Quantized Chiral Soliton as an Alternative to the Skyrme Model and γNΔ Vertex

The problem of soliton stability in the chiral sigma model is investigated. After the brief introductory relations the relevant expression for the Hamiltonian appropriate to the quantization of rotational and vibrational modes as well as the pion mass term is presented. Corresponding equation of motion is exhibited, from which the effective potential is extracted. The existence of minimum of this potential is established and the energy of the ground state is found. It is shown that stability may be achieved only after the breaking of chiral symmetry by pion mass term. The profile function is constructed which guarantees the stability. Mass spectra of nucleon and its resonances are derived. This is analogous to WKB quantization formula. E_n=m_π(-_4a^c)^1/2 [W_eff(Y₀)+√2W_eff^''(Y₀) (n+1/2)] where expressions for entering here parameters are given in the main text, Eqs. (15). Unfortunately the profile functions applied do not satisfy to the equation of motion, therefore their status is unclear. Nevertheless the existence of minimum is a remarkable property for this problem and it underlines the importance of quantum consideration. Therefore it is interesting to calculate appropriate profile function. In this purpose the calculation scheme is proposed for the profile function in the Skyrme anzatz, which then may be applied to delta-nucleon transition problem. The most profound task is a reconstruction of the profile function from the integral relations. For the present only phenomenological consideration shows that by choosing of appropriate test profile functions rather good description of nucleon resonance masses may be achieved. (author)