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An efficient integral equation based solver is constructed for the electrostatic problem on domains with cuboidal inclusions. It can be used to compute the polarizability of a dielectric cube in a dielectric background medium at virtually…
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows,…
Quantum field theory has formed the conceptual framework of most of physics for more than sixty years. It incorporates a complete revision of our conception of the nature of matter and existence itself. Yet it is rarely taught, or even…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
Traditionally, Electromagnetism is taught following the chronological development of the matter. The final product of this path is a presentation of Electromagnetism realized by adding one layer over another with the risk of transferring…
We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…
Although Quantum field theory has been very successful in explaining experiment, there are two aspects of the theory that remain quite troubling. One is the no-interaction result proved in Haag's theorem. The other is the existence of…
Spin transport properties at finite electric and magnetic fields are studied by using the generalized semiclassical Boltzmann equation. It is found that the spin diffusion equation for non-equilibrium spin density and spin currents involves…
We use covariance and dimensional analysis to find expressions for the discontinuity of the potential and normal electric field across a flat surface with multipolar charge surface density in vacuum.
Force-free electrodynamics (FFE) is a closed set of equations for the electromagnetic field of a magnetically dominated plasma. There are strong arguments for the existence of force-free plasmas near pulsars and active black holes, but FFE…
Based on Gauss's law for the electric field, new integral formulas are deduced. Although the applications are not limited within the physics realm, an application is also presented, for the sake of practicability, specifically in the area…
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
A new finite-range electromagnetic (EM) theory containing both electric and magnetic charges constructed using two vector potentials A^{} and Z^{} is formulated in the spacetime algebra (STA) and in the algebra of the three-dimensional…
We construct the effective theory of electrically charged, spatially extended, infinitely heavy objects at leading power. The theory may be viewed as a generalization of NRQED for particles with a finite charge distribution where the charge…
Textbooks frequently extol plate tectonics theory without questioning what might be wrong with the theory or without discussing a competitive theory. How can students be taught to challenge popular ideas when they are only presented a…
The aim of this article is to prove strong convergence results on the difference between the solution to highly oscillatory problems posed in thin domains and its two-scale expansion. We first consider the case of the linear diffusion…
A physical field has an infinite number of degrees of freedom since it has a field value at each location of a continuous space. Therefore, it is impossible to know a field from finite measurements alone and prior information on the field…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
In most introductory courses on electrodynamics, one is taught the electric charge is quantised but no theoretical explanation related to this law of nature is offered. Such an explanation is postponed to graduate courses on…
In the perfect conductivity problem of composites, the electric field may become arbitrarily large as $\varepsilon$, the distance between the inclusions and the matrix boundary, tends to zero. The main contribution of this paper lies in…