Path-ordered Phase Factors in Scalar Quantum Electrodynamics
  Starting from linear equations for the complex scalar field, the two- and three-point Green's functions are obtained in the infrared approximation. We show that the infrared singularity factorizes in the vertex function as in spinorial QED, reproducing in a straightforward way the result of lenghty perturbative calculations. 
B. M. Pimentel and J. L. Tomazelli