Spontaneous symmetry breaking leads to particle mass from "summary" of The Quantum Theory of Fields by Steven Weinberg,Weinberg S
Spontaneous symmetry breaking is a concept that plays a crucial role in the understanding of particle mass within the framework of quantum field theory. Symmetry breaking occurs when the ground state of a system does not exhibit the same symmetries as the underlying laws of the system. This breaking of symmetry leads to the emergence of mass for certain particles. In the context of the Higgs mechanism, spontaneous symmetry breaking is responsible for the generation of mass for elementary particles such as the W and Z bosons. The Higgs field, which permeates all of space, undergoes spontaneous symmetry breaking, leading to the acquisition of mass by these particles. This mechanism provides a compelling explanation for the origin of mass in the Standard Model of particle physics. The Higgs field is characterized by a potential that possesses a Mexican hat shape, with the symmetry of the field being broken to a specific direction in the field space. As a result, the excitations of the field manifest as particles with mass. The interaction between the Higgs field and other particles gives rise to the phenomenon of mass generation through the Higgs mechanism. Moreover, the Higgs mechanism also elucidates the mechanism by which other particles acquire mass. By interacting with the Higgs field, fermions such as quarks and leptons acquire mass through a process known as Yukawa coupling. This coupling between the fermions and the Higgs field is crucial for the generation of mass in the Standard Model. In summary, spontaneous symmetry breaking plays a fundamental role in the generation of mass for elementary particles within the framework of quantum field theory. The Higgs mechanism provides a comprehensive explanation for how particles acquire mass through interactions with the Higgs field. This concept has profound implications for our understanding of the origin of mass in the universe and has been validated by experimental observations, such as the discovery of the Higgs boson at the Large Hadron Collider.
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