  We use an algebraic approach based on representations of de Sitter group to
construct covariant quantum fields in arbitrary dimensions. We study the
complementary and the discrete series which correspond to light and massless
fields and which lead new feature with respect to the massive principal series
we previously studied (hep-th/0606119). When considering the complementary
series, we make use of a non-trivial scalar product in order to get local
expressions in the position representation. Based on these, we construct a
family of covariant canonical fields parametrized by SU(1,1)/U(1). Each of
these correspond to the dS invariant alpha-vacua. The behavior of the modes at
asymptotic times brings another difficulty as it is incompatible with the usual
definition of the in and out vacua. We propose a generalized notion of these
vacua which reduces to the usual conformal vacuum in the conformally massless
limit. When considering the massless discrete series we find that no covariant
field obeys the canonical commutation relations. To further analyze this
singular case, we consider the massless limit of the complementary scalar
fields we previously found. We obtain canonical fields with a deformed
representation by zero modes. The zero modes have a dS invariant vacuum with
singular norm. We propose a regularization by a compactification of the scalar
field and a dS invariant definition of the vertex operators. The resulting
two-point functions are dS invariant and have a universal logarithmic infrared
divergence.
