The bi-adjoint scalar ℓ-loop planar integrand recursion and graded inverse variables
Abstract
A bstract Previously in [1], we constructed the ℓ -loop planar integrands using loop components and loop kernels by some recursion rules. In this paper, we propose a new formalism to express the loop kernel recursion. We define “graded inverse variables” to make the loop kernel recursion more elegant. And the graph factor, including the symmetry factor, can be figured out from each monomial of some variables. This new formalism makes the previous ℓ -loop integrand recursion clearer.
Fields of Study & Subjects
Quantum chaos and dynamical systems
Numerical methods for differential equations
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Journal of High Energy Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 2026
- Issue
- 3
- Publication date
- 18 March 2026
- Language
- EN