The chiral soliton in the proper-time regularization scheme

Abstract

The effective chiral action (quark loop in the presence of external meson fields) is evaluated in terms of the eigenvalues of the corresponding Dirac operator. This splits the effective action into a vacuum part (Dirac sea contribution) and a valence (anti-) quark part. The vacuum part is regularized by using the proper-time regularization. This regularization scheme is worked out for time-independent external (meson) fields, thereby expressing the vacuum energy in terms of the eigenvalues of the corresponding Hamilton operator. The resulting expression is used to establish the connection between the O(4)-invariant proper-time regularization and the non-O(4)-invariant regularization schemes. A static heat-kernel expansion is developed which allows to link the static chiral soliton to the low-energy meson physics. Finally, the chiral soliton is quantized in a semiclassical fashion. For the valence quarks the semiclassical quantization is equivalent to the familiar cranking approach, while for the sea quarks it is an O(4)-invariant regularized extension of the latter.