Fourier Calculus from Intersection Theory

TL;DR

This paper applies intersection theory to Fourier integrals, enabling exact evaluations of master integrals with respect to spacetime dimension D, with applications in gravitational and scattering processes.

Contribution

It introduces a novel approach combining intersection theory and differential equations for Fourier integral evaluation, providing exact D-dependent results.

Findings

Exact D-dependent master integrals computed.

Applications demonstrated in gravitational bremsstrahlung.

Enhanced computational techniques for Fourier integrals.

Abstract

Building on recent advances in studying the co-homological properties of Feynman integrals, we apply intersection theory to the computation of Fourier integrals. We discuss applications pertinent to gravitational bremsstrahlung and deep inelastic scattering in the saturation regime. After identifying the bases of master integrals, the latter are evaluated by means of the differential equation method. Finally, new results with exact dependence on the spacetime dimension D are presented.