Hamiltonian light-front field theory in a basis function approach

TL;DR

This paper develops a basis function approach to Hamiltonian light-front quantum field theory, enabling non-perturbative calculations of bound states and parton amplitudes with potential applications to QED and gauge theories.

Contribution

It introduces a basis function method using a harmonic oscillator basis for light-front gauge theories, connecting with AdS/QCD models and adapting nuclear many-body techniques.

Findings

Demonstrated the approach with non-interacting systems in a cavity.

Outlined steps towards solving QED in this framework.

Discussed computational challenges in basis space calculations.

Abstract

Hamiltonian light-front quantum field theory constitutes a framework for the non-perturbative solution of invariant masses and correlated parton amplitudes of self-bound systems. By choosing the light-front gauge and adopting a basis function representation, we obtain a large, sparse, Hamiltonian matrix for mass eigenstates of gauge theories that is solvable by adapting the ab initio no-core methods of nuclear many-body theory. Full covariance is recovered in the continuum limit, the infinite matrix limit. There is considerable freedom in the choice of the orthonormal and complete set of basis functions with convenience and convergence rates providing key considerations. Here, we use a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall AdS/QCD model obtained from light-front holography. We outline our approach and present illustrative features of some non-interacting systems in a cavity. We illustrate the first steps towards solving QED by obtaining the mass eigenstates of an electron in a cavity in small basis spaces and discuss the computational challenges.