Photon mass in a background of thermal particles

The mass of the photon in the presence of thermal background particles is studied. We present a general proof that all contributions to the photon's thermal mass from low-temperature thermal backgrounds are suppressed by a huge exponential factor at least as large as $e^{\frac{m_e}{2kT}}$. We explicitly show that there is no contribution to the photon's thermal mass of order ${\left(\alpha G_F\right)}^{\frac{1}{2}}{\left(k{T}_{\nu }\right)}^2$ from two-loop diagrams involving thermal neutrinos at temperature $T_{\nu }$. The largest contribution to the photon's thermal mass from the observed 3°K background is also calculated.