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 δm(Ω, s)/m = α(2/π)(Ω/m) sinh(s), where Ω and s stand for the mode frequency and the squeeze parameter and α for the fine structure constant, respectively. The correction to the anomalous magnetic moment of the electron is δae(s) = −(4α/π) sinh (s). The dependece of the scattering matrix on the vacuum state of the theory and on exterior parameters has been studied for the thermal equilibrium [1], in cavity–quantum electrodynamics [2], on fractal space–time support [3] and, to some extent, in the presence of strong electromagnetic fields [4, 5]. Here, quantum electrodynamics is investigated in the presence of squeezed vacuum fluctuations [6]; i.e., fluctuations with reduced noise in amplitude or phase. The squeezed vacuum state [7] exhibits a nonvanishing average photon density proportional to sinh(s) per squeezed mode, where s is the squeeze parameter [8]. This can be accounted for in the perturbation series by the introduction of a causal photon propagator as follows [9]. Denote the squeezed vacuum by |sv〉. The photon propagator in the Landau gauge is Dμν(x − y) = −i〈sv|T [Aμ(x)Aν (y)]|sv〉