Nonperturbative light-front Hamiltonian methods

Abstract

We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

Baryons as relativistic three-quark bound states

“…[161][162][163][164][165][166] for reviews) take a different route in this respect. Motivated by the triviality of the vacuum in light-cone quantization, the goal is to calculate the eigenstates of the gauge-fixed QCD Hamiltonian directly by solving large-scale eigenvalue problems.…”

“…In that way the light-cone wave functions move into the center of interest: once calculated, in principle they can be used to compute hadronic matrix elements of currents as overlaps of light-cone wave functions. Although corresponding methods have been successfully employed to a variety of quantum field theories including QED, the systematic application of this machinery to QCD is quite nontrivial and awaits to be further explored [166].…”

Coulomb-quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex

“…In a departure from the usual approach in [8] the coupling constant is sought to be related with the energy eigenvalues in the defining expression (22). The energy-dependent coupling constant, and the freedom in choosing normalization length scale, let us say, η, in (22) allow the possibility of exploring new physics. As an illustration, for N = 0 setting η equal to the classical electron charge radius e 2 mc 2 and oscillator frequency ω = mc 2 h we find 2D hydrogen atom coupling constant…”

Trends and Progress in Nuclear and Hadron Physics: A Straight or Winding Road

“…[11] for a review), nuclear physics (see Ref. [12] for a review) and it has also been introduced into light-front field theory with promising results [13].…”