Crystalline lattice

Lattice QCD

In physics, lattice quantum chromodynamics (lattice QCD) is a theory of quarks and gluons formulated on a space-time lattice. That is, it is a lattice model of quantum chromodynamics, a special case of a lattice gauge theory or lattice field theory. At the moment, this is the most well established non - perturbative approach to solving the theory of Quantum Chromodynamics. Analytic or perturbative solutions in QCD are hard or impossible due to the highly nonlinear nature of the strong force. The formulation of QCD on a discrete rather than continuous space-time naturally introduces a momentum cut off at the order 1/a, which regularizes the theory. As a result lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides the framework for investigation of non-perturbative phenomena such as confinement and quark-gluon plasma formation, which are intractable by means of analytic field theories.

In lattice QCD spacetime is represented not as continuous but as a crystalline lattice, vertices connected by lines. Quarks may reside only on vertices and gluons can only travel along lines. While this is understood to be a fiction, the hope is that as the spacing between vertices is reduced to zero, or to the Planck length, the theory will yield meaningful results.

This technique is only applicable in the domain of low density and high temperature; at higher densities, the region alas of greatest interest, the fermion sign problem renders the results useless. Lattice QCD predicts that confined quarks will become released to quark-gluon plasma around energies of 170 MeV. Lattice QCD's limitation to low density does not allow investigation of the color flavor locked states (CFL) at higher densities.

Lattice QCD has already made contact with experiments at various fields with good results. A particular important tool of the theory showing the confinement of the underlying fields is the Wilson loop variable, described in a separate article.


  • Creutz, Michael "Quarks, Gluons and Lattices" (Cambridge, 1983)
  • Wilson, K.G., and Kogut, J., "Lattice Gauge Theory ...", Rev. Mod. Phys. 55 , 775 (1983)
  • Degrand and De Tar "Lattice Methods for Quantum Chromodynamics" (World Scientific, 2006)
  • Montvay and Münster "Quantum Fields on a Lattice" (Cambridge 1997)

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