The sequence of ideas in a re-discovery of the Colombeau algebras
arXiv:0807.0529
Abstract
This is a gentle introduction to Colombeau nonlinear generalized functions, a generalization of the concept of distributions such that distributions can freely be multiplied. It is intended to physicists and applied mathematicians who prefer a `step-by-step approach' to a `top-down indoctrination.' No particular prerequisite knowledge is necessary -- and in less than one hour you should know everything you need to know and were afraid to ask about Colombeau algebras and their applications in physics... A selected bibliography is appended, giving examples of applications to partial differential and wave equations, electrodynamics, hydrodynamics, general relativity, and quantum field theory.
28 pages. Minor corrections and additional references
References in corpus (7)
- The use of Generalised Functions and Distributions in General Relativity
- Generalized functions as a tool for nonsmooth nonlinear problems in mathematics and physics
- Colombeau solutions to nonlinear wave equations
- On the electromagnetic momentum of static charge and steady current distributions
- The Heisenberg-Pauli canonical formalism of quantum field theory in the rigorous setting of nonlinear generalized functions (Part I)
- Nonlinear generalized functions and nonlinear numerical simulations in fluid and solid continuum mechanics
- Nonlinear generalized functions and the Heisenberg-Pauli foundations of Quantum Field Theory
Cited by in corpus (5)
- First-order quantum perturbation theory and Colombeau generalized functions
- The self-interaction force on an arbitrarily moving point-charge and its energy-momentum radiation rate: A mathematically rigorous derivation of the Lorentz-Dirac equation of motion
- Derivation of the self-interaction force on an arbitrarily moving point-charge and of its related energy-momentum radiation rate: The Lorentz-Dirac equation of motion in a Colombeau algebra
- The classical point-electron in the sequence algebra (C^infinity)^I
- An introduction to generalised functions in periodic quantum theory