Study Of Fermi Condensation In Two-dimensional Gravitational Solitons And String Ricci Flow Solitons

In this thesis,the problems of Fermi condensation in two-dimensional gravity solitons and string Ricci flow solitons are studied.In Chapter 1,the research status of gravitational solitons and variational functional integrals method are introduced,the development histories of Ricci flow and renormalized group flow are reviewed.In Chapter 2,the sine-Gordon soliton metric,naked singularity metric and Ad S₂ space-time metric are derived,the cigar soliton metric in Wess-Zumino-Witten model is also deduced,and the scalar curvature corresponding to each metric is calculated respectively.In Chapter 3,the gravitational correction factor and Fermi condensation density formula in sine-Gordon-Thirring model are derived by using variational functional integrals method,the critical impurity coordinates with different mass parameters and impurity numbers are calculated,the influence of impurity coordinates on Fermi condensation is analyzed.In Chapter 4,the Weyl anomaly coefficients in two-loop Ricci flow equation are derived,and the asymptotic perturbation solution of the Cigar soliton is obtained,the variation rule of the perturbation field with momentum scaling is discussed.In Chapter 5,the perturbation gravity correction factor and Fermi condensation density in sine-Gordon-Thirring model are derived by using variational functional integrals method,the impurity coordinates under different Ricci flow parameters,string coupling coefficients and perturbation coefficients are calculated,and the influence of impurity coordinates on Fermi condensation is discussed.In addition,the principal curvature of two-dimensional space-time surface in quantum Ricci flow perturbation is derived,and the umbilical point coordinates and the principal curvature of the space-time surface are calculated.Chapter 6 is the summary and prospect of this thesis.The innovative works in this thesis are as follows:1.The Fermi condensation densities the sine-Gordon soliton metric,naked singularity metric andAd S₂ space-time metric are derived according to the variational integrals method,the critical impurity coordinates with different mass parameters and impurity numbers are calculated.2.The Fermi condensation density in perturbation cigar soliton metric is derived according to the variational integrals method,the critical impurity coordinates under different Ricci flow parameters,string coupling coefficients and perturbation coefficients are calculated,the influence of impurity coordinates on Fermi condensation is discussed.In addition,the umbilical point coordinates of different Ricci flow parameters and the principal curvature of the surface are calculated.