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Getting Your Quarks in a Row

A tidy lattice is the key to computing with quantum fields

Brian Hayes

A%20simulation%20of%20quarks%20and%20quantum%20fieldsClick to Enlarge Image The theories known as QED and QCD are the mismatched siblings of particle physics. QED, or quantum electrodynamics, is the hard-working, conscientious older brother who put himself through night school and earned a degree in accounting. QED describes all the electromagnetic phenomena of nature, and it does so with meticulous accuracy. Calculations carried out within the framework of QED predict properties of the electron to within a few parts per trillion, and those predictions agree with experimental measurements.

QCD, or quantum chromodynamics, is the brilliant but erratic young rebel of the family, who ran off to a commune and came back with tattoos. The theory has the same basic structure as QED, but instead of electrons it applies to quarks; it describes the forces that bind those exotic entities together inside protons, neutrons and other subatomic particles. By all accounts QCD is a correct theory of quark interactions, but it has been a stubbornly unproductive one. If you tried using it to make quantitative predictions, you were lucky to get any answers at all, and accuracy was just too much to ask for.

Now the prodigal theory is finally developing some better work habits. QCD still can't approach the remarkable precision of QED, but some QCD calculations now yield answers accurate to within a few percent. Among the new results are some thought-provoking surprises. For example, QCD computations have shown that the three quarks inside a proton account for only about 1 percent of the proton's measured mass; all the rest of the mass comes from the energy that binds the quarks together. We already knew that atoms are mostly empty space; now we learn that the nuclei inside atoms are mere puffballs, with almost no solid substance.

These and other recent findings have come from a computation-intensive approach called lattice QCD, which imposes a gridlike structure on the space and time inhabited by quarks. In this artificial rectilinear microcosm, quarks exist only at the nodes, or crosspoints, of the lattice, and forces act only along the links between the nodes. That's not the way real spacetime is constructed, but the fiction turns out to be helpful in getting answers from QCD. It's also helpful in understanding what QCD is all about.

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