We study double Higgs production in the e+e− and γγ modes
of the linear collider. It is also shown how one can probe the scalar potential
in these reactions. We discuss the effective longitudinal W approximation in
γγ processes and the WL​WL​ luminosities in the two modes of a
high-energy linear collider. A generalised non-linear gauge-fixing condition,
which is particularly useful for tree-level calculations of electroweak
processes for the laser induced collider, is presented. Its connection with the
background-field approach to gauge fixing is given.Comment: 60 pages, LateX, uses epsf, needs FEYNMAN.tex, 26 figs. (eqs. 4.1 and
4.10 changed), full paper (including figs) is also available via www at
http://lapphp0.in2p3.fr/preplapp/psth/doublehiggs.ps.gz or via anonymous ftp
at ftp://lapphp0.in2p3.fr/pub/preprints-theorie/doublehiggsf.u