On The Nonrelativistic Limit Of Quantum Electrodynamics

Quantum electrodynamics (QED) is a quantum field theory describing light-matter interaction processes on all energy scales. In QED, not only photons are represented as occupied modes of a quantum field, but also electrons (matter) and positrons (antimatter). The necessity of the introduction of antimatter, which goes back to P.A.M. Dirac, has finally the consequence that the QED quantum field cannot be decomposed into its components (particles and photons), since in this sector of light-matter interactions there are processes allowed which violate the particle number conservation. This radically distinguishes QED from the low-energy sector of the light-matter interactions on the energy scale of atomic physics. Starting from the QED Hamiltonian in the Coulomb gauge, a unitary transformation is therefore sought that leads to a unitary equivalent QED Hamiltonian that manifestly preserves the particle number. This is feasible applying Wegner's flow equation in combination with perturbation theory, with the fine structure constant serving as the expansion parameter. In this way, first, high-energy photons, and second, modes of high matter and antimatter densities are eliminated from the QED quantum field up to second order. The resulting Hamiltonian preserves the particle number, is completely symmetric in all its constituents and in all interactions, and also includes terms which renormalize the bare mass of the electron (or the positron). Since this Hamiltonian is still in the Dirac representation, the matter and antimatter degrees of freedom must be decoupled from each other with the help of the Eriksen transformation. By this decoupling, the bare mass of the electron is consistently renormalized, and the anomalous magnetic moment is found in agreement with the Schwinger result. It is thus possible to establish the nonrelativistic limit of full QED as the low-energy sector of light-matter interaction processes in which the electron (or positron) can be interpreted as a classical point particle with the measurable attributes of mass, charge and spin, and in which the particle number is a conservation quantity.

Taking a heuristic approach to relativistic quantum mechanics, Practical Quantum Electrodynamics provides a complete introduction to the theory, methodologies, and calculations used for explaining the physical interaction of charged particles. This book combines the principles of relativity and quantum theory necessary for performing the calculations of the electromagnetic scattering of electrons and positrons and the emission and absorption of photons. Beginning with an introduction of the wave equations for spin-0 and spin-1/2 particles, the author compares and contrasts the relativistic and spin effects for both types of particles. He emphasizes how the relativistic treatment of quantum mechanics and the spin-1/2 degree of freedom are necessary to describe electromagnetic interactions involving electron scattering and points out the shortfalls of the wave-equation approach to relativistic quantum mechanics. Developing the Feynman rules for quantum electrodynamics by example, the book offers an intuitive, hands-on approach for performing fundamental calculations. It also illustrates how to perform calculations that can be related to experiments such as diagrams, lifetimes, and cross sections. Practical Quantum Electrodynamics builds a strong foundation for further studies and research in theoretical and particle physics, particularly relativistic quantum field theory or nonrelativistic many-body theory.

We are pleased by the positive resonance of our book which now necessitates a fourth edition. We have used this opportunity to implement corrections of misprints and amendments at several places, and to extend and improve the discussion of many of the exercises and examples. We hope that our presentation of the method of equivalent photons (Example 3. 17), the form factor of the electron (Example 5. 7), the infrared catastrophe (Example 5. 8) and the energy shift of atomic levels (Example 5. 9)arenow even better to understand. The new Exercise 5. 10 shows in detail how to arrive at the non-relativistic limit for the calculation of form factors. Moreover, we have brought up-to-date the Biographical Notes about physicists who have contributed to the dev- opment of quantum electrodynamics, and references to experimental tests of the t- ory. For example, there has been recent progress in the determination of the electric and magnetic form factors of the proton (discussed in Exercise 3. 5 on the Rosenbluth formula) and the Lamb shift of high-Z atoms (discussed in Example 5. 9 on the energy shift of atomic levels), while the experimental veri cation of the birefringence of the QED vacuum in a strong magnetic eld (Example 7. 8) remains unsettled and is a topic of active ongoing research.

Several significant additions have been made to the second edition, including the operator method of calculating the bremsstrahlung cross-section, the calcualtion of the probabilities of photon-induced pair production and photon decay in a magnetic field, the asymptotic form of the scattering amplitudes at high energies, inelastic scattering of electrons by hadrons, and the transformation of electron-positron pairs into hadrons.

The main unique feature of this book is its discussion of Hilbert space and rigged Hilbert space. Suitable for advanced undergraduate students as well as graduate students.

Introduction to Electrodynamics and Radiation introduces the reader to electrodynamics and radiation, with emphasis on the microscopic theory of electricity and magnetism. Nonrelativistic quantum electrodynamics (QED) is presented as a logical outgrowth of the classical theory, both relativistic and nonrelativistic. The advanced mathematical and diagrammatic techniques of the relativistic quantum field theory are also described in a simple and easily understood manner. Comprised of 16 chapters, this book opens with an overview of the special theory of relativity and some of its consequences. The following chapters deal with classical relativistic electrodynamics, touching on topics such as tensor analysis and Riemannian spaces; radiation from charged particles; radiation scattering from electrons; and the classical theory of charged particles. The second part of the book is entirely quantum mechanical in outlook, beginning with the quantization of the Hamiltonian formulation of classical electrodynamics. The many-body formalism leading to Fock-space techniques is also considered, along with self-energies and renormalization. The final chapter is devoted to the covariant formulation of QED as well as the validity of QED. This monograph is written primarily for graduate students in elementary classical and quantum mechanics, electricity and magnetism, and modern physics courses.