Figure 2 represents the complete set of BCFW diagrams required to calculate the same process. The amplitude is obtained by adding up a total of 220 diagrams.īecause the number of Feynman diagrams needed to calculate an amplitude can climb into the thousands, increasingly clever tricks have been developed to bypass their direct computation. Each Feynman diagram pictorially represents a specific way in which this process can happen, and is associated with a complicated mathematical expression. This process will occur several hundred times a second at the LHC. The many graphs depicted in Figure 1 represent a small sample of the Feynman diagrams necessary to compute the amplitude for producing four outgoing gluons from the collision of two incoming ones. Feynman diagrams provide a way of calculating scattering amplitudes in a manner that is consistent with quantum mechanics and special relativity and more recently they have been used for increasingly complex calculations related to the physics being probed at high-energy particle accelerators, such as the Large Hadron Collider (LHC). Their broad utility was due initially in large part to the seminal work of Freeman Dyson, Professor Emeritus in the School of Natural Sciences. Physicists have used Feynman diagrams as a tool for calculating scattering amplitudes that describe particle interactions for more than six decades.
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