Advanced Electromagnetism: Foundations, Theory and Applications
Terence W. Barrett · Dale M. Grimes
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In one page
Advanced Electromagnetism is a 791-page collection edited by Terence Barrett and Dale Grimes and published by World Scientific in 1995. Its subject is what the four Maxwell equations, in the compact form every engineering course teaches, leave out. Twenty-six chapters by authors from Brazil, France, Britain, Poland, Germany, Switzerland and the United States are set in three parts — Foundations, Theory, Applications. R. Aldrovandi opens on gauge theories and beyond; Gerald Marsh writes on helicity and the topology of electromagnetic fields; Georges Lochak on the symmetry between electricity and magnetism and the magnetic monopole; Donald Reed on Beltrami vector fields; Boguslaw Broda on the non-Abelian Stokes theorem; A. K. T. Assis proposes gravitation as a fourth-order electromagnetic effect; Barrett’s own chapter treats the Sagnac effect as conservation of action in a multiply joined topology of coherent fields. The last part is laboratory work — experiments with magnetic charge, tests of the Ampère force, localised waves. The thread through all of it is that electromagnetism carries structure the field strengths alone do not record.
Why it matters hereChapter 10 is the site’s chapter on the vector potential and structured fields — the claim that phase and topology, not just field strength, are physical. This volume is where that programme was collected in one place by the people pursuing it, and it is the direct ancestor of Barrett’s later topological formulation, which is what the corpus reaches for when it talks about winding up a field rather than merely radiating one.
What it claims
01The volume’s organising claim is that classical electromagnetism has structure beyond what the electric and magnetic field strengths record — helicity, topology, gauge, phase — and that the structure is physical rather than a bookkeeping convenience. Twenty-six chapters develop that claim across foundations, theory and experiment.Volume structure as deposited: Foundations pages 3 to 354, Theory pages 357 to 589, Applications pages 593 to 791
Published and peer-reviewed02Barrett’s own chapter argues that the Sagnac effect — the phase shift a rotating interferometer imposes on counter-propagating beams — is a consequence of the conservation of action arising from global conformal invariance of the gauge field in a multiply joined topology of coherent fields. The explanation is topological: what matters is how the path is joined, not the local field strength along it.Chapter 9, pages 278 to 313
Published and peer-reviewed03The non-Abelian mathematics that such a formulation needs is set out in the volume as its own chapter: Boguslaw Broda’s treatment of the non-Abelian Stokes theorem, which is the generalisation of the ordinary loop-integral theorem to gauge fields that do not commute — the step from ordinary electromagnetism to the SU(2) form.Chapter 17, pages 496 to 505
Settled physics04Gerald Marsh, writing from Argonne National Laboratory, gives the volume its topological spine directly: helicity and electromagnetic field topology — the linking and knotting of field lines as a conserved, measurable property of a field configuration.Chapter 2, pages 52 to 76
Published and peer-reviewed05A. K. T. Assis contributes a chapter proposing gravitation as a fourth-order electromagnetic effect — an attempt to derive the gravitational interaction from electrodynamics itself rather than to add it alongside. It is the volume’s clearest statement of the ambition the site’s chapter 13 is about: one field, not two.Chapter 10, pages 314 to 331
What to watch06The third part is experimental, not speculative: Mikhailov’s six experiments with magnetic charge, Rémi Saumont’s experimental tests of the Ampère force, Peter Graneau on Newtonian electrodynamics and its experimental foundation, and Matthew Palmer on localised waves and limited-diffraction beams. What to watch here is replication — each of these is a measurement that would settle a foundational question if it were reproduced at scale.Chapters 21 to 24, pages 593 to 681
What to watch
The way in
https://doi.org/10.1142/9789812831323SOURCE NOT REACHED IN FULL. The book is sold by World Scientific and carries no open licence. On 2026-09-08 the publisher’s own page for it answered a JavaScript bot-challenge rather than the page, and no scan of it is held by the Internet Archive. No text of the book is reproduced here. EDITORS. Crossref records Terence W. Barrett and Dale M. Grimes as editors of the volume; the registry skeleton carried Barrett alone, and Grimes is added here. Grimes is also a contributor, twice. WHAT WAS READ, AND WHAT THE CLAIMS REST ON. The publisher deposited a separate Crossref record for every chapter, and all twenty-six were retrieved and read on 2026-09-08 — title, authors, affiliations and page range for each — which gives the volume’s table of contents from the publisher’s own deposit rather than from a bookseller’s copy. The page ranges run continuously from 3 to 791 with breaks at pages 355 to 356 and 590 to 592, which is where the three parts named in the subtitle divide: Foundations, chapters 1 to 11, pages 3 to 354; Theory, chapters 12 to 20, pages 357 to 589; Applications, chapters 21 to 26, pages 593 to 791. Chapter titles are deposited in capitals and are given here in ordinary case, and contributors are named exactly as the publisher deposited them, initials unexpanded, because no record consulted gives their given names in full. Every locator below is a chapter number and page range from that deposit. A NOTE ON WHAT IS NOT IN THIS VOLUME. The corpus reached this book expecting chapters on Whittaker’s potentials, on the Aharonov–Bohm effect and on SU(2) electrodynamics. The deposited contents show no separate chapter on any of the three. Barrett’s own contribution here is the Sagnac-effect chapter, chapter 9, and the non-Abelian gauge mathematics of the volume sits in Boguslaw Broda’s chapter on the non-Abelian Stokes theorem, chapter 17. Barrett’s SU(2) extension of Maxwell theory is set out at length elsewhere — in his 2008 book Topological Foundations of Electromagnetism, which this site holds, and in his essay Electromagnetic phenomena not explained by Maxwell’s equations, published in a different World Scientific volume, Essays on the Formal Aspects of Electromagnetic Theory, edited by Akhlesh Lakhtakia in 1993. Lakhtakia is a contributor here too, at chapter 14.
How to cite it
Terence W. Barrett, Dale M. Grimes (1995) Advanced Electromagnetism: Foundations, Theory and Applications. doi:10.1142/9789812831323
Where it sits in the curriculum
Scalar waves and the field behind the fieldsThe unified picture