#### 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

This webpage is being based on the free web template named "metamorph_blueglowing" provided by The Metamorphosis Design : 2009. It is being distributed ounder a Creative Commons license. For support visit http://www.metamorphozis.com/contact/contact.php. Design by Metamorphosis Design.

This webpage is hosted on the servers of Missouri University
of Science and Technology, Rolla, Missouri, USA

### Points of Interest

### Recent Events

**08-DEC-2017**

## Chandra Adhikari: Schaerer Prize.

Graduate student Chandra Adhikari has received Second Prize at the annual Schaerer Prize Competition.

**01-SEP-2017**

## Textbook published.

A textbook on advanced classical electrodynamics has been published.

**20-MAR-2017**

## Long-range van der Waals interaction tails.

Research has been published in Physical Review Letters.

**02-FEB-2017**

## Research on long-range interactions.

Two longer articles have been published in Physical Review A, on van der Waals and Casimir-Polder interactions.

**16-JAN-2017**

## Textbook on classical electrodynamics.

A textbook on classical electrodynamics has been submitted to World Scientific Publishers.

**09-DEC-2016**

## Chandra Adhikari: Schaerer Prize.

Graduate student Chandra Adhikari has received Third Prize at the annual Schaerer Prize Competition.

**28-NOV-2016**

## Textbook on classical electrodynamics.

A project concerning a textbook on classical electrodynamics is nearing completion.

**28-DEC-2015**

## Missouri Research Board grant.

A grant from the Missouri Research Board will help in research projects concerned with general relativity.

**12-DEC-2015**

## Faculty Research Award.

Ulrich Jentschura receives a faculty research award of Missouri University of Science and Technology.

**05-DEC-2015**

## Jonathan Noble: Schaerer Prize.

Graduate student Jonathan Noble has won this year's Schaerer Prize Competition (First Prize).

**11-MAY-2015**

## Graduate Student Seminar

Students Jonathan Noble and Chandra Adhikari won First and Third Prize in the graduate student seminar series for the spring semester 2015.

**17-APR-2015**

## Promotion to Full Professor

The promotion to full professor has been approved and taken effect in September 2015.

**13-FEB-2015**

## Gravitational Correction to Vacuum Polarization

An article on the interplay of general relativity and quantum electrodynamic effects has appeared in print.

**19-NOV-2014**

## Fine-Structure Constant and String Theory

An article on the determination of the fine-structure constant, the renormalization group and string theory has appeared at arXiv.org.

**02-JUL-2014**

## Conference at CERN

A conference at CERN discusses generalized perturbative expansions (so-called transseries) which are useful in the description of quantum phenomemna (energy levels and nonperturbative effects in field theory).

**17-APR-2014**

## J. Phys. G: LabTalk

A recent particle physics paper in J.Phys.G on the "rabbit paradox" has been discussed in a LabTalk.

**27-DEC-2013**

## Faculty Research Award.

Ulrich Jentschura receives a faculty research award of Missouri University of Science and Technology.

**12-DEC-2013**

## Jonathan Noble (news #2).

Joint work with graduate student Jonathan Noble has been accepted for publication. A preprint on the "Foldy-Wouthuysen Transformation, Scalar Potentials and Gravity" will appear at arXiv.org soon.

**06-DEC-2013**

## Jonathan Noble (news #1).

Graduate student Jonathan Noble has been awarded a recognition at the annual Schaerer Prize Competition (Third Prize).

**02-DEC-2013**

## APS Fellow.

An APS fellowship has been received in recognition of the contributions to theoretical atomic physics (Division of Atomic, Molecular and Optical Physics, APS).

**30-JUL-2013**

## Invited Talk at Melbourne University.

Invited talk at the School of Physics of Melbourne University on July 30, 2013.

**03-JUL-2013**

## Invited Talk at PHHQP conference.

Invited talk at the PHHQP conference at Koc University on July 2, 2013.

**15-APR-2013**

## Invited Talk at APS meeting.

Invited talk Q5.00001 at the April meeting of the American Physical Society in Denver, Colorado.

**01-APR-2013**

## Tenure decision.

Ulrich has been granted tenure and promoted to Associate Professor. Finally.

**10-MAR-2013**

## Three entangled photons from QED.

A paper on triple Compton scattering (generation of high-energy entangled photons) has been published.

**10-FEB-2013**

## General Relativity and Relativistic Quantum Mechanics.

A paper on the Dirac equation in curved space-time, and antimatter has been accepted for publication in Phys. Rev. A.

**10-JAN-2013**

## Distinguished Guest Scientist of the Academy Institute in Debrecen, Hungary.

In an interview with the Hungarian Academy, Ulrich tried to argue for the role of science in society.

**23-OCT-2012**

## Quantum Physics with Non-Hermitian Operators.

A paper on the tachyonic Dirac equation has been published in a special issue of J. Phys. A: Math. Theor. on non-Hermitian quantum dynamics.

**10-AUG-2012**

## Triplet States in Helium and g Factor.

A paper on the quantum electrodynamic corrections to the g factor of helium triplet states has been published in Physical Review A.

**01-MAY-2012**

## Physical Review Letter.

A paper triple Compton scattering has been published; it constitutes a theoretical verification of an experiment for which no theory has been available for more than 40 years.

**24-JAN-2012**

## Physical Review Letter.

A paper has been published on drag forces experienced by atoms in interstellar space.

**12-JAN-2012**

## Neutrino Physics Paper.

A paper on neutrinoless double beta decay has been accepted for publication in a particle physics journal.

**18-OCT-2011**

## Faculty Excellence Award.

An award has been received to honour continued excellence in teaching and research.

**01-SEP-2011**

## NSF Grant.

The National Science Foundation has awarded a grant entitled "Advanced Computational Physics in Atomic and Laser Science".

**11-JUL-2011**

## Research Paper.

A paper about higher-order corrections to the muonic hydrogen spectrum has appeared in Physical Review A. These include radiative-recoil effects.

**18-APR-2011**

## Collaboration with NIST.

The 150th publication of the group has appeared in print. The paper results from a collaboration with the National Institute of Standards and Technology and treats blackbody radiation corrections to the dynamic polarizability of helium.

**10-MAR-2011**

## Matter 'n Motion.

The 2011 newletters of the faculty is out and may be downloaded.

**05-JAN-2011**

## PRL Title Page.

An article about novel states of the radiation field has appeared on the title page of Physical Review Letters.

**01-JAN-2011**

## PRA Editorial Advisory Board.

As of 01-JAN-2011, Ulrich Jentschura has been appointed as a member of the Editorial Advisory Board of Physical Review A (term 2011-2013).

**10-DEC-2011**

## Faculty Research Award.

Ulrich Jentschura receives a faculty research award of Missouri University of Science and Technology.

**05-DEC-2010**

## Schaerer Prize.

Benedikt Wundt has been awarded the Schaerer Prize 2010 by the physics faculty of Missouri S&T for the most interesting graduate research project.

**05-NOV-2009**

## Outstanding Referee Certificate.

Ulrich Jentschura has been awarded an Outstanding Referee Certificate by the American Physical Society.