Geometric interpretation of generalized Zakharov–Mikhailov amplitudes

Derive a more elegant geometric interpretation of the scattering amplitudes of generalized Zakharov–Mikhailov theory, whose interaction term computes an oriented volume in momentum space.

Background

The generalized Zakharov–Mikhailov interaction is constructed from spacetime Levi–Civita tensors and derivatives, so its vertex is naturally interpreted as an oriented momentum-space volume. The paper establishes soft behavior, recursion, and nonzero amplitudes in higher dimensions but does not identify a deeper geometric formulation of those amplitudes.

A geometric interpretation could explain the special determinant structures, color–kinematics duality, and amplitude properties of the higher-dimensional generalization.