Maxwell meets Reeh-Schlieder: the quantum mechanics of neutral bosons

TL;DR

This paper develops a covariant biorthogonal quantum mechanics framework for neutral bosons, linking photon detection probabilities with quantum field theory and localized measurement devices.

Contribution

It introduces a covariant position operator with localized eigenvectors in biorthogonal quantum mechanics, connecting photon counting with electromagnetic energy density detection.

Findings

Position eigenvalues correspond to spatial parameters in quantum fields.

Transition probabilities match the first order Glauber correlation function.

Framework unifies photon detection with covariant quantum field theory.

Abstract

We find that biorthogonal quantum mechanics with a scalar product that counts both absorbed and emitted particles leads to covariant position operators with localized eigenvectors. In this manifestly covariant formulation the probability for a transition from a one-photon state to a position eigenvector is the first order Glauber correlation function, bridging the gap between photon counting and the sensitivity of light detectors to electromagnetic energy density. The position eigenvalues are identified as the spatial parameters in the canonical quantum field operators and the position basis describes an array of localized devices that instantaneously absorb and re-emit bosons.