Lattice Gauge Theory - Measurements and Calculations

Measurements and Calculations

Quantities such as particle masses are stochastically calculated using techniques such as the Monte Carlo method. Gauge field configurations are generated with probabilities proportional to, where is the lattice action and is related to the lattice spacing . The quantity of interest is calculated for each configuration, and averaged. Calculations are often repeated at different lattice spacings so that the result can be extrapolated to the continuum, .

Such calculations are often extremely computationally intensive, and can require the use of the largest available supercomputers. To reduce the computational burden, the so-called quenched approximation can be used, in which the fermionic fields are treated as non-dynamic "frozen" variables. While this was common in early lattice QCD calculations, "dynamical" fermions are now standard. These simulations typically utilize algorithms based upon molecular dynamics or microcanonical ensemble algorithms.

The results of lattice QCD computations show e.g. that in a meson not only the particles (quarks and antiquarks), but also the "fluxtubes" of the gluon fields are important.