Mathematics: “Particle collisions are somehow linked to mathematical ‘motives.’”

Posted by News on November 22nd, 2016

From math and computer science writer Kevin Hartnett at Quanta:

Over the last decade physicists and mathematicians have been exploring a surprising correspondence that has the potential to breathe new life into the venerable Feynman diagram and generate far-reaching insights in both fields. It has to do with the strange fact that the values calculated from Feynman diagrams seem to exactly match some of the most important numbers that crop up in a branch of mathematics known as algebraic geometry. These values are called “periods of motives,” and there’s no obvious reason why the same numbers should appear in both settings. Indeed, it’s as strange as it would be if every time you measured a cup of rice, you observed that the number of grains was prime.

“There is a connection from nature to algebraic geometry and periods, and with hindsight, it’s not a coincidence,” said Dirk Kreimer, a physicist at Humboldt University in Berlin.

Now mathematicians and physicists are working together to unravel the coincidence. For mathematicians, physics has called to their attention a special class of numbers that they’d like to understand: Is there a hidden structure to these periods that occur in physics? What special properties might this class of numbers have? For physicists, the reward of that kind of mathematical understanding would be a new degree of foresight when it comes to anticipating how events will play out in the messy quantum world. More.