Quark model of superconducting type and nondiagonal P-A transitions

Conclusions

We discuss the obtained results. We note that the solution to the problem of the elimination of the unphysical interactions that arise through the P-A diagnonalization has been obtained at the prescriptional level. We have found that to eliminate the unphysical vertices due to the P-A diagnonalization, it is sufficient to replace the effective Lagrangian (22) by the Pauli-Villars regularized Lagrangian (33). The regularization is needed because of the nonuniqueness of the calculation of the individual quark diagrams that describe the new interaction vertices. The Pauli-Villars regularization corresponds to subtraction from the quark diagram of a quantity determined by the same diagram but in which all the masses of the virtual quarks are replaced by the masses of the fermions — the regularizers M. Application of the regularization for the complete effective Lagrangian has the consequence that an appropriate contribution of the regularizers is subtracted from any vertex that arises as a result of shift of the axial fields (4). This is sufficient for the correct description of the interaction vertices that arise from the P-A diagonalization.