Chinese name: Higgs mechanism mbth: Higgs Mechani *** field: introduction to quantum mechanics, history, U( 1) Higgs mechanism, overview, spontaneous symmetry breaking, SU(2)×U( 1) Higgs mechanism, see standard model, introduction in standard model, Higgs mechanism (in standard model). The Higgs mechanism can explain this problem. The Higgs mechanism uses spontaneous symmetry breaking to give the gauge boson mass. When observing gauge theory, this is the simplest mechanism among all possible mechanisms to give gauge boson mass. According to the Higgs mechanism, Higgs field is all over the universe, and some elementary particles gain mass because of their interaction with Higgs field. To explain more carefully, in gauge field theory, in order to satisfy the localized gauge invariance, the mass of gauge boson must be set to zero. Because the vacuum expectation of the Higgs field is not equal to zero, which leads to spontaneous symmetry breaking, the gauge boson will gain mass and produce a zero-mass boson, which is called the Goelz-pass boson. The Higgs boson is a particle accompanying the Higgs field and is the vibration of the Higgs field. By choosing a suitable specification, the GoldSi Tong boson will be cancelled, leaving only the Higgs boson with mass and the vector field with mass specification. Fermions also gain mass by interacting with Higgs field, but the way they gain mass is different from that of W boson and Z boson. In gauge field theory, in order to satisfy the localized gauge invariance, the mass of fermions must be set to zero. Fermions can also gain mass due to spontaneous symmetry breaking through Yukawa coupling. The mathematical expression of this term requires readers to know something about quantum field theory. All equations obey Einstein's contract. According to the convention of particle physics, the unit of physical quantity adopts CGS unit system, and the value of light speed and reduced Planck constant is set to. From 65438 to 0964, three groups of research groups independently studied the Higgs mechanism almost at the same time. Among them, one group was Francois Englert and Robert bulut, the other group was peter higgs, and the third group was Gerard Gulani, Carl Hagen and Tom Kibor. Gulani published further papers in 1965 and Higgs in 1966 to discuss the properties of this model. These papers show that if gauge invariance's theory and the concept of spontaneous symmetry breaking are linked in some special way, the gauge boson will inevitably gain mass. 1967, steven weinberg and abdul sallam used Higgs mechanism to break the weak symmetry of electricity for the first time, and expressed how Higgs mechanism was incorporated into Sheldon Glashow's weak theory, which later became a part of the standard model. The three papers published by six physicists are recognized as milestone papers in the literature celebrating the 50th anniversary of Physical Review Letters. In 20 10, they won the sakurai prize for theoretical particle physics. Engler and Higgs won the Nobel Prize in Physics in 20 13 because "the theory of subatomic particle mass generation mechanism has promoted human understanding in this respect, and it has recently been confirmed by the ring instrument of the Large Hadron Collider under the European Organization for Nuclear Research and the elementary particles discovered by the compact muon coil detector". Overview of U( 1) Higgs mechanism U( 1) Higgs mechanism is a very simple mechanism to endow quality, which is suitable for U( 1) gauge field theory. The gauge transformation of U( 1) gauge field theory involves phase transition: where is the complex Higgs field and phase? This transformation is a U( 1) transformation, which involves Abelian groups, so it is an Abelian Higgs mechanism. Suppose that the Higgs field of the whole universe is a complex scalar field composed of two real functions: where is the four-dimensional coordinate. For this scalar field with zero spin, zero mass and zero potential energy, Klein-King Lagrangian quantity temporarily assumes that the mass term does not exist, so the form of Klein-King Lagrangian quantity becomes one of them, which is a four-dimensional derivative operand. This is a wave equation, which can be used to describe the physical behavior of electromagnetic waves at potential. From this equation, it seems that no trace of mass can be found, but if the potential energy Taylor expands to: Note that, is a constant. In this expansion, we can vaguely observe the form of high-quality projects. The vacuum of spontaneous symmetry breaking quantum mechanics is different from that of general cognition. In quantum mechanics, vacuum is not an empty space, and virtual particles will be randomly generated or annihilated at any position in the space, thus causing mysterious quantum effects. After considering these quantum effects, the lowest energy state in space is the lowest energy state of all energy states, also known as ground state or "vacuum state". The space of the lowest energy state is the vacuum of quantum mechanics. When a symmetric group transformation is envisaged, only the lowest energy state can be transformed into itself, that is, the lowest energy state is "invariant" to this transformation, that is, the lowest energy state has this symmetry. Although the Lagrangian quantity of a physical system is invariant to a symmetric group transformation, it does not mean that its lowest energy state is invariant to this symmetric group transformation. If the Lagrangian quantity and the lowest energy state have the same invariance, it is said that the physical system has "obvious symmetry" for this transformation; If only the Lagrangian quantity remains unchanged and the lowest energy state remains unchanged, it is said that the symmetry of this physical system is spontaneously broken, or the symmetry of this physical system is hidden. This phenomenon is called "spontaneous symmetry breaking". SU(2)×U( 1) Higgs mechanism in the standard model, SU(2)×U( 1) Higgs mechanism is the simplest mechanism to give mass, which is suitable for the SU(2)×U( 1) gauge field theory of weak-current interaction. The standard model adopting this mechanism is called the minimum standard model. In this model, Higgs field is a complex-valued double field: they are all real functions. This Higgs field consists of two complex scalar fields or four real scalar fields, two of which are charged and two are neutral. In this model, there are four zero-mass gauge bosons, which are transverse fields and have two degrees of freedom like photons. In a word, a * * * has twelve degrees of freedom. After spontaneous symmetry breaking, a * * * has three gauge bosons to gain mass, and at the same time, each gauge boson adds a longitudinal field. The total * * * has nine degrees of freedom, and a zero-mass gauge boson has two degrees of freedom, and the remaining degrees of freedom are the Higgs boson with mass. The three bosons with mass specifications are W, W and Z bosons. The zero-mass gauge boson is a photon. Standard Model In the standard model, if the temperature is high enough, the weak symmetry of the physical system will not be broken, and all elementary particles have no mass. When the temperature drops below the critical temperature, the Higgs field will become unstable and jump to the lowest energy state, that is, the vacuum of quantum mechanics, so the continuous symmetry of the whole physical system will spontaneously break, and the W boson, Z boson and Fermion will also gain mass. Explore the time axis of Higgs boson with reference to the experimental exploration of Higgs boson