Parton Distribution Functions in the Schwinger Model with Tensor Networks

TL;DR

This paper demonstrates the calculation of parton distribution functions in the Schwinger model using tensor network methods, providing a Minkowski-space approach as an alternative to traditional Euclidean Monte Carlo techniques.

Contribution

It introduces a novel application of tensor networks to compute PDFs directly in Minkowski space within the Schwinger model, highlighting an efficient Hamiltonian formalism approach.

Findings

PDFs successfully computed in the Schwinger model

Tensor network methods enable direct Minkowski-space calculations

Potential for extending to more complex theories

Abstract

Parton distribution functions (PDFs) describe universal properties of bound states and allow us to calculate scattering amplitudes in processes with large momentum transfer. Calculating PDFs involves the evaluation of matrix elements with a Wilson line in a light-cone direction. In contrast to Monte Carlo methods in Euclidean spacetime, these matrix elements can be directly calculated in Minkowski-space using the Hamiltonian formalism. The necessary spatial- and time-evolution can be efficiently applied using established tensor network methods. We present PDFs in the Schwinger model calculated with matrix product states.