  We present a field theoretical proof of the conjectured KLT relation which
states that the full tree-level scattering amplitude of gluons can be written
as a product of color-ordered amplitude of gluons and color-ordered amplitude
of scalars with only cubic vertex. To give a proof we establish the KK relation
and BCJ relation of color-ordered scalar amplitude using BCFW recursion
relation with nonzero boundary contributions. As a byproduct, an off-shell
version of fundamental BCJ relation is proved, which plays an important role in
our work.
