Influences Of Conformal Transformation With Bellini Connection On Scalar Field And Its Mass And Astrophysics

Conformal symmetries play an important role in the field theory.For example,the conformal symmetry can greatly simplify the renormalization process in the study of the non-equilibrium Hawking radiation near the event horizon of black holes,by method of thermal kernel expansion.In this thesis,we will focus on whether the conformal symmetry can be used to study the gravitational field and scalar field with Bellini connection and its consequences.We start with the Bellini connection to investigate the influence of conformal invariance on the early universe,the movement of matter around black holes,the generating functional of scalar fiels and the mass of the sccalar particles.Firstly,we assume that the field equation with the Bellini connection can be reduced to the situation with the Christoffel one by the conformal transformation.Bellini connection is to give the concrete form of scalar field,which is equivalent to determining a gauge and plays the role of conformal transformation.By using the Higgs mechanism,we study inflation of the universe.Then we believe that a complete symmetry of the scalar field can be realized by a ultra-high temperature at the early universe,and the entire spacetime is a complete de Sitter manifold until the temperature drops to a certain value at a certain time.Secondly,considering gravitons as dark matter,a black hole model is proposed,wich can absorb scalar particles.The model reflects the ratio of scalar field particle mass to graviton mass,and the relationship between the distance from the black hole and the black hole rotation curve.By using this model,the mass limitation of the scalar particle field is obtained.Finally,we study the algorithm of the generating functional for the scalar field under certain conditions,and scattering matrices corresponding to the generating functional and two-point graph,and their physical meanings in quantum field theory.