Expressing the Field Operator in Terms of Currents and Densities

TL;DR

This paper derives a formula expressing the field operator as a function of observable currents and densities, clarifies its Fock space representation, and conjectures its uniqueness.

Contribution

It introduces a novel formula linking field operators with observable bilinears and proposes a conjecture on the uniqueness of this correspondence.

Findings

Derived a formula for annihilation operators in terms of currents and densities

Clarified the Fock space representation of these formulas

Proposed a conjecture on the uniqueness of the operator-current-density correspondence

Abstract

A formula is written down for the annhilation operator(bose or fermi) in terms of the corresponding observable bilinears namely currents and densities. The Fock space representation of these formulas is clarified. A conjecture is written down that shows that such a correspondence is unique.