Investigation of nonlinear realizations of chiral groups by the method of generating functions

An exhaustive description is given of nonlinear realizations of the chiral groups $U_n\times U_n$ and $SU_n\times SU_n$ which are linearized on the subgroups $U_n$ and $SU_n$, respectively. The description is carried out by the method os generating functions using Sylvester – Lagrange polynomials. It is proved that the nonlinear realizations of the chiral group $SU_n\times SU_n$ are stipulated uniquely with an accuracy of up to a canonical redefinition of the field variables; under these conditions the method of generating functions allows explicit indication of the required substitution of field variables. It is shown that unlike semisimple groups, the non-semisimple group $U_n\times U_n$ has nonequivalent nonlinear realizations.