Textbook on Advanced Classical Electrodynamics

The home page for the text book can be found here.

In the textbook, several aspects of classical electrodynamics are discussed under a new light. For example, it is well known that the action-at-a-distance solution for the scalar potential in Coulomb gauge has been a problem in the physical interpretation of certain solutions of the classical field equations; in the book, the solution is shown to reduce to an overall retarded integral, as it should be, if a certain consistency condition relevant to the Coulomb-gauge coupling of the potential to the sources, is taken into account. The discussion supplements other, perhaps more cursory, discussion found elsewhere in the literature. It is also shown that dimensional regularization, a method otherwise known from particle physics, can be used with good effect in the evaluation of certain potentials in the classical theory, explaining the concept of integrals in 0.99 or 1.99 dimensions to a wider audience, and giving a concrete interpretation to otherwise abstract concepts. The exact multipole decomposition of radiation (both electric as well as magnetic multipoles) is discussed in full generality to arbitrary orders, using the method of vector spherical harmonics which add the orbital angular momenta of the photons to the photon spin. Finally, electrodynamics is discussed for curved space-times, in a (hopefully) rather understandable fashion. In general, the aim of the book is to provide a concise, yet complete discussion of important aspects of electrodynamics, suitable for a one- or two-semester course, with an emphasis on modern mathematical and theoretical techniques which can be used outside of the original scope of the book.

Ulrich D. Jentschura, Professor of Physics

The main subject of research of the group is to investigate fundamental physics questions in the low-energy domain, using a combination of computational physics methods and field-theoretical tools. The importance of atomic physics theory and experiment for the study of fundamental field-theoretical questions should not be underestimated. The most accurately known physical constant today, the Rydberg constant, has been determined to 12 significant decimals using a combination of highly accurate atomic theory and experimental data. Laboratory-based limits to the variation of fundamental constants with time have been derived on the basis of high-precision experiments. Rather sophisticated field-theoretical and numerical methods have to be employed in order to reach this accuracy. The subject has attracted considerable renewed interested because of an observed discrepancy of theory and experiment for the Lamb shift transition is muonic hydrogen.

In addition, the group studies laser-physics related questions in the high-energy domain. The Furry picture, which was originally developed for the Dirac-Coulomb problem (electrons bound in a strong Coulomb field), needs to be generalized to a modified Furry picture, for electrons moving in a strong time- and space-dependent laser field (Dirac-Volkov propagator). These investigations have topical importance because of the ongoing construction of high-power laser laboratories all around the World.

The group has also been studying anharmonic oscillators and their physical properties. These fundamental quantum mechanical Hamiltonians give rise to manifestly divergent perturbation series, and the energy of a bound quantum state in an anharmonic potential cannot be described by a convergent perturbation series. The large-order growth of perturbative coefficients is described by so-called Bender-Wu formulas. It has been possible to generalize the Bender-Wu formulas from even anharmonic oscillators to odd anharmonic oscillators, and to supplement these studies by field-theoretical methods. Furthermore, the so-called Bender-Wu cuts of the resonance energies of odd anharmonic oscillators on the second sheet of the Riemann surface of the coupling parameter have been identified for odd anharmonic oscillators.

These activities are complemented by studies on the renormalization-group flow of theories with periodic self-interactions in two dimensions, where the so-called sine-Gordon model undergoes a Kosterlitz-Thouless transition. Recent projects include the generalization of the path-integral analysis of the O(N) anharmonic oscillators to D spatial dimensions, which is equivalent to a D-dimensional statistical field theory undergoing a phase transition.

A common and unifying theme of the investigations is the use of modern computers. A couple of algorithms have been developed which have found useful applications beyond their originally intended realm of application. These include the so-called combined nonlinear-condensation transformation which was published in 1999. It is intended to accelerate the convergence of slowly convergent series with nonalternating terms, which constitutes a hard problem in numerical analysis. Traditional one-step acceleration methods like Pade-approximants fail because of excessive numerical cancellations in higher orders.

Main Research Fields

Quantum Field Theory and Atomic Systems

Relativistic Quantum Dynamic Processes in High-Power Laser Fields

Novel States of the Light Field (Twisted Photons)

Computational Physics and Related Algorithms

Path-Integral Analysis of Instantons for Quantum-Mechanical Problems

Renormalization-Group and Critical Phenomena

[Associate Professor at Missouri S&T]

[Adjunct Professor at Heidelberg University (Unpaid Appointment)]

Acknowledgments

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