Related papers: The deceiving simplicity of problems with infinite…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
We apply the Thermal Field Theory (TFT) methods to study the propagation of photons in a plasma wire, that is, a system in which the electrons are confined to a one-dimensional tube or wire, but are otherwise free. We find the appropriate…
There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…
Mathematical conception of infinite quantities forms a cornerstone of many disciplines of modern mathematics --- from differential calculus to set theory. In fact, it could be argued that the most significant revolutions in mathematics in…
Is field space infinite? If not, it either loops back on itself or ends altogether. Periodic boundary conditions are of course familiar, but field space endpoints--which appear in real-world systems--are far less explored. In this paper we…
We examine the spatial distribution of electrons generated by a fixed energy point source in uniform, parallel electric and magnetic fields. This problem is simple enough to permit analytic quantum and semiclassical solution, and it harbors…
A solid ionic conductor with cation conductivity in the interelectrode region is studied. Due to their large size, the anions are considered fixed and form a homogeneous neutralizing electric background. The model can be used to describe…
``The plasma approximation'' is, in the words of Pauli, ``not even wrong,'' as it expresses a disbelief in the symmetries of the underlying gauge field theory. The electrostatic field in question is divergenceful yet has no sources or…
The equations of electrostatics are presented in pre-metric form, and it is pointed out that if the origin of the nonlinearity is the constitutive law for the medium then the differential equations themselves remain linear, while the…
I define the fields that describe electrical macrostructure, and their rates of change, in terms of the microscopic charge density, electric field, electric potential, and their rates of change. To deduce these definitions, I lay some new…
Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged…
The field of a point electric dipole in an infinite dielectric is obtained by placing the dipole at the center of a spherical cavity of radius $R$ inside the dielectric and then letting $R\to 0$. The result disagrees with the elementary…
We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is…
The insulated and perfect conductivity problems arising from high-contrast composite materials are considered in all dimensions. The solution and its gradient, respectively, represent the electric potential and field. The novelty of this…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Surfaces of ionic solids interacting with an ionic solution can build up charge by exchange of ions. The surface charge is compensated by a strip of excess charge at the border of the electrolyte forming an electric double layer. These…
Pulsar electrodynamics is reviewed emphasizing the role of the inductive electric field in an oblique rotator and the incomplete screening of its parallel component by charges, leaving `gaps' with $E_\parallel\ne0$. The response of the…
Electromagnetic quantities such as energy density, momentum, spin, and helicity bring meaning and intuition to electromagnetism and possess intricate interrelations, particularly prominent in complex non-paraxial near-fields. These…
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations…
Quantum field theory offers physicists a tremendously wide range of application; it is both a language with which a vast variety of physical processes can be discussed and also it provides a model for fundamental physics, the so-called…