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

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.

Ab Initio Hamiltonian Approach to Light-Front Quantum Field Theory

“…I outline here a Hamiltonian basis function approach following Refs. (4)(5)(6)(7)(8)(9)(10) that exploits recent advances in solving the non-relativistic strongly interacting nuclear many-body problem (11; 12). There are many issues faced in common -i.e.…”