Accuracy estimate for a relativistic Hamiltonian approach to bound-state problems in theories with asymptotic freedom

TL;DR

This paper evaluates the accuracy of a relativistic Hamiltonian approach for bound-state problems in asymptotically free theories, demonstrating it achieves comparable precision to established methods in a solvable matrix model.

Contribution

It introduces and tests a relativistic weak-coupling expansion method for bound-state problems, showing it attains high accuracy in a simple, exactly solvable model.

Findings

Method matches benchmark accuracy of a few percent

Achieves sixth-order precision in the expansion

Validates the approach for theories with asymptotic freedom

Abstract

Accuracy of a relativistic weak-coupling expansion procedure for solving the Hamiltonian bound-state eigenvalue problem in theories with asymptotic freedom is measured using a well-known matrix model. The model is exactly soluble and simple enough to study the method up to sixth order in the expansion. The procedure is found in this case to match the precision of the best available benchmark method of the altered Wegner flow equation, reaching the accuracy of a few percent.