Basis Light-front Quantization has been developed as a first-principles nonperturbative approach to quantum field theory. In this article we report our recent progress on the applications to the single electron and the positronium system in QED. We f
ocus on the renormalization procedure in this method.
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.
Basis Light-front Quantization has been proposed as a nonperturbative framework for solving quantum field theory. We apply this approach to Quantum Electrodynamics and explicitly solve for the light-front wave function of a physical electron. Based o
n the resulting light-front wave function, we evaluate the electron anomalous magnetic moment. Nonperturbative mass renormalization is performed. Upon extrapolation to the infinite basis limit our numerical results agree with the Schwinger result obtained in perturbation theory to an accuracy of 0.06%.
We introduce a nonperturbative, first-principles approach to time-dependent problems in quantum field theory. In this approach, the time-evolution of quantum field configurations is calculated in real time and at the amplitude level. This method is p
articularly suitable for treating systems interacting with a time-dependent background field. As a test problem, we apply this approach to QED and study electron acceleration and the associated photon emission in a time- and space-dependent electromagnetic background field.
We present a nonperturbative, first-principles numerical approach for time-dependent problems in the framework of quantum field theory. In this approach the time evolution of quantum field systems is treated in real time and at the amplitude level. A
s a test application, we apply this method to QED and study photon emission from an electron in a strong, time-dependent external field. Coherent superposition of electron acceleration and photon emission is observed in the nonperturbative regime.
We investigate charmonium production in the hot medium created by heavy-ion collisions by setting up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD (lQCD) and subsequently implemented into kinetic approach
es. A Boltzmann transport equation is employed to describe the time evolution of the charmonium phase space distribution with the loss and gain term accounting for charmonium dissociation and regeneration (from charm quarks), respectively. The momentum dependence of the charmonium dissociation rate is worked out. The dominant process for in-medium charmonium regeneration is found to be a 3-to-2 process. Its corresponding regeneration rates from different input charm-quark momentum spectra are evaluated. Experimental data on $J/psi$ production at CERN-SPS and BNL-RHIC are compared with our numerical results in terms of both rapidity-dependent inclusive yields and transverse momentum ($p_t$) spectra. Within current uncertainties from (interpreting) lQCD data and from input charm-quark spectra the centrality dependence of $J/psi$ production at SPS and RHIC (for both mid- and forward rapidity) is reasonably well reproduced. The $J/psi$ $p_t$ data are shown to have a discriminating power for in-medium charmonium properties as inferred from different interpretations of lQCD results.
We apply the Basis Light-Front Quantization (BLFQ) approach to the Hamiltonian field theory of Quantum Electrodynamics (QED) in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in light-front
gauge. Based on the resulting non-perturbative ground state light-front amplitude we evaluate the electron anomalous magnetic moment. The numerical results from extrapolating to the infinite basis limit reproduce the perturbative Schwinger result with relative deviation less than 0.6%. We report significant improvements over previous works including the development of analytic methods for evaluating the vertex matrix elements of QED.
We set up a framework in which in-medium charmonium properties are constrained by thermal lattice QCD and subsequently implemented into a thermal rate equation enabling the comparison with experimental data in heavy-ion collisions. Specifically, we e
valuate phenomenological consequences for charmonium production originating from two different scenarios in which either the free or the internal energy are identified with the in-medium 2-body potential between charm and anti-charm quarks. These two scenarios represent $J/psi$ melting temperatures of approximately 1.25,$T_c$ (weak binding) and 2,$T_c$ (strong binding), respectively. Within current uncertainties in dissociation rates and charm-quark momentum spectra, both scenarios can reproduce the centrality dependence of inclusive $J/psi$ yields in nuclear collisions at SPS and RHIC reasonably well. However, the strong-binding scenario associated the the internal energy as the potential tends to better reproduce current data on transverse momentum spectra at both SPS and RHIC.
