Hamiltonian Light-Front Field Theory: Recent Progress and Tantalizing Prospects

TL;DR

This paper reviews recent advances in Hamiltonian Light Front Field Theory, highlighting computational methods that enable non-perturbative analysis of fundamental quantum field theories like QED and QCD.

Contribution

It introduces basis function approaches that preserve symmetries and discusses large-scale computational solutions for eigenvalue problems in quantum field theory.

Findings

Development of basis function methods preserving symmetries.

Solution of large sparse matrix eigenvalue problems with up to 20 billion basis states.

Application to the electron's anomalous magnetic moment.

Abstract

Fundamental theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are required for physics to span from one scale to the next. I outline recent theoretical and computational progress to build these bridges and provide illustrative results for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries. Regulating the theory with an external field that can be removed to obtain the continuum limit offers additional possibilities as seen in an application to the anomalous magnetic moment of the electron. Recent progress capitalizes on algorithm and computer developments for setting up and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 20 billion basis states are now solved on leadership-class computers for their low-lying eigenstates and eigenfunctions.