81.
Complex geometry and pre-metric electromagnetism
- Delphenich, D. H.
The intimate link between complex geometry and the problem of the pre-metric
formulation of electromagnetism is explored. In particular, the relationship
between 3+1 decompositions of R4 and the decompositions of the vector space of
bivectors over R4 into real and imaginary subspaces relative to a choice of
complex structure is emphasized. The role of the various scalar products on the
space of bivectors that are defined in terms of a volume element on R4 and a
complex structure on the space of bivectors that makes it C-linear isomorphic
to C3 is discussed in the context of formulation of a theory of
electromagnetism in which the Lorentzian metric on...
82.
Lorenz or Coulomb in Galilean Electromagnetism ?
- Rousseaux, Germain
Galilean Electromagnetism was discovered thirty years ago by Levy-Leblond &
Le Bellac. However, these authors only explored the consequences for the fields
and not for the potentials. Following De Montigny & al., we show that the
Coulomb gauge condition is the magnetic limit of the Lorenz gauge condition
whereas the Lorenz gauge condition applies in the electric limit of
L\'{e}vy-Leblond & Le Bellac. Contrary to De Montigny & al. who used Galilean
tensor calculus, we use orders of magnitude based on physical motivations in
our derivation.
83.
The Principle of Equivalence and Electromagnetism
- Filewood, G
The problem of unification of Gravitation and Electromagnetism in four
dimensions; some new ideas involving mixtures of commuting and anti-commuting
co-ordinates. Maxwell's equations are extracted in terms of the curvature of
the anti-commuting component of space-time. The profound difference in the size
of the coupling constants of the two forces is interpreted in terms of the
degree of expansion of the two kinds of space-time with evolution of the
universe. Uncertainty in the quantum realm is interpreted in terms of an
unmeasurable component of anti-commuting space-time.
84.
On the Axioms of Topological Electromagnetism
- Delphenich, D. H.
The axioms of topological electromagnetism are refined by the introduction of
the de Rham homology of k-vector fields on orientable manifolds and the use of
Poincare duality in place of Hodge duality. The central problem of defining the
electromagnetic constitutive law is elaborated upon in the linear and nonlinear
cases. The manner by which the spacetime metric might follow from the
constitutive law is examined in the linear case. The possibility that the
intersection form of the spacetime manifold might play a role in defining a
topological basis for the constitutive law is explored. The manner by which
wave motion might follow from the electromagnetic structure is also...
85.
Abelian BF-Theory and Spherically Symmetric Electromagnetism
- Bojowald, Martin
Three different methods to quantize the spherically symmetric sector of
electromagnetism are presented: First, it is shown that this sector is
equivalent to Abelian BF-theory in four spacetime dimensions with suitable
boundary conditions. This theory, in turn, is quantized by both a reduced phase
space quantization and a spin network quantization. Finally, the outcome is
compared with the results obtained in the recently proposed general quantum
symmetry reduction scheme. In the magnetically uncharged sector, where all
three approaches apply, they all lead to the same quantum theory.
86.
A Full Review of the Theory of Electromagnetism
- Funaro, D.
We will provide detailed arguments showing that the set of Maxwell equations,
and the corresponding wave equations, do not properly describe the evolution of
electromagnetic wave-fronts. We propose a nonlinear corrected version that is
proven to be far more appropriate for the modellization of electromagnetic
phenomena. The suitability of this approach will soon be evident to the reader,
through a sequence of astonishing congruences, making the model as elegant as
Maxwell's, but with increased chances of development. Actually, the new set of
equations will allow us to explain many open questions, and find links between
electromagnetism and other theories that have been searched for a long time, or
not...
87.
A uniform description of electromagnetism and wave mechanics
- Roza, Engel
The paper shows the relationship between the major wave equations in quantum
mechanics and electromagnetism, such as Schroedinger's equation, Dirac's
equation and the Maxwell equations. It is shown that they can be derived in a
striking simple way from a common root. This root is the relativistic
fourvector formulation of the momentum conservation law. This is shown to be a
more attractive starting-point than Einstein's energy relationship for moving
particles, which is commonly used for the purpose. The theory developed gives a
new interpretation for the origin of antiparticles.
88.
Tecnología y filosofía wiki aplicadas al electromagnetismo computacional
- De la Cruz Calvo, Daniel
Este trabajo de fin de carrera se ha realizado en la Escola Politècnica Superiorde Castelldefels (EPSC) en colaboración con el Centre Internacional deMètodes Numèrics en Enginyeria (CIMNE) con el objetivo de explorar lasposibilidades de la tecnología wiki aplicada al ámbito de investigación deCIMNE: el electromagnetismo computacional.De acuerdo con la Wikipedia, “un (o una) wiki es un sitio web colaborativo quepuede ser editado por varios usuarios. Los usuarios de una wiki pueden asícrear, editar, borrar o modificar el contenido de una página web, de una formainteractiva, fácil y rápida; dichas facilidades hacen de una wiki una herramientaefectiva para la escritura colaborativa.”En...
89.
Non-linear electromagnetism and special relativity
- Denis Serre; École Normale Supérieure; De Lyon
To my friend Li Ta-tsien (Li Da-qian), on the occasion of his 70th anniversary We continue the study of nonlinear Maxwell equations for electromagnetism in the formalism of Coleman & Dill. We exploit here the assumption of Lorentz invariance. In particular, we show that nonlinearity forbids the convexity of the electromagnetic energy density. This justifies the study of rank-one convex and of polyconvex densities, begun in [7, 12]. We also show the alternative that either electrodynamics is linear, or dispersion is lost as the electromagnetic field becomes intense. 1
90.
Spacetime Deformations and Electromagnetism in Material Media
- da Rocha, R.; Freire, I. L.
This paper is intended to investigate the relation between electrodynamics in
anisotropic material media and its analogous formulation in an spacetime, with
non-null Riemann curvature tensor. After discussing the electromagnetism via
chiral differential forms, we point out the optical activity of a given
material medium, closely related to topological spin, and the Faraday rotation,
associated to topological torsion. Both quantities are defined in terms of the
magnetic potential and the electric and magnetic fields and excitations. We
revisit some properties of material media and the associated Green dyadics.
Some related features of ferrite are also investigated. It is well-known that
the constitutive tensor is essentially equivalent to the Riemann...
91.
Students' Models of Newton's Second Law in Mechanics and Electromagnetism
- Itza-Ortiz, Salomon; Rebello, N. Sanjay; Zollman, Dean A.
We investigated students' use of Newton's second law in mechanics and
electromagnetism contexts by interviewing students in a two-semester
calculus-based physics course. We observed that students' responses are
consistent with three mental models. These models appeard in mechanics contexts
and were transferred to electromagnetism contexts. We developed an inventory to
help instructors identify these models and direct students towards the correct
one.
92.
On the genesis of Post constraint in modern electromagnetism
- Lakhtakia, Akhlesh
The genesis of the Post constraint is premised on two attributes of modern
electromagnetism: (i) its microscopic nature, and (ii) the status of e and b as
the primitive electromagnetic fields. This constraint can therefore not arise
in EH--electromagnetism, wherein the primitive electromagnetic fields are the
macroscopic fields E and H.
93.
The gauge non-invariance of Classical Electromagnetism
- Rousseaux, Germain
"Physical theories of fundamental significance tend to be gauge theories.
These are theories in which the physical system being dealt with is described
by more variables than there are physically independent degree of freedom. The
physically meaningful degrees of freedom then reemerge as being those invariant
under a transformation connecting the variables (gauge transformation). Thus,
one introduces extra variables to make the description more transparent and
brings in at the same time a gauge symmetry to extract the physically relevant
content. It is a remarkable occurrence that the road to progress has invariably
been towards enlarging the number of variables and introducing a more powerful
symmetry rather than conversely...
94.
Gravity And Electromagnetism In Noncommutative Geometry
- Giovanni Landi; Nguyen Ai Viet; Kameshwar C. Wali
We present a unified description of gravity and electromagnetism in the framework of a Z 2 noncommutative differential calculus. It can be considered as a "discrete version" of Kaluza-Klein theory, where the fifth continuous dimension is replaced by two discrete points. We derive an action which coincides with the dimensionally reduced one of the ordinary Kaluza-Klein theory. PACS. 04.20.Jb, 04.40. +c, 11.15. -q, 14.80.Hv On leave from Dipartimento di Matematica, Universit`a di Trieste, P.le Europa 1, I-34100, Trieste, Italy. Also INFN, Sezione di Napoli, Napoli, Italy. Fellow of the Italian National Council of Research (CNR) under Grant No. 203.01.60. y...
95.
Space-time Curvature of Classical Electromagnetism
- Woodside, R. W. M.
The space-time curvature carried by electromagnetic fields is discovered and
a new unification of geometry and electromagnetism is found. Curvature is
invariant under charge reversal symmetry. Electromagnetic field equations are
examined with De Rham co homology theory. Radiative electromagnetic fields must
be exact and co exact to preclude unobserved massless topological charges.
Weyl's conformal tensor, here called ``the gravitational field'', is decomposed
into a divergence-free non-local piece with support everywhere and a local
piece with the same support as the matter. By tuning a local gravitational
field to a Maxwell field the electromagnetic field's local gravitational field
is discovered. This gravitational field carries the electromagnetic field's
polarization or phase information,...
96.
On Felix Klein's Geometric Model of Electromagnetism
- Vesely, S. L.; Vesely, A. A.
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for
further developments of general relativity. Klein had a peculiar way to
consider the relationship between mathematics and physics, based on his
Erlanger Programm and geometrical modeling of physical phenomena. He was aiming
at a physical foundation for non Euclidean geometry. However, the letters he
wrote to Einstein had no sequel.
We think that F. Klein's ideas still deserve some attention, as they can be
useful for modeling Maxwell's equations with a radically different approach
than resorting to field theories. One reason for looking for alternatives is
that current field theories use geometry exclusively as...
97.
Electrodinámica quiral: eslabón para la unificación del electromagnetismo y la gravitación
- Torres Silva, Héctor
An alternative to the theory of quantum gravity, not yet discovered, is the Theory Simplified Total (TTS) proposal, which aims to unify gravity with the EM taking as a corollary the essential quantum Dirac equation. Thus, this article proposes a whole program of unification in which chiral electromagnetism plays the main role. TTS is derived from the original equations of Einstein-Hilbert , where the Einstein tensor is unchanged. The EM tensor instead is chiral and the mass of the particles has an electromagnetic nature. In the case of the electron the consequence of this is that, for the first time,...
98.
Lattice p-Form Electromagnetism and Chain Field Theory
- Wise, Derek K.
Since Wilson's work on lattice gauge theory in the 1970s, discrete versions
of field theories have played a vital role in fundamental physics. But there is
recent interest in certain higher dimensional analogues of gauge theory, such
as p-form electromagnetism, including the Kalb-Ramond field in string theory,
and its nonabelian generalizations. It is desirable to discretize such `higher
gauge theories' in a way analogous to lattice gauge theory, but with the
fundamental geometric structures in the discretization boosted in dimension. As
a step toward studying discrete versions of more general higher gauge theories,
we consider the case of p-form electromagnetism. We show that discrete p-form
electromagnetism admits a simple...
99.
The Nature is Simple in Essence - Blueprint for Unification of Gravity
and Electromagnetism
- Drafta, Viorel
The Temporal Fluctuation Model proposed in present paper represents an
attempt for a unitary vision for gravity, inertia and electromagnetism. We
obtain the main results of General Relativity and Electromagnetism and the
theory, until now, don't contain self-contradictions. As well, we obtain the
"unified potential" which has terms that coupling gravitation with
electromagnetism and who could be the basis for future technological
applications.
100.
On Duality Rotations in Light-Like Noncommutative Electromagnetism
- Aschieri, Paolo
We study electric-magnetic duality rotations for noncommutative
electromagnetism (NCEM). We express NCEM as a nonlinear commutative U(1) gauge
theory and show that it is self-dual when the noncommutativity parameter \theta
is light-like (e.g. \theta^{0i}=\theta^{1i}). This implies, in the slowly
varying field approximation, self-duality of NCEM to all orders in \theta.
