Nonperturbative light-front Hamiltonian methods

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, ϕ4 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.

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

Light-front quantization
Nonperturbative Hamiltonian methods
Pauli–Villars regularization
Quantum chromodynamics
effective Hamiltonian: light front
field theory: quantization
quantization: light front
field theory: nonperturbative
field theory: Yukawa
field theory: scalar

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