相关论文: A concise introduction to Colombeau generalized fu…
A fully relativistically covariant formulation of the classical Maxwell electrodynamics of an arbitrarily-moving point charge is presented, purely in terms of gauge invariant potentials without entailing any gauge fixing. A new,…
We prove Banach, Newton-Raphson and Brouwer fixed point theorems in the framework of generalized smooth functions, a minimal extension of Colombeau's theory (and hence of classical distribution theory) which makes it possible to model…
This is the first in a two-part series in which we extend non-relativistic stochastic mechanics, in the ZSM formulation [1, 2], to semiclassical Newtonian gravity (ZSM-Newton) and semiclassical Newtonian electrodynamics (ZSM-Coulomb), under…
We introduce an intrinsic notion of Hoelder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hoelder space this is shown to be consistent. The definition is motivated by the…
Nonlinear Maxwell equations are written up to the third-power deviations from a constant-field background, valid within any local nonlinear electrodynamics including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear electric…
The classical theory of radiating point-charges is revisited: the retarded potentials, fields, and currents are defined as nonlinear generalized functions and all calculations are made in a Colombeau algebra. The total rate of…
As follows from the Schwartz Impossibility Theorem, multiplication of two distributions is in general impossible. Nevertheless, often one needs to multiply a distribution by a discontinuous function, not by an arbitrary distribution. In the…
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its response is governed by a system of linear ordinary…
The assumption is made that only transversely polarized photons are needed for a correct description of Quantum Electrodynamics. A simple mathematical transformation is used to introduce new field operators which satisfy the full Maxwell…
We present a unified framework for studying Coulomb interactions in arbitrary environments using macroscopic quantum electrodynamics on the basis of the electromagnetic Green's function. Our theory can be used to derive the Coulomb…
We set-up and solve the Cauchy problem for Schr\"odinger-type differential operators with generalized functions as coefficients, in particular, allowing for distributional coefficients in the principal part. Equations involving such kind of…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
Nonlinear electrodynamics with two parameters is studied. It is shown that singularities of point-like electric charges are absent and the electromagnetic energy is finite. Corrections to Coulomb's law are found. The finite static electric…
Classical Electrodynamics is not a consistent theory because of its field inadequate behaviour in the vicinity of their sources. Its problems with the electron equation of motion and with non-integrable singularity of the electron self…
Faraday's and Furry's formulas for the electromagnetic momentum of static charge distributions combined with steady electric current distributions are generalised in order to obtain full agreement with Poynting's formula in the case where…
We present a construction of algebras of generalized functions of Colombeau-type which, instead of asymptotic estimates with respect to a regularization parameter, employs only topological estimates on certain spaces of kernels for its…
To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…
Collisionless damping of electrical waves in plasma is investigated in the frame of the classical formulation of the problem. The new principle of regularization of the singular integral is used. The exact solution of the corresponding…