Real and Imaginary Mass Generation in the Presence of External Fields   and Axions
  Small fluctuations around a constant electric or constant magnetic field F are analyzed in a theory with pseudo scalar [phi] with a coupling g[phi]F~F. It is found that a magnetic external field leads to mass generation for the small perturbations, while an electric field suffers from a tachyonic mass generation in the case in which the field strength is higher than a critical value (related to the pseudo scalar mass). The vacuum energy can be exactly evaluated and it is found that an imaginary part is present when the external electric field exceeds its critical value. 
Stefano Ansoldi, Eduardo I. Guendelman, Euro Spallucci