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Lattice Boltzmann method for quantum field theory

It is shown that a (1 + 1)-dimensional lattice Boltzmann discretization of the Klein–Gordon and Dirac equations complies with equal-time-commutation-relations. As a result, the lattice Boltzmann discretization leads to a consistent lattice formulation of the quantum field theory in 1 + 1 dimensions. The present kinetic approach may offer a significant simplification over previous Hamiltonian formulations, because the quantum fields move along simple classical trajectories defined by the causal lightcones. This should facilitate both analytical manipulations and symbolic computer implementations of the method.