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Contents Ann. Phys. 9-102008

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Ann. Phys. (Berlin) 17, No. 9–10, 613 – 615 (2008) / DOI 10.1002/andp.200817013
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Page 617
Friedrich W. Hehl
Page 619 – 630
Thibault Damour
What is missing from Minkowski’s “Raum und Zeit” lecture
This contribution tries to highlight the importance of Minkowski’s “Raum und
Zeit” lecture in a “negative” way, where negative is taken in the photographic
sense of reversing lights and shades. Indeed, we focus on the “shades” of
Minkowski’s text, i.e. what is missing, or misunderstood. In particular, the
article focuses on two issues: (i) why are Poincaré’s pioneering contributions
to four-dimensional geometry not quoted by Minkowski (while he abundantly
quoted them a few months before the Cologne lecture)?, and (ii) did Minkowski
fully grasp the physical (and existential) meaning of “time” within spacetime?
Page 631 – 690
H. A. Kastrup
On the advancements of conformal transformations and their
associated symmetries in geometry and theoretical physics
The historical developments of conformal transformations and symmetries
are sketched: Their origin from stereographic projections of the globe, their
blossoming in two dimensions within
the field of analytic complex functions,
the generic role of transformations by
reciprocal radii in dimensions higher
than two and their linearization in
terms of polyspherical coordinates
by Darboux, Weyl’s attempt to extend General Relativity, the slow rise of finite dimensional conformal transformations in classical field theories and the
problem of their interpretation, then since about 1970 the rapid spread of their
acceptance for asymptotic and structural problems in quantum field theories
and beyond, up to the current AdS/CFT conjecture.
P (ξ,η,ζ )
P̂ (x,y )
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Page 691 – 704
Friedrich W. Hehl
Maxwell’s equations in Minkowski’s world: their premetric
generalization and the electromagnetic energy-momentum tensor
In December 1907, Minkowski expressed the Maxwell equations in the very
beautiful and compact 4-dimensional form: lor f = −s, lor F ∗ = 0. Here
‘lor’, an abbreviation of Lorentz, represents the 4-dimensional differential
operator. The Minkowski’s derivation is studied and it is shown how these
equations generalize to their modern premetric form. It is discussed how
Minkowski arrived at it and how its premetric formulation looks like.
Page 705 – 727
Bahram Mashhoon
Nonlocal special relativity
In the special theory of relativity, Lorentz invariance is extended in Minkowski
spacetime from ideal inertial observers to actual observers by means of the
hypothesis of locality, which postulates that accelerated observers are always
pointwise inertial. A critical examination reveals its domain of validity: it is
true for pointwise coincidences, but is in conflict with wave-particle duality. To
remedy this situation, a nonlocal theory of accelerated systems is presented that
reduces to the standard theory in the limit of small accelerations.
Page 728 – 768
Sergio Cacciatori, Vittorio Gorini, and Alexander Kamenshchik
Special relativity in the 21st century
This paper rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space lead
to a formulation of special relativity based on the appearance
of two universal constants: a limiting speed c and a cosmological constant Λ. That these constants should exist is an
outcome of the underlying symmetries and is confirmed by
experiments and observations, which furnish their actual values. On this basis,
main aspects of the theory of special relativity based on SO(1, 4) (de Sitter
relativity) are developed.
Page 769 – 786
Y. Itin and Y. Friedman
Backwards on Minkowski’s road.
From 4D to 3D Maxwellian electromagnetism
Minkowski’s concept of a four-dimensional physical space is a central
paradigm of modern physics. Is the (1+3) decomposition of the covariant
four-dimensional form unique? How do the different sign assumptions of electrodynamics emerge from this decomposition? Which of these assumptions are
fundamental and which of them may be modified? How does the Minkowski
space-time metric emerge from this preliminary metric-free construction? This
paper looks for answers to the problems mentioned.
© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Ann. Phys. (Berlin) 17, No. 9–10 (2008)
Page 787 – 802
Ari Sihvola and Ismo V. Lindell
Perfect electromagnetic conductor medium
This article presents a review of a novel concept
in electromagnetics, the Perfect Electromagnetic
M >0
Conductor (PEMC). In the Minkowskian represenPEMC
tation of the material response to electromagnetic
fields, PEMC corresponds to the axion part of the
constitutive tensor. From the electrical engineering
point of view, PEMC is a generalization of the perfect electric conductor (PEC)
and perfect magnetic conductor (PMC) materials which are useful concepts
as ideal boundaries in the modeling of electromagnetic problems. This paper
discusses how the PECM medium generalizes earlier known electromagnetic
Page 803 – 829
Florian Loebbert
The Weinberg-Witten theorem on massless particles: an essay
This essay deals with the Weinberg-Witten theorem
which imposes limitations on massless particles.
First, a classification of massless particles given
by the Poincaré group as the symmetry group of
Minkowski spacetime is motivated. Then the fundamental structure of the background in the form of
Poincaré covariance is used to derive restrictions on
charged massless particles known as the WeinbergWitten theorem. Possible misunderstandings in the proof of this theorem are
addressed, and the consequences of the theorem are discussed.
matrix elements between
massless one particle states
p , ±j|J μ |p, ±j or p , ±j|T μν |p, ±j
• physical measurement
• Poincar´e covariance
• non-vanishing charges
= 0
Lorentz rotation of
• particle states |p, ±j
• currents J μ or T μν
= 0 for j >
or j > 1
Page 830 – 851
Yuri N. Obukhov
Electromagnetic energy and momentum in moving media
The problem of the electromagnetic energy-momentum tensor is among the
oldest and the most controversial in macroscopic electrodynamics. In the center
of the issue is a dispute about the Minkowski and the Abraham tensors for
moving media. An overview of the current situation is presented.
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© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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