Spectrum Density Factor of Photons and Its Application in the Casimir Force**Supported by the National Natural Science Foundation of China under Grant No. 11774316, and the Natural Science Foundation of Zhejiang Province under Grant No. Z15A050001

Abstract

The observables of continuous eigenvalues are defined in an infinite-dimensional ket space. The complete set of such eigenstates demands a spectrum density factor, for example, for the photons in the free space and electrons in the vacuum. From the derivation of the Casimir force without an artificial regulator we determine the explicit expression of the spectrum density factor for the photon field to be an exponential function. The undetermined constant in the function is fixed by the experimental data for the Lamb shift. With that, we predict that there exists a correction to the Casimir force.