Ebook: Relativistic Quantum Mechanics and Introduction to Field Theory

A fully relativistic treatment of the quantum mechanics of particles requires the introduction of quantum field theory, that is to say, the quantum mechan­ ics of systems with an infinite number of degrees of freedom. This is because the relativistic equivalence of mass and energy plus the quantum possibility of fluctuations imply the existence of (real or virtual) creation and annihilation of particles in unlimited numbers. In spite of this, there exist processes, and energy ranges, where a treat­ ment in terms of ordinary quantum mechanical tools is appropriate, and the approximation of neglecting the full field-theoretic description is justified. Thus, one may use concepts such as potentials, and wave equations, clas­ sical fields and classical currents, etc. The present text is devoted precisely to the systematic discussion of these topics, to which we have added a gen­ eral description of one- and two-particle relativistic states, in particular for scattering processes. A field-theoretic approach may not be entirely avoided, and in fact an introduction to quantum field theory is presented in this text. However, field theory is not the object per se of this book; apart from a few examples, field theory is mainly employed to establish the connection with equivalent potentials, to study the classical limit of the emission of radiation or to discuss the propagation of a fermion in classical electromagnetic fields.

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This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.

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This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.
Content:
Front Matter....Pages I-XII
Relativistic Transformations. The Lorentz Group....Pages 1-22
The Klein-Gordon Equation. Relativistic Equation for Spinless Particles....Pages 23-34
Spin 1/2 Particles....Pages 35-66
Dirac Particle in a Potential....Pages 67-88
Massive Particles with Spin 1. Massless Spin 1 Particle: Photon Wave Functions. Particles with Higher Spins (3/2, 2, …)....Pages 89-107
General Description of Relativistic States....Pages 109-128
General Description of Relativistic Collisions: S Matrix, Cross-sections and Decay Rates. Partial Wave Analyses....Pages 129-158
Quantization of the Electromagnetic Field. Interaction of Radiation with Matter....Pages 159-188
Quantum Fields: Spin 0, 1/2, 1. Covariant Quantization of the Electromagnetic Field....Pages 189-228
Interactions in Quantum Field Theory. Nonrelativistic Limit. Reduction to Equivalent Potential....Pages 229-265
Relativistic Collisions in Field Theory. Feynman Rules. Decays....Pages 267-290
Relativistic Interactions with Classical Sources....Pages 291-308
Back Matter....Pages 309-332

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This is an advanced textbook meant as a primer in quantum theory for graduate students. A full relativistic treatment of particle dynamics needs to be based on quantum field theory. However, there exists a variety of processes that can be discussed with concepts like potentials, classical current distributions, prescribed external fields dealt with in the framework of relativistic quantum mechanics. Then, in an introduction to field theory the author emphasizes the deduction of the said potentials or currents. The unique feature of this book is the modern presentation of the subject together with many exercises and furthermore the underlying concept to combine a reference book on relativistic quantum mechanics with an introduction into quantum field theory.
Content:
Front Matter....Pages I-XII
Relativistic Transformations. The Lorentz Group....Pages 1-22
The Klein-Gordon Equation. Relativistic Equation for Spinless Particles....Pages 23-34
Spin 1/2 Particles....Pages 35-66
Dirac Particle in a Potential....Pages 67-88
Massive Particles with Spin 1. Massless Spin 1 Particle: Photon Wave Functions. Particles with Higher Spins (3/2, 2, …)....Pages 89-107
General Description of Relativistic States....Pages 109-128
General Description of Relativistic Collisions: S Matrix, Cross-sections and Decay Rates. Partial Wave Analyses....Pages 129-158
Quantization of the Electromagnetic Field. Interaction of Radiation with Matter....Pages 159-188
Quantum Fields: Spin 0, 1/2, 1. Covariant Quantization of the Electromagnetic Field....Pages 189-228
Interactions in Quantum Field Theory. Nonrelativistic Limit. Reduction to Equivalent Potential....Pages 229-265
Relativistic Collisions in Field Theory. Feynman Rules. Decays....Pages 267-290
Relativistic Interactions with Classical Sources....Pages 291-308
Back Matter....Pages 309-332
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