EXERCISE S10.11. At the A-transition in He4, gauge symmetry is broken. The generator of a gauge transformation is the number operator, N=fdr (r)(r), where (r) and (r) are boson field operators which create and destroy particles, respectively, at point r (cf. Appendix B). Show that if [eg, N] 0 so that gauge symmetry of the system is broken (where Peq is the equilibrium state of the system), then ((r)) = Tr[eq(r)] is the order parameter.