” During the interaction of subatomic particles something unique happens: Any variety of extra particles can briefly pop in and out of presence”, Prof. Dr. Stefan Weinzierl discusses. “When making theoretical forecasts of such interactions, the more of the these additional particles are taken into consideration, the more exact the computation will be to the real result.”

Feynman integrals are mathematical objects which describe this result, summing in impact all possible ways particles can appear and immediately disappear again.

Calabi– Yau Geometries: An Interplay of Mathematics and Physics

A crucial property figuring out the complexity of a Feynman important is its geometry. A lot of the most basic Feynman integrals have the geometry of a sphere or a torus– the mathematical term for a donut shape. Such integrals are nowadays well understood.

However, there exist entire households of geometries, so-called Calabi– Yau geometries, which are generalizations of the donut case to greater measurements. These have actually proven to be an abundant field of research study in pure Mathematics, and have actually discovered comprehensive application in string theory in the last decades.

In current years it was found that also many Feynman integrals are related to Calabi– Yau geometries. Due to the intricacy of the geometry, the effective assessment of such integrals has remained an obstacle.

In their current publication, Dr. Sebastian Pögel, Dr. Xing Wang, and Prof. Dr. Stefan Weinzierl provide a method that permits them to deal with integrals of Calabi– Yau geometries. In their research study, they studied a simple household of Calabi– Yau Feynman integrals, called banana integrals.

Therefore they could find for the first time a so-called “epsilon-factorized kind” for these integrals. “It opens the door to a broad range of hitherto unreachable Feynman integrals,” says Dr. Xing Wang.

According to Dr. Sebastian Pögel, it is a nice example of how pure mathematics feeds into phenomenological forecasts for high-energy experiments. “We are grateful to our associates in mathematics, and in specific to the group of Prof. Dr. Duco van Straten, as we develop on their work and now were able to attain this interesting result”, sums up Prof. Dr. Stefan Weinzierl.

Recommendation: “Taming Calabi-Yau Feynman Integrals: The Four-Loop Equal-Mass Banana Integral” by Sebastian Pögel, Xing Wang and Stefan Weinzierl, 8 March 2023, Physical Review Letters.DOI: 10.1103/ PhysRevLett.130.101601.

Feynman integrals are mathematical tools used to explain the habits of particles in quantum field theory. These integrals are named after physicist Richard Feynman, who initially introduced them in the 1940s. An essential residential or commercial property figuring out the intricacy of a Feynman important is its geometry. Many of the most basic Feynman integrals have the geometry of a torus or a sphere– the mathematical term for a donut shape. “It opens the door to a broad variety of hitherto inaccessible Feynman integrals,” states Dr. Xing Wang.

Feynman integrals are mathematical tools utilized to describe the habits of particles in quantum field theory. These integrals are called after physicist Richard Feynman, who initially presented them in the 1940s. They offer a way to calculate the possibility of a particle taking a particular course and have ended up being an important element in our understanding of the subatomic world.

Researchers at Mainz University have found a technique to assess highly intricate Feynman integrals.

What does the world look like at the tiniest scales? This is a question that scientists are striving to fix through particle accelerator experiments, such as the Large Hadron Collider at CERN in Switzerland. In order to assess the results of these experiments, theoretical physicists need significantly accurate forecasts based on the basic design, our existing understanding of the interactions between fundamental particles.

A key ingredient in these predictions are so called Feynman integrals. Recently, a group of the PRISMA+ Cluster of Excellence at Mainz University, including Dr. Sebastian Pögel, Dr. Xing Wang and Prof. Dr. Stefan Weinzierl established a method to effectively calculate a brand-new class of these Feynman integrals, associated to Calabi– Yau geometries.

This research study is now published in the prominent journal Physical Review Letters and opens the path to high-precision theoretical forecasts of particle interactions, and to better understand the sophisticated mathematical structure underpinning the world of particle physics.