Two-loop electron self-energy in the bound-electron <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> factor: Diagrams in momentum-coordinate representation

The two-loop electron self-energy correction is one of the most problematic QED effects and, for a long time, was the dominant source of uncertainty in the theoretical prediction of the bound-electron <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>g</a:mi> </a:math> factor in hydrogenlike ions. A major breakthrough was recently achieved by B. Sikora [], who calculated this effect without any expansion in the nuclear binding strength parameter <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>Z</b:mi> <b:mi>α</b:mi> </b:mrow> </b:math> (where <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>Z</c:mi> </c:math> is the nuclear charge number and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>α</d:mi> </d:math> is the fine-structure constant). In this paper we describe our calculations of one of the most difficult parts of the two-loop self-energy, represented by Feynman diagrams that are treated in the mixed momentum-coordinate representation.