Spectral Analysis of Charges

Many field theory solitons have particularly interesting properties when they are coupled to fermions, because they act as strong background fields that can drastically alter the Dirac spectrum. Solitons that break C and CP invariance can introduce asymmetries in the Dirac spectrum, which cause the soliton to carry fermion number, as we have seen in Chap. 4. In case of a non-topological soliton we may interpolate continuously between the trivial background and the soliton background and observe this fermion number as a level crossing in the Dirac spectrum. In this chapter we will derive results like eq. (4.98) that enable us to precisely trace back these level crossings.