Diffraction phenomena studied in electromagnetism, acoustics, and elastodynamics are often modeled using integrals, such as the well-known Sommerfeld integral. The far field asymptotic evaluation of such integrals obtained using the method of steepest descent leads to the classical Geometrical Theory of Diffraction (GTD). It is well known that the method of steepest descent is inapplicable when...

Computational electromagnetism is concerned with the numerical study of Maxwell equations. By choosing a discrete Gaussian measure on prism lattice, we use discrete exterior calculus and lattice gauge theory to construct discrete Maxwell equations in vacuum case. We implement this scheme on Java development plateform to simulate the behavior of electromagnetic waves.

Efforts have been made recently to reformulate traditional Kaluza-Klein theory by using a generalized definition of a higher-dimensional extended space-time. Both electromagnetism and gravity have been studied in this context. We review some of the models which have been proposed, with a special effort to keep the mathematical formalism to a very minimum.

Within the linear theory of the electromagnetism for the ionosphere we give a general closed expression for the minimum free energy in terms of Fourier-transformed quantities, when the integrated history of the electric field is chosen to characterize the state of the material. Another equivalent expression is derived and also used to study the particular case of a discrete spectrum model.

Transformation media are at the heart of invisibility devices, perfect lenses and artificial black holes. In this paper, we consider their quantum theory. We show how transformation media map quantum electromagnetism in physical space to QED in empty flat space. PACS 42.50.Nn, 78.67.-n.

A reconciliation of gravitation and electromagnetism has eluded physics for neearly a century. It is argued here that this is because both quantum physics and classical physics are set in differentiable space time manifolds with point particles. Once we consider extended particles as in Quantum Superstring theory, and the consequential underlying Non-Commutative geometry, then a reconciliation ...

This paper is an introduction to discrete physics based on a non-commutative calculus of finite differences. This gives a context for the Feynman-Dyson derivation of non-commutative electromagnetism, and for generalizations of this result. The paper discusses these ideas and their relations with quantum groups and topological quantum field theory.

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integ...

In this paper, we develop the quantum field theory of off-shell electromagnetism, and use it to calculate the Møller scattering cross-section. This calculation leads to qualitative deviations from the usual scattering cross-sections, which are, however, small effects, but may be visible at small angles near the forward direction.