Symmetry Breaking And Its Applications In Physics

Symmetry breaking, which has been widely applied to many fields of physics, is one of the most important concepts in modern physics and plays a significant role in the development of quantum field theory. In this thesis, we mainly concentrate on spon-taneous symmetry breaking in quantum field theory and investigate its applications to two specific models related to the phenomena of spontaneous symmetry breaking—the dynamical chiral symmetry breaking (DCSB) in (2+1)-dimensional quantum electro-dynamics (QED3) and the influence of gravitational correction on the renormalization of Φ4theory with spontaneously broken symmetry.In chapter1, we offer a review of quantum field theory and symmetry breaking, and then briefly introduce two works in the thesis. In order to investigate spontaneous symmetry breaking, in chapter2, we listed the indispensable background knowledge and methods of calculation.In chapter3, we consider QED3with a gauge field coupling to massless Dirac fermions and non-relativistic scalar bosons to study the DCSB and the influence of fermion velocity renormalization on it. First of all, we give a detailed introduction to QED3, Dyson-Schwinger (DS) equations, and DCSB. And then we investigate DCSB and the influence of fermion velocity renormalization on it by using the DS equation. It is found that DCSB takes place even after including the scalar bosons as long as the bosonic compressibility parameter ξ is sufficiently small. In addition, the fermion velocity renormalization enhances DCSB.In chapter4, we discuss a complex scalar Φ4theory with spontaneously broken global U(1) symmetry, minimally coupling to perturbatively quantized Einstein grav-ity which is treated as an effective theory, to obtain the influence of the gravitational correction on the renormalization of Higgs sector in this model. Both the lowest order pure real scalar correction and gravitational correction to the renormalizations of Higgs sector in this model have been investigated. Our results show that the gravitational cor-rection renders the renormalization of Higgs sector in this model inconsistent while the pure real scalar correction to it leads to a compatible renormalization. In order for comparison, we also discuss the consistence of renormalization of scalar quantum electrodynamics with spontaneously broken local U(1) symmetry.We summarize our results and give an outlook in chapter5.