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, ${\varphi }^4$ 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.

67 pages, 14 figures; review to appear in Progress in Particle and Nuclear Physics

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Cited by in corpus (6)

• The non-triviality of the vacuum in light-front quantization: An elementary treatment
• Trends and Progress in Nuclear and Hadron Physics: a straight or winding road
• Computation of effective front form Hamiltonians for massive Abelian gauge theory
• Coulomb- quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex
• Symmetry breaking in light-front ${\varphi }^4$ theory
• Convergence of the light-front coupled-cluster method in quenched scalar Yukawa theory