Imagine trying to organize a library with a million books, but instead of sorting by title or checkout date, you had to read every single book first to know where it belongs. That was the challenge physicists faced with something called Feynman integrals — until now.
Scientists at Johannes Gutenberg University Mainz in Germany have developed a new method that makes this organizing work almost 1,000 times faster. The team, led by Professor Stefan Weinzierl, published their findings in two leading physics journals this year.
Feynman integrals are mathematical equations that scientists use to make predictions about tiny particles — the kind of tiny particles studied at the Large Hadron Collider in Switzerland, the world's most powerful particle accelerator. Some processes they want to study need up to one million of these integrals calculated, which takes enormous amounts of computer time.
Weinzierl explains the breakthrough using a library analogy. "You could sort books by purchase date, but it's much more useful to sort by content: poetry on one shelf, thrillers on another," he said. "To do that, you have to look inside each book. We do the same for Feynman integrals: We look 'inside,' specifically at their geometric structure, rather than relying on superficial labels."
The team created a two-step algorithm (a step-by-step set of instructions for computers). First, they sort integrals by their hidden geometric shapes instead of arbitrary labels. Second, they clean up the calculations by removing unnecessary complexity.
The practical result? Researchers can now tackle calculations that were previously too time-consuming to attempt. "With the new method, we can now make precision predictions for many more processes that were not feasible before," Weinzierl said.
The method works automatically — computer programs can apply it without humans having to guide each step. This means more scientists around the world can use it for their own research.
"We are looking forward to using our new method for ever better predictions," Weinzierl said. "And also to seeing what our colleagues around the world achieve with it."
The research was part of the PRISMA++ Cluster of Excellence at JGU and involved scientists Iris Bree and colleagues, published in Physical Review Letters and Physical Review D.