook on relativistic quantum mechanics.

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"This book addresses undergraduate and graduate physics students, as well as young scientists in physics and applied mathematics who are interested in the theory of relativistic quantum mechanics in the 'narrow sense' and its connections to quantum field theories. The notions presented in the book are clearly arranged and each section contains a short summary and exercises with solutions. Important equations and relationships are summarized in boxes to allow the reader a well-structured understanding and easy reference." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, March, 2014)

"The main focus of this book is the extent to which relativistic quantum mechanics can be applied. ... This textbook is written very clearly ... . a valuable asset for teaching purposes. Its main value is the detailed discussion of relativistic corrections to non-relativistic problems in quantum mechanics, which could be very useful for anyone interested in such contributions. ... the book is equally well suited as a basis for lectures, for self-study, or as a reference work for active research." (Axel Maas, Mathematical Reviews, Issue 2011 m)

"This book addresses undergraduate and graduate physics students, as well as young scientists in physics and applied mathematics who are interested in the theory of relativistic quantum mechanics in the 'narrow sense' and its connections to quantum field theories. The notions presented in the book are clearly arranged and each section contains a short summary and exercises with solutions. Important equations and relationships are summarized in boxes to allow the reader a well-structured understanding and easy reference." (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1205, 2011)

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Non-Fiction Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Nuclear Physics Particle & High-Energy Physics

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Published: 1st December 2012

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List of Exercises	p. XV
Relativistic Description of Spin-0 Particles	p. 1
Klein-Gordon Equation	p. 4
Canonical and Lorentz-covariant Formulations of the Klein-Gordon Equation	p. 4
Hamilton Formulation of the Klein-Gordon Equation	p. 9
Interpretation of Negative Solutions, Antiparticles	p. 12
Exercises	p. 18
Symmetry Transformations	p. 21
Active and Passive Transformations	p. 21
Lorentz Transformations	p. 23
Discrete Transformations	p. 24
Exercises	p. 29
One-Particle Interpretation of the Klein-Gordon Theory	p. 30
Generalized Scalar Product	p. 30
One-particle Operators and Feshbach- Villars Representation	p. 33
Validity Range of the One-particle Concept	p. 39
Klein Paradox	p. 42
Exercises	p. 46
Nonrelativistic Approximation of the Klein-Gordon Theory	p. 51
Nonrelativistic Limit	p. 51
Relativistic Corrections	p. 53
Exercises	p. 58
Simple One-Particle Systems	p. 61
Potential Well	p. 62
Radial Klein-Gordon Equation	p. 66
Free Particle and Spherically Symmetric Potential Well	p. 68
Coulomb Potential	p. 73
Oscillator-Coulomb Potential	p. 77
Exercises	p. 82
Relativistic Description of Spin-1/2 Particles	p. 85
Dirac Equation	p. 86
Canonical Formulation of the Dirac Equation	p. 86
Dirac Equation in Lorentz-Covariant Form	p. 93
Properties of -Matrices and Covariant Bilinear Forms	p. 97
Spin Operator	p. 100
Projection Operators	p. 103
Interpretation of Negative Solutions, Antiparticles and Hole Theory	p. 106
Exercises	p. 113
Symmetry Transformations	p. 121
Proper Lorentz Transformations	p. 121
Spin of Dirac Solutions	p. 126
Discrete Transformations	p. 127
Exercises	p. 133
One-Particle Interpretation of the Dirac Theory	p. 137
One-Particle Operators and Feshbach- Villars Representation	p. 137
Validity Range of the One-Particle Concept	p. 141
Klein Paradox	p. 143
Exercises	p. 145
Nonrelativistic Approximation of the Dirac Theory	p. 151
Nonrelativistic Limit	p. 151
Relativistic Corrections	p. 153
Exercises	p. 158
Simple One-Particle Systems	p. 160
Potential Well	p. 160
Radial Form of the Dirac Equation	p. 163
Free Particle and Centrally Symmetric Potential Well	p. 166
Coulomb Potential	p. 169
Exercises	p. 175
Relativistic Scattering Theory	p. 177
Review: Nonrelativistic Scattering Theory	p. 178
Solution of the General Schrödinger Equation	p. 179
Propagator Decomposition by Schrödinger Solutions	p. 183
Scattering Formalism	p. 185
Coulomb Scattering	p. 193
Exercises	p. 196
Scattering of Spin-1/2 Particles	p. 202
Solution of the General Dirac Equation	p. 203
Fourier Decomposition of the Free Fermion Propagator	p. 206
Scattering Formalism	p. 210
Trace Evaluations with -Matrices	p. 215
Exercises	p. 220
Spin-1/2 Scattering Processes	p. 222
Coulomb Scattering of Electrons	p. 224
Electron-Proton Scattering (I)	p. 232
Electron-Proton Scattering (II)	p. 244
Preliminary Feynman Rules in Momentum Space	p. 252
Electron-Electron Scattering	p. 255
Electron-Positron Scattering	p. 261
Compton Scattering against Electrons	p. 266
Electron-Positron Annihilation	p. 274
Conclusion: Feynman Diagrams in Momentum Space	p. 279
Exercises	p. 283
Higher Order Corrections	p. 292
Vacuum Polarization	p. 295
Self-Energy	p. 301
Vortex Correction	p. 306
Physical Consequences	p. 310
Exercises	p. 317
Scattering of Spin-0 Particles	p. 319
Solution of the General Klein-Gordon Equation	p. 319
Scattering Formalism	p. 321
Coulomb Scattering of Pions	p. 324
Pion-Pion Scattering	p. 327
Pion Production via Electrons	p. 331
Compton Scattering against Pions	p. 336
Conclusion: Enhanced Feynman Rules in Momentum Space	p. 341
Exercises	p. 343
Appendix	p. 349
Theory of Special Relativity	p. 349
Bessel Functions, Spherical Bessel Functions	p. 355
Legendre Functions, Legendre Polynomials, Spherical Harmonics	p. 357
Dirac Matrices and Bispinors	p. 359
Index	p. 363
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Theoretical and Mathematical Physics

At a Glance

Hardcover

Industry Reviews

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You Can Find This Book In

Other Editions and Formats

Paperback

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