Quantum electrodynamics in the squeezed vacuum state: Feynman rules and corrections to the electron mass and anomalous magnetic moment

Due to the nonvanishing average photon population of the squeezed vacuum state, finite corrections to the scattering matrix are obtained. The lowest order contribution to the electron mass shift for a one mode squeezed vacuum state is given by $\delta m(\Omega ,s)/m=\alpha (2/\pi )(\Omega /m)^2\sinh^2(s)$, where $\Omega$ and $s$ stand for the mode frequency and the squeeze parameter and $\alpha$ for the fine structure constant, respectively. The correction to the anomalous magnetic moment of the electron is $\delta a_e(s)=-(4\alpha /\pi )\sinh^2(s)$.