Semiclassical projection of hedgehog models with quarks

A simple semiclassical method is presented for calculating physical observables in states with good angular momentum and isospin for models whose mean-field solutions are hedgehogs. The method is applicable for theories which have both quark and meson degrees of freedom. The basic approach is to find slowly rotating solutions to the time-dependent mean-field equations. A nontrivial set of differential equations must be solved to find the quark configuration for these rotating hedgehogs. The parameters which specify the rotating solutions are treated as the collective degrees of freedom. They are requantized by imposing a set of commutation relations which ensures the correct algebra for the SU(2)×SU(2) group of angular momentum and isospin. Collective wave functions can then be found and with these wave functions all matrix elements can be calculated. The method is applied to a simple version of the chiral quark-meson model. A number of physical quantities such as magnetic moments, charge distributions, $g_A$, $g_{\pi \mathrm{NN}}$, N-Δ mass splitting, properties of the N-Δ transition, etc., are calculated.