Functional integrals and 1/h expansion in the boson-fermion model

The effective action of boson-fermion model is derived by means of the functional integrals method and Popov-Faddeev canonical transformations. The energy gap equation and excitation spectrum equation are obtained from first order and second order perturbation expansions of functional determinant. In the long wave approximation, some analytical expressions of excitation spectrum are calculated by using the 1/h expansion technique, the results showed that analytical calculation is in good agreement with the numerical calculation. Moreover, the Nambu sum rules of Higgs bosons are analyzed and discussed.