When a (frequency–domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the chosen material and a näive application of the usual boundary conditions. It is shown here that the conflict vanishes when the boundary conditions are properly...

We propose a naive unification of Electromagnetism and General Relativity based on enlarging the gauge group of Ashtekar’s new variables. We construct the connection and loop representations and analyze the space of states. In the loop representation, the wavefunctions depend on two loops, each of them carrying information about both gravitation and electromagnetism. We find that the Chern-Simo...

A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford a...

The genesis of the Post constraint is premised on two attributes of modern electromagnetism: (i) its microscopic nature, and (ii) the status of ẽ (x, t) and b̃ (x, t) as the primitive electromagnetic fields. This constraint can therefore not arise in EH–electromagnetism, wherein the primitive electromagnetic fields are the macroscopic fields Ẽ (x, t) and H̃ (x, t). Available experimental evidence...

Standard formulae of classical electromagnetism for the forces between electric charges in motion derived from retarded potentials are compared with those obtained from a recently developed relativistic classical electrodynamic theory with an instantaneous inter-charge force. Problems discussed include small angle Ruther-ford scattering, Jackson's recent 'torque paradox' and circular Keplerian ...

If the conformal invariance of electromagnetism is broken during inflation, then primordial magnetic fields may be produced. If this symmetry breaking is generated by the coupling between electromagnetism and a scalar field—e.g. the inflaton, curvaton, or Ricci scalar—then these magnetic fields may be correlated with primordial density perturbations, opening a new window to the study of nonGaus...

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs Xl,m associated to regular tessellations of hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick [FP94]) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs a...

We reconstruct a 3+1 formalism of general relativistic electromagnetism, and derive the equations of motion of charged particles in the pulsar magnetosphere, taking account of the inclination between the rotation axis and the magnetic axis. Apart from the previous works where space charge is evaluated by assuming the flow velocity being the light speed, we analyze particle motion in the polar c...

One of the most important facets of collaborative learning is the interaction between individual and collaborative learning activities – between divergent perspectives and shared knowledge building. Individuals bring divergent ideas into a collaborative environment. While individuals bring their own unique knowledge and perspectives, the second important aspect of collaborative learning is how ...

In this paper we describe a high order spectral algorithm for solving the time-harmonic Navier equations in the exterior of a bounded obstacle in three space dimensions, with Dirichlet or Neumann boundary conditions. Our approach is based on combined-field boundary integral equation (CFIE) reformulations of the Navier equations. We extend the spectral method developped by Ganesh and Hawkins [12...