Quantum mechanics

Constructive

Process (computing)

Engineering

Aerospace engineering

Pure mathematics

Mathematical physics

Quantum field theory

Scattering amplitude

Scattering

Operating system

Canonical form

Computer science

Feynman integral

Physics

Mathematics

Politics

Political science

Feynman diagram

Quantum

Representation (politics)

Intersection (aeronautics)

Algebra over a field

Path integral formulation

Journal of High Energy Physics

A bstract The method of canonical differential equations is an important tool in the calculation of Feynman integrals in quantum field theories. It has been realized that the canonical bases are closely related to d -dimensional d log-form integrands. In this work, we explore the generalized loop-by-loop Baikov representation, and clarify its relation and difference with Feynman integrals using the language of intersection theory. We then utilize the generalized Baikov representation to construct d -dimensional d log-form integrands, and discuss how to convert them to Feynman integrals. We describe the technical details of our method, in particular how to deal with the difficulties encountered in the construction procedure. Our method provides a constructive approach to the problem of finding canonical bases of Feynman integrals, and we demonstrate its applicability to complicated scattering amplitudes involving multiple physical scales.

Baikov representations, intersection theory, and canonical Feynman integrals