Functional Integrals Method And Study Of Excitation Spectrum In The High Temperature Superconductivity

In this thesis,the excitation spectrum in high temperature superconductivity were studied by using the functional integral method. The development and application of functional integral method were introduced in chapter 1; the mathematical methods in superconductivity theory were presented in chapter 2, such as Bogoliubov’s second quantization method and Popov’s functional integral method. The excitation spectrum in Dicke model was analyzed in chapter 3, then energy gap equation and excitation spectrum equation were derived for boson-fermion superconductivity model, the analytical solutions of excitation spectrum were calculated by means of the 1/h expansion technique, analytical result with numerical calculation were also compared. Moreover the Nambu sum rules of excitation spectrum in various model were discussed;In chapter 4,the free Green’s function of three-band Hubbard model was derived according to the functional integral methods, the normal and abnormal Green’s functions were obtained by the matrix form of Dyson-Grokov equations, these Green’s functions can describe the physical properties of antiferromagnetic state and the superconducting state. In the long wave approximation, the excitation spectrum was calculated when the antiferromagnetic order vector coexist in copper and oxygen lattices. Moreover, the influence of antiferromagnetic order vector on the energy spectrum was also discussed.The new works of this thesis are as follows:1.The energy gap equation and excitation spectrum equation in b-f model were derived according to functional integrals method and Popov-Faddeev canonical transformation.2. In the long wave approximation, the analytical expression of excitation spectrums are obtained by using the 1/h expansion technique, the results showed that the excitation spectrums in the analytical calculation are good agreement with the numerical calculation.3. The Nambu sum rule of the excitation spectrum in b-f model was studied, it was compared with the sum rule of Higgs boson.4. Based on Popov’s functional integral method and Dyson-Gorkov equation in the temperature Green function, the excitation spectrum was calculated when the antiferromagnetic order vector coexist in copper and oxygen lattices,the influence of antiferromagnetic order vector on the energy spectrum was also discussed.