UL(N) x UR(N)-Invariant Four-Fermion Interactions and Nambu-Goldstone Mechanism at Finite Temperature

In a chiral U_L(N) x U_R(N) fermion model of NJL-form, we prove that, if all the fermions are assumed to have equal masses and equal chemical potentials, then at the finite temperature T below the symmetry restoration temperature T_c, there will be N² massive scalar composite particles and N² massless pseudoscalar composite particles (Nambu-Goldstone bosons). This shows that the Goldstone theorem at finite temperature for spontaneous symmetry breaking U_L(N) x U_R(N) → U_L+R(N) is valid and consistent with the real-time formalism of thermal field theory in this model.