Applications of Basis Light-Front Quantization to QED

TL;DR

This paper applies basis light-front quantization to QED, enabling non-perturbative calculations of relativistic systems' properties, including scattering processes in strong, time-dependent fields, by solving large sparse Hamiltonian matrices.

Contribution

It introduces a novel approach combining light-front gauge, basis function representation, and ab initio methods to study QED non-perturbatively, connecting to AdS/QCD models.

Findings

Non-perturbative evaluation of non-linear Compton scattering.

Recovery of full covariance in the continuum limit.

Effective modeling of relativistic electron dynamics in strong laser fields.

Abstract

Hamiltonian light-front quantum field theory provides a framework for calculating both static and dynamic properties of strongly interacting relativistic systems. Invariant masses, correlated parton amplitudes and time-dependent scattering amplitudes, possibly with strong external time-dependent fields, represent a few of the important applications. By choosing the light-front gauge and adopting an orthonormal basis function representation, we obtain a large, sparse, Hamiltonian matrix eigenvalue problem for mass eigenstates that we solve by adapting ab initio no-core methods of nuclear many-body theory. In the continuum limit, the infinite matrix limit, we recover full covariance. Guided by the symmetries of light-front quantized theory, we adopt a two-dimensional harmonic oscillator basis for transverse modes that corresponds with eigensolutions of the soft-wall anti-de Sitter/quantum chromodynamics (AdS/QCD) model obtained from light-front holography. We outline our approach and present results for non-linear Compton scattering, evaluated non-perturbatively, where a strong and time-dependent laser field accelerates the electron and produces states of higher invariant mass i.e. final states with photon emission.