Functional Integrals Method And Energy Density Fluctuations Of Matter On Black Hole Background

Abstract:Generally, two methods can be used to study the statistical physics properties of one-dimensional nonlinear quantum field model, that is Bethe ansatz or functional integrals (FI) methods. First method can give exact solutions, but this method can study only in low-dimensional physics models. Functional Integrals method can applied to any nonlinear physics system, the approximation solution of physics model are obtained according to perturbation theory.The statistical physics properties of 1-d quantum sine-Gordon-Thirring model are studied by using FI method. The phase structure and stability are analyzed by using perturbation and varitation functional integrals method. The energy density fluctuation of Fermi matter on black hole background and non-commutative space-time are studied, the parturition of gravitational field in black hole are also analysed.The energy density fluctuation of scalar field and Bose-Thirring model are studied in this theory. They are compared with Fermi matter in same black hole background.Then the energy-density fluctuations of scalar fields and Bose Thirring model are obtained in this thesis, they are compared with Fermi matter in the same black hole background.In final part, the energy density fluctuations of Bose and Fermi fields on black hole background are studied by using heat-Kert functional integrals method, they are compared with the results of variation functional integral.The new works of this thesis are as follow: 1. Effect potential and free energy of sine-Gordon-Thirring model are derived by funcatioal integrals method, the phase structure and the stability are studied in the weak and strong couping cases.2. Effect potential and free energy of sine-Gordon-Thirring model are derived on black hole background, energy density fluctuation of Fermi matter are calculated in weak and strong coupling cases. Influence of gravitational field perturbation for Fermi matter is also analyzed.3. The energy-density fluctuations of scalar field and Bose Thirring model are calculated, they are compared with energy-density fluctuation of Fermi field in the same black hole background.4. Energy density fluctuation of Bose and Fermi fields are calculated by means of heat-Kert functional integrals, they are compared with the results of variational functional integrals method.