Paper detail

Photon position observable

In biorthogonal quantum mechanics, the eigenvectors of a quasi-Hermitian operator and those of its adjoint are biorthogonal and complete and the probability for a transition from a quantum state to any one of these eigenvectors is positive definite. We apply this formalism to the long standing problem of the position observable in quantum field theory. The dual bases are positive and negative frequency one-particle states created by the field operator and its conjugate and biorthogonality is a consequence of their commutation relations. In these biorthogonal bases the position operator is covariant and the Klein-Gordon wave function is localized. We find that the invariant 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.