  We study in detail the algebra of free ghost fields which we realize in a
Hilbert-Fock space with positive metric. The investigation of causality
clarifies the exact reason for the failure of the spin-statistics theorem and
leads to the introduction of the Krein Operator. We study the charge algebra of
the ghost fields which gives a representation of ${\rm gl}(2,{\cal C})$. The
symmetries of the $S$-matrix in ghost space are pointed out.
