- Lattice field theory
In
physics , lattice field theory is the study of lattice models ofquantum field theory , that is, of field theory on a spacetime that has been discretized onto a lattice. Although most lattice field theories are notexactly solvable , they are of tremendous appeal because they can be studied by simulation on a computer. One hopes that, by performing simulations on larger and larger lattices, while making the lattice spacing smaller and smaller, one will be able to recover the behaviour of the continuum theory.Just as in all lattice models, numerical simulation gives access to field configurations that are not accessible to
perturbation theory , such assoliton s. Likewise, non-trivialvacuum state s can be discovered and probed.The method is particularly appealing for the quantization of a
gauge theory . Most quantization methods keepPoincare invariance manifest but sacrifice manifestgauge symmetry by requiringgauge fixing . Only afterrenormalization cangauge invariance be recovered. Lattice field theory differs from these in that it keeps manifest gauge invariance, but sacrifices manifest Poincaré invariance— recovering it only afterrenormalization . The articles onlattice gauge theory andlattice QCD explore these issues in greater detail.References and external links
* M. Creutz, "Quarks, gluons and lattices"
* I. Montvay and G. Münster, "Quantum Fields on a Lattice"
* J. Smit, "Introduction to Quantum Fields on a Lattice"
* [http://www.fermiqcd.net FermiQCD] A standard library of algorithms for lattice QCD
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