On the Wave aspect of Relativistic Quantum Fields

TL;DR

This paper introduces a wave-based basis for relativistic quantum fields, emphasizing their wave nature over particle aspects, and constructs this representation explicitly for free neutral fields, with potential applications in quantum optics.

Contribution

A novel wave-representation for relativistic quantum fields based on eigenstates of field operators, highlighting the wave aspect of quantum systems.

Findings

Explicit construction of the wave-representation for free neutral fields

Mathematical analysis of the wave-representation's properties

Discussion of potential applications in quantum optics

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.