Abstract
In this chapter, we discuss some of the problems which are not yet fully understood in the calculations of quantum field theory. First, we discuss the neutron EDM in terms of the vertex corrections from the W± bosons. Then, we present the calculation of the weak charge which may arise from the parity violating interaction. Also, we discuss the Lamb shifts in muonic hydrogen as well as in muonium, and present the calculation of the center of mass corrections in these exotic atoms. It is shown that the effect of the center of mass corrections destroys the close agreement between theory and experiment in muonic hydrogen. In addition, the effect in muonium is so large that it destroys the excellent agreement between Bethe’s calculation and experiment of the Lamb shifts, and this may well affect on the understanding of the fundamental mechanism of the Lamb shifts.
Keywords: open problem, neutron EDM, Lamb shifts, muonic hydrogen, muonium, vacuum polarization potential, center of mass corrections, infra-red singularity, CP transformation, Bethe’s calculation of Lamb shifts.