Hamiltonian light-front field theory in a basis function approach

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.Comment: 35 pages, 15 figures, Revised to correct Fig. 7 and add new Fig. 15 with spectral results for electron in a transverse cavit

Nonperturbative light-front Hamiltonian methods

“…The Hamiltonian eigenvalue problem is then transformed into a coupled set of integral equations for these wave functions, with the invariant mass of the eigenstate as the eigenvalue. As such, the approach lends itself well to numerical solution by discretization [12,2] and by basis-function expansions [13,14].…”

“…For example, a basis-function expansion [14] for the wave functions is truncated, to establish a finite matrix representation of the original integral equations. The truncation provides a regularization which is removed in the limit of infinite basis size.…”

QCD on the Light-Front

“…Thus the light-front holographic approach provides an analytic frame-independent first approximation to the color-confining dynamics, spectroscopy, and excitation spectra of the relativistic light-quark bound states of QCD. It is systematically improvable in full QCD using the basis light-front quantization (BLFQ) method [31] and other methods.…”

“…Consequently, alternative methods and approximations are necessary to better understand the nature of relativistic bound-states in the strongcoupling regime. One of the most promising methods for solving nonperturbative (3+1) QCD is the "Basis Light-Front Quantization" (BFLQ) method [31]. In the BLFQ method one constructs a complete orthonormal basis of eigenstates based on the eigensolutions of the effective light-front Schrödinger equation derived from light-front holography, in the spirit of the nuclear shell model.…”

Charmonium spectrum and diffractive production in a light-front Hamiltonian approach

“…Recently, a new description of heavy quarkonium system has emerged [13,14] within the basis lightfront quantization (BLFQ) approach [15][16][17]. The mass spectra for charmonium and bottomonium are obtained by diagonalizing a Hamiltonian within the BLFQ framework, with the one-gluon exchange interaction and a confining potential inspired by lightfront holography [13].…”