The two-point approximation for the Casimir energy in the self-consistent chiral soliton model of the nucleon

The two-point approximation for strongly non-local effective actions is studied in the particular case of the chiral soliton model of the nucleon. Sea-quark effects are included self-consistently (within the approximation), and a self-consistent soliton obtained with observables differing (for physically relevant quark masses) by about 20% from those found from the corresponding exact calculation. The theory is defined with a momentum-space cut-off, and the effect of different choices of cut-off is investigated. An analytically much simpler (pole) form of the basic approximation is also described, which leads to a simple algebraic self-consistent equation for the soliton profile function, the solution of which is essentially indistinguishable from the full two-point approximation. This pole form of the approximation therefore provides a reasonably accurate, practical and efficient approach to such non-local problems. (orig.)