Unitary perturbation theory on the light cone using adiabatic switching

Abstract

Light-cone perturbation theory is a powerful tool for calculating high-energy scattering amplitudes, particularly for quantum particles such as electrons, photons, or protons scattering off heavy nuclei, a process analogous to potential scattering. Central to these computations are the light-cone wave functions of incoming and outgoing particles, representing the projection of dressed initial and final states onto partonic Fock states. The dressed states are obtained by applying an evolution operator in the Dirac picture to bare partonic states, which may be interpreted physically as a time evolution from preparation to interaction. In standard approaches, a non-unitary operator is used, and proper normalization is imposed a posteriori. Here, we systematically develop perturbation theory from a perturbatively unitary evolution operator, using adiabatic switching to regularize the infinite-time limits. This provides a theoretically coherent framework for organizing calculations, reproducing known results entirely diagrammatically without enforcing unitarity by hand. We illustrate the method with a simple quantum mechanical model, enabling calculations to arbitrary perturbative orders, and then evaluate wave functions in field theories quantized on the light cone, focusing on a massive scalar theory with cubic interaction at one-loop accuracy.