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.
Bibliographical noteFunding Information:
Some of the reported work was done by the author, in collaboration with several researchers, including S.J. Brodsky, S.S. Chabysheva, G. McCartor, S.S. Pinsky, and U. Trittmann. This work was supported in part by the US Department of Energy through Contract No. DE-FG02-98ER41087 and in part by the Minnesota Supercomputing Institute of the University of Minnesota with grants of computing resources.
© 2016 Elsevier B.V.
- Light-front quantization
- Nonperturbative Hamiltonian methods
- Pauli-Villars regularization
- Quantum chromodynamics