Mathematics of Scattering Amplitudes

Introduction

MaScAmp proposes a new paradigm for fundamental interactions in physics in the form of a unified mathematical approach to scattering amplitudes. The project brings together a multidisciplinary team with expertise in pure mathematics and theoretical physics who will develop a set of novel and efficient algorithmic methods with applications in mathematics, particle physics, and gravity.

Importance of Scattering Amplitudes

Discoveries in many areas of fundamental physics depend upon a detailed understanding of the scattering of particles. Modern experiments, such as particle colliders and gravitational-wave detectors, demand high-precision theoretical computations to make new discoveries.

These computations are deduced from physical models by a highly labor-intensive process relying on the calculation of scattering amplitudes, which assign probabilities to particle interactions. Despite a tremendous worldwide effort over many decades, the methods used to compute increasingly complex scattering amplitudes remain disparate and fragmented.

Need for a New Approach

The work of the PIs in distinct domains suggests unexpected symmetries and universal rules obeyed by scattering amplitudes in different-looking areas of physics. This calls for a radically new way of studying scattering amplitudes.

Objectives of MaScAmp

MaScAmp will create a unified framework for the calculation of general scattering amplitudes by building upon the latest research in mathematics, notably in algebraic geometry and number theory.

As a result, MaScAmp will:

1. Overcome longstanding computational bottlenecks.
2. Push the boundaries of numerous areas of theoretical physics, such as quantum field theory, gravity, and string theory.
3. Inspire new mathematical research.

Implementation and Impact

A widely applicable computer software implementation will enable physicists to make previously inaccessible predictions for present and future experiments.

A project of MaScAmp’s scope and ambition is only achievable by combining the unique expertise of the PIs in complementary areas of mathematics and physics.