On the Wave aspect of Relativistic Quantum Fields

Abstract

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.