The trace condition you mentioned, also called anonymous coefficient, is a general expression calculated regardless of triangle graph, Fujikawa or exponential theorem. Nature is related to different representations, and this relationship is provided by the corresponding representation of each vertex currently corresponding. You know all the elementary particles, their corresponding Lie groups and their representations. You can write all triangles, and the sum is really zero after calculation.
In addition, why there is only a triangle diagram or a quadrilateral diagram, or if you continue to go up, there will be an exception. This is related to the dimensions of your theory, which can be determined by Ward's identity combined with the number and dimensional analysis of Lorentz tensor constants in different dimensions. Look at the part about locality and finiteness in this note.
In peskin20.2, the graphs of all three external lines and three fermion internal lines are listed, and the trace conditions are obtained by the abnormal cancellation equation, and then the value of particle overload is obtained. Can this condition ensure that all similar figures are eliminated (of course, but why)? On the other hand, in the sixth chapter of Fujikawa's book Path Integral and Quantum Anomaly, the elimination condition (trace condition) obtained by Jacobian of regular transformation is also the same result. Is there some inevitability for Jacobian condition to correspond to triangle graph?
Accelerators have many applications. Let's see how many financial agents are investing in accelerator projects in the United States.
1 the high energy physics office supports the research of high energy physics, and the collider or the accelerator related to the collider is supported by the office. . Proton or heavy ion accelerators, such as LHC, RHIC and tevatron in America, have energy as high as 100 GeV or even TeV. The BEPCII in China is the same. So is the FCC to be built in the future. High-energy accelerator mainly studies elementary particles, supersymmetric matter, quantum chromodynamics and simulating the basic phenomena of the universe. Different colliders and different energy segments have different applications. For example, within two years, RHIC will be converted into lersic, and the energy will be reduced to detect critical phenomena. It is not easy to transform a high-energy accelerator into a low-energy accelerator. If the energy is low, it is necessary to maintain the same current intensity, and the space charge effect will increase. Space charge effect means that two particles with the same charge will repel each other when put together. This effect can be offset by the self-magnetic field at high energy, and it is very strong when the energy is reduced. This leads to the appearance of cooling devices for the collider, including random cooling or electron cooling, and coherent electron cooling. Among them, electron cooling needs to accelerate the electron accelerator from mA to A to several tens of MeV to interact with ions and reduce the emittance of high-energy ions. These are all related to high energy.
The office of nuclear physics supports the research of nuclear physics or reactors, and its energy is lower than that of the collider. Usually by shooting. For example, CEBAF of JLab. The energy is more than ten GeV. There are many such accelerators to produce nuclides. It is also useful to study the critical reactor of accelerator-controlled nuclear reactor in order to become the safest nuclear reactor in the future.
The Photonic Science Office and the military support the research on the light generated by the accelerator, mainly including synchrotron radiation light source, free electron laser, Compton light source and terahertz. Mainly accelerating electrons, the energy is several MeV THz light source to GeV hard X-ray light source. Many of these light sources are user equipment, which provides a means to observe microscopic and ultrafast processes of materials, biology and chemistry. There are LCLS and NSLSII in the United States, Shanghai light source in China, Shanghai free electron laser, and future northern light sources, such as Compton light source in Tsinghua and terahertz in Peking University. The military is very interested in the application of free electron laser in weapons. In the last two years, the military has lost patience and is no longer interested.
The heavy ion accelerator supported by 4 NIH is used in cancer treatment, and the Bragg peak of heavy ions can be released at different positions according to different energy, so it has a very important application in cancer treatment. Only the cancer tissue was damaged, and the normal tissue was not damaged. China Lanzhou Institute of Heavy Ions already has this device. Accelerators are widely used in medicine, such as X-ray machines and electron flow to beat cancer cells. Many big companies, such as Siemens, make accelerators.
Accelerator testing supported by company or military. The most successful is Tsinghua VIOS container inspection equipment. These energies are very low, all in the order of mega-electron volts.
6 small company accelerator project. Such as radiation sterilization, radiation breeding, radiation pollution discharge and so on. Many seafood in China need an accelerator to take pictures and then sell them. There are many such accelerators in Jiangsu and Zhejiang.
The electron microscope of materials science uses electrons from 1000 to 1000 electron volts for imaging. Several mev are also used for ultrafast electron diffraction or ultrafast imaging.
The simplest accelerator mentioned above, such as cathode ray tube.