  The problem of dynamical heating of galactic discs by spiral density waves is
discussed using the shearing sheet model. The secular evolution of the disc is
described quantitatively by a diffusion equation for the distribution function
of stars in the space spanned by integrals of motion of the stars, in
particular the radial action integral and an integral related to the angular
momentum. Specifically, disc heating by a succession of transient, `swing
amplified' density waves is studied. It is shown that such density waves lead
predominantly to diffusion of stars in radial action space. The stochastical
changes of angular momenta of the stars and the corresponding stochastic
changes of the guiding centre radii of the stellar orbits induced by this
process are much smaller.
