Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for their computation. We review some of the most recent advances in our understanding of the analytic structure of multiloop Feynman integrals in dimensional regularisation. In particular, we give an overview of modern approaches to computing Feynman integrals using differential equations, and we discuss some of the properties of the functions that appear in the solutions. We then review how dimensional regularisation has a natural mathematical interpretation in terms of the theory of twisted cohomology groups, and how many of the well-known ideas about Feynman integrals arise naturally in this context.
|Number of pages||56|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Early online date||4 Nov 2022|
|Publication status||Published - 30 Nov 2022|
- Feynman integrals
- iterated integrals
- perturbative quantum field theory