Double Higgs Production at the Linear Colliders and the Probing of the Higgs Self-Coupling

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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 $W_L W_L$ 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.
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.uu

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