Let particle physicists calculate algorithms greater than 2

Thomas Gelman remembers One day 20 years ago, a large number of mathematical expressions poured down from his computer screen.

He tried to calculate the probability that three beams of elementary particles would be ejected from the collision of two particles. This is a basic calculation that physicists often do to check whether their theory matches the experimental results.However, more accurate predictions require longer calculation times, and Gehrman Is getting bigger.

Using the standard method devised by Richard Feynman more than 70 years ago, he sketched the ways in which hundreds of possible colliding particles could deform and interact before emitting three jets. Adding the individual probabilities of these events will give the overall probability of the three-jet outcome.

But Gehrman needs software to calculate the 35,000 terms in his probability formula. As for the calculation? At that time “you raise the flag of surrender and talk to your colleagues,” he said.

Fortunately for him, one of his colleagues happened to know that an unpublished technique could significantly shorten this formula. Using the new method, Gehrman saw thousands of terms merge together and disappear. In the remaining 19 computable expressions, he glimpsed the future of particle physics.

Today, a simplified procedure called the Laporta algorithm has become the main tool for generating accurate predictions about particle behavior. “It’s everywhere,” said Matt von Hipper, A particle physicist at the University of Copenhagen.

Although the algorithm has spread all over the world, its inventor Stefano Laporta is still unknown. He rarely attended meetings and did not direct large numbers of researchers. “Many people thought he was dead,” Von Hipper said. On the contrary, Laporta lives in Bologna, Italy, and he is gradually completing the calculations he cares most about. This calculation has given birth to his pioneering method: a more precise assessment of how electrons move in a magnetic field.

One, two, more

The challenge of predicting the subatomic world is that an infinite number of things can happen. Even an electron that only cares about its own business can spontaneously emit and then recover a photon. And the photon can summon additional fleeting particles during this period. All these busy people have slightly interfered with electronic affairs.

exist Feynman’s calculation scheme, The particles that existed before and after the interaction become lines that enter and exit the cartoon sketch, while those that appear briefly and then disappear form a loop in the middle. Feynman figured out how to convert these graphs into mathematical expressions, where the loop becomes a summation function called Feynman integral. The more likely events are those with fewer cycles. But physicists must consider rarer and more complex possibilities when making precise predictions that can be tested in experiments; only in this way can they discover subtle signs of new elementary particles that may have been missed in their calculations. As the number of cycles increases, the points will increase exponentially.