Scientists at Mainz University have discovered a method to evaluate highly complex Feynman integrals. What does the world look like at the smallest scales? This is a question that researchers are striving to solve through particle accelerator experiments, such as the Large Hadron Collider at CERN i
Feynman integrals are mathematical tools used to describe the behavior of particles in quantum field theory. These integrals are named after physicist Richard Feynman, who first introduced them in the 1940s. They provide a way to calculate the probability of a particle taking a particular path and have become an essential component in our understanding of the subatomic world.
A key ingredient in these predictions are so called Feynman integrals. Recently, a team of the PRISMA+ Cluster of Excellence at Feynman integrals are mathematical objects which describe this effect, summing in effect all possible ways particles can appear and immediately disappear again.An important property determining the complexity of a Feynman integral is its geometry. Many of the simplest Feynman integrals have the geometry of a sphere or a torus – the mathematical term for a donut shape. Such integrals are nowadays well understood.
In their recent publication, Dr. Sebastian Pögel, Dr. Xing Wang, and Prof. Dr. Stefan Weinzierl present a method that allows them to tackle integrals of Calabi–Yau geometries. In their research, they studied a simple family of Calabi–Yau Feynman integrals, called banana integrals.
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