Chuck Darwin‘#Resurgence' Could Save Particle Physics From Infinities
To spot #nonperturbative pieces, you need to know a frightening number of #perturbative #terms. In his recent research, for instance, Serone picked quantum field theories with mathematical backdoors that let him generate thousands of terms.
But for the strong force, calculating just eight or nine is currently out of the question.
Even pioneers of the method don’t mince their words about when they expect to see it produce a real number like the mass of the proton (a mathematical feat worth a million-dollar prize).
“It’s extremely difficult,” Ünsal said, sighing. “I don’t see an immediate way.”
“What Écalle was saying is that the answer is rigorously there in principle. But to actually get the answer is really, really hard,” Bender said. “My advice would be, don’t stand on one foot while you’re waiting.”
https://www.quantamagazine.org/alien-calculus-could-save-particle-physics-from-infinities-20230406/
‘Alien Calculus’ Could Save Particle Physics From Infinities | Quanta Magazine
In the math of particle physics, every calculation should result in infinity. Physicists get around this by just ignoring certain parts of the equations — an approach that provides approximate answers. But by using the techniques known as “resurgence,” researchers hope to end the infinities and end up with perfectly precise predictions.