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UNITEXT for Physics
Kurt Lechner
A Modern Perspective
UNITEXT for Physics
Series editors
Michele Cini, Dipartimento di Fisica, University of Rome Tor Vergata, Roma, Italy
Attilio Ferrari, Università di Torino, Turin, Italy
Stefano Forte, Università di Milano, Milan, Italy
Guido Montagna, Università di Pavia, Pavia, Italy
Oreste Nicrosini, Dipartimento di Fisica Nucleare e Teorica, Università di Pavia,
Pavia, Italy
Luca Peliti, Dipartimento di Scienze Fisiche, Università Napoli, Naples, Italy
Alberto Rotondi, Pavia, Italy
Paolo Biscari, Dipartimento di Fisica, Politecnico di Milano, Milan, Italy
Nicola Manini, Department of Physics, Università degli Studi di Milano, Milan,
Morten Hjorth-Jensen, Department of Physics, University of Oslo, Oslo, Norway
UNITEXT for Physics series, formerly UNITEXT Collana di Fisica e Astronomia,
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Kurt Lechner
Classical Electrodynamics
A Modern Perspective
Kurt Lechner
Department of Physics and Astronomy Galileo Galilei
University of Padua
Padua, Italy
Istituto Nazionale di Fisica Nucleare
Sezione di Padova
Padua, Italy
ISSN 2198-7882 ISSN 2198-7890 (electronic)
UNITEXT for Physics
ISBN 978-3-319-91808-2 ISBN 978-3-319-91809-9 (eBook)
Library of Congress Control Number: 2018942192
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The experimental evidence on the behavior of matter on subatomic scales collected
so far leads to the conclusion that all microscopic physical phenomena can be
explained by the assumption that matter is made up of elementary particles,
structureless fundamental constituents of the Universe, which are subject to four
types of fundamental interactions: gravitational, electromagnetic, weak, and strong.
These interactions are, however, not transmitted via direct contacts, but they are
rather mediated by a particular type of elementary particles, called intermediate
gauge bosons. Whereas the gravitational interaction is one of the most ancient
phenomena known in nature, the electromagnetic one has been studied and
understood most thoroughly, having found a solid theoretical formulation known as
quantum electrodynamics, during the first half of the last century. Most of the
everyday physical phenomena – from the stability of matter to the plethora of
phenomena related to the propagation of light – are, in fact, explained by this
theory. The weak and strong interactions that, unlike the electromagnetic and
gravitational ones, manifest themselves only at microscopic scales, met a similar
firm theoretical foundation in the standard model of elementary particles, which
includes quantum electrodynamics itself. In contrast, at present, gravity still appears
to conflict with the laws of quantum physics, notwithstanding the recent progress
accomplished within the promising framework of superstring theory.
Despite their common role of force mediators between the elementary con-
stituents of nature, each fundamental interaction is characterized by unique features
which imply peculiar physical phenomena: The strong interaction, mediated by
gauge bosons called gluons, is the only one that gives rise to the phenomenon of
confinement, which traps the quarks and the gluons themselves inside the nucleons,
while the weak interaction is the only one to be mediated by massive gauge bosons,
the particles W� and Z0. On the other hand, the electromagnetic interaction is the
only one to be mediated by particles, the photons, that, being electrically neutral,
are not subject to a mutual electromagnetic interaction. Finally, the gravitational
interaction is the only one that affects all elementary particles, including the
intermediate gauge bosons themselves, and, in addition, it is mediated by particles
of spin two, the gravitons, whereas the intermediate gauge bosons of the remaining
interactions all carry spin one.
In the light of these important distinctions, it may appear somewhat surprising
that all fundamental interactions are governed by a common, mathematically robust
and elegant, theoretical framework, strongly constraining their general structure, a
framework whose profound physical origin is still to be uncovered. Among the
cornerstones of this unifying framework, let us quote the most significant ones: All
fundamental interactions satisfy Einstein’s principle of relativity and admit a
manifestly covariant formulation that automatically implies the conservation of the
total energy, momentum, and angular momentum of the Universe. Furthermore,
each interaction is transmitted via exchange of one or more dedicated particles – the
intermediate gauge bosons – that mathematically are represented by vector or tensor
fields, whose dynamics is controlled by a fundamental symmetry, called gauge
invariance. Noether’s theorem then associates with each of these symmetries, and
hence with each intermediate gauge boson, a conserved quantity. Last but not least,
perhaps the most mysterious, but nonetheless, less fundamental cornerstone of the
common theoretical framework is that the dynamics of all four fundamental
interactions can be derived from a variational principle.
The core of this book on classical electrodynamics is a series of lectures on
electromagnetic fields, held by the author in the years 2004–2011 for the master’s
degree in physics at the University of Padua. Its actual content covers, however,
research topics that are far more advanced than what could be taught in a graduate
course. A special concern of the book is to emphasize, on the one hand, those
aspects that unite electrodynamics with the other fundamental interactions,
including the cornerstones mentioned above, and, on the other, to highlight, where
possible, their most significant differences. The major waiver implied by this per-
spective is an almost complete neglect of the important topic of electromagnetic
fields in matter.
Classical electrodynamics is presented as a theory founded on a system of
postulates: Einstein’s principle of relativity, and the Maxwell and Lorentz equa-
tions. The whole