Effective action for Dirac spinors in the uniform electromagnetic   background fields
  Some new expressions are found, concerning the effective action as a regularized path-integral for Dirac's spinors in {\it 3+1} dimensions, in the presence of general uniform (i.e., constant and homogeneous) electric and magnetic fields. The rate of $e^+e^-$ pairs production is computed and briefly discussed. 
Roberto Soldati, Lorenzo Sorbo