We will consider here the technical questions of how to deal with the
Fourier modes of a single-component real scalar field in numerical
simulations. This includes how to organize them in order to avoid
over-counting the degrees of freedom, how to index them into vectors and
how to build the transformations from position space to momentum space
and back in an efficient way, so that they can be executed very fast, for
use in stochastic simulations. It is important to note that the type of
implementation presented here is *not* what is usually known as the
Fast Fourier Transform (FFT). It may be described rather as an Indexed
Fourier Transform, and is meant specifically for the relatively small
lattices used in the stochastic simulations of field-theoretical models
in space-time dimensions ranging from to .

- Organizing the Degrees of Freedom
- Indexing in Momentum Space
- The Transform and its Inverse
- Fortran Routines