Abstract
We revisit the formalism involved in atomic spectroscopy modeling under the assumption that the photon has a finite mass. Starting from the Proca Lagrangian, we build a Hamiltonian suitable for the calculation of line shapes and intensities. Two consequences of finite photon mass are: (i) a dispersion of electromagnetic waves propagating in free space; (ii) the occurrence of a longitudinal polarization state. We illustrate these effects by addressing the spontaneous emission of a massive photon by an excited atom. The Einstein A coefficient and the power spectrum are calculated as an example. If the photon has a finite mass, deviations to standard formulas are showed to occur at energies comparable to the mass energy. A discussion based on the current upper bound estimates for the photon mass is done.
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