A survey of existing and proposed classical and quantum approaches to the photon mass

Over the past twenty years, there have been several careful experimental, observational and phenomenological investigations aimed at searching for and establishing ever tighter bounds on the possible mass of the photon. There are many fascinating and paradoxical physical implications that would arise from the presence of even a very small value for it, and thus such searches have always been well motivated in terms of the new physics that would result. We provide a brief overview of the theoretical background and classical motivations for this work and the early tests of the exactness of Coulomb's law that underlie it. We then go on to address the modern situation, in which quantum physics approaches come to attention. Among them we focus especially on the implications that the Aharonov-Bohm and Aharonov-Casher class of effects have on searches for a photon mass. These arise in several different ways and can lead to experiments that might involve the interaction of magnetic dipoles, electric dipoles, or charged particles with suitable potentials. Still other quantum-based approaches employ measurements of the g-factor of the electron. Plausible target sensitivities for limits on the photon mass as sought by the various quantum approaches are in the range of 10-53 to 10-54 g. Possible experimental arrangements for the associated experiments are discussed. We close with an assessment of the state of the art and a prognosis for future work. (authors)