Nonperturbative light-front Hamiltonian methods

TL;DR

This paper reviews the current nonperturbative light-front Hamiltonian methods used in quantum field theories, covering techniques, applications, and potential for solving QCD through wave functions.

Contribution

It provides a comprehensive survey of numerical techniques and applications in nonperturbative light-front Hamiltonian approaches, serving as an introduction and reference.

Findings

Survey of key numerical methods like Pauli--Villars regularization and basis light-front quantization.

Discussion of applications to scalar, Yukawa, supersymmetric, QED, and QCD theories.

Highlights the potential for wave-function-based solutions to QCD.

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, $\phi^4$ 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.