A Study Of The Effective Potential And The Normative Correlation Of Related Physical Quantities

In this thesis,we mainly study the gauge depedence of the Coleman-Weinberg model.At the beginning of the thesis,we introduce the vacuum stability of the stan-dard model and effective potential.For the Standard Model and other gauge theories,the effective potential is always gauge dependent.In chapter 2,we introduce the path integral formalism of quantum field theory,gauge theory and other theoretical tools In Chapter 3,we introduce the effective action and effective potential.We discuss the application of effective potential in vacuum stability.In order to describe the gauge dependence of the effective potential,we derive the Nielsen identity in detail.By using Nielsen identity,we formally prove that the gauge invariance of Vminand the exponen-tial part of vacuum decay rate.In Chapter 4,we study the gauge dependence of the effective potential and physical quantities in the Coleman-Weinberg model.We show that after considering Daisy Resummation and treating the vacuum value correctly,the Vmin to order e6 is indeed gauge independent.Finally,we take Daisy Resumation into account in the so-called dressed propagator.We use dressed propagator to calculate the contribution of the one-loop self-energy graphs to the pole mass of the vector meson.We expand the self-energy graphs at P2=0 and p2=e2(?)2,respectively.Finally,we found that when Daisy Resummation is considered,the pole mass of the vector meson is gauge independent to the order e4.