  We study homogeneous quantum L\'{e}vy processes and fields with independent
additive increments over a noncommutative *-monoid. These are described by
infinitely divisible generating state functionals, invariant with respect to an
endomorphic injective action of a symmetry semigroup. A strongly covariant GNS
representation for the conditionally positive logarithmic functionals of these
states is constructed in the complex Minkowski space in terms of canonical
quadruples and isometric representations on the underlying pre-Hilbert field
space. This is of much use in constructing quantum stochastic representations
of homogeneous quantum L\'{e}vy fields on It\^{o} monoids, which is a natural
algebraic way of defining dimension free, covariant quantum stochastic
integration over a space-time indexing set.
