  In the state-vector space for relativistic quantum fields a new set of basis
vectors are introduced, which are taken to be eigenstates of the field
operators themselves. The corresponding eigenvalues are then interpreted as
representing matter waves associated with the respective quantum fields. The
representation, based on such basis vectors, or the wave-representation
naturally emphasizes the wave aspect of the system, in contrast with the usual,
Fock or particle-representation emphasizing the particle aspect. For the case
of a relativistic, free neutral field, the wave-representation is explicitly
constructed, and its mathematical properties as well as physical implications
are studied in detail. It is expected that such an approach will find useful
applications, e.g., in quantum optics.
