This appendix develops the mathematical machinery of screening and Green’s functions needed for electrostatics and magnetostatics. Starting from the screened Coulomb potential, it computes its Fourier transform, takes the unscreened limit, and thereby derives the standard free-space Green’s function and its representation as a Fourier integral. The appendix then examines convergence issues and the definition of the delta function, showing how to regularize Fourier representations with exponential factors. Translational invariance is used to motivate partial Fourier transforms when only some coordinates are symmetric, reducing Poisson’s equation to an ordinary differential equation in the remaining variable. These methods are applied to construct the Green’s function for half-space bounded by a grounded conducting plane, from which one obtains the induced surface charge, the potential, and the force on a point charge near the conductor.

The Dirac delta generalized function with its definition, representations and properties, and in particular its expansion in an orthogonal basis set, as employed in the text to obtain order parameters are introduced.

We spell out a useful lemma in the theory of distributions.

This chapter provides an introduction to the notion of physical dimension, to the specific notations which are used in physics, as well a brief review of some basic mathematics: an introduction to informal distribution theory, to the delta function and the Fourier transform.