Infrared singularities in the dimensional regularization scheme

Infrared singularities arising in some renormalized amplitudes of quantum electrodynamics are analyzed using the dimensional regularization method. We define infrared and ultraviolet convergent regions in the ν complex plane (ν is the number of dimensions of space time). It turns out that these regions do not overlap for quantum electrodynamics. Nevertheless, it is shown that there exists a unique analytic continuation from the infrared convergent region which allows us to interpret the infrared divergence in the renormalized electron self-energy amplitude as an isolated singularity at ν = 4. This statement seems to be true at all orders of perturbation theory. We also prove that the double limit μ → 0, ν → 4 (μ is the auxiliary photon mass) does not exist in quantum electrodynamics and we conjecture that this lack of uniformity provides theoretical support for the ansatz of Marciano and Sirlin.