SO YOU WANT TO BE A LATTICE THEORIST? Page: 4 of 8
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FIGURE 2. Lattices can have good flavors. But beware of lurking tastes.
crucial experimental implications. These extend to many areas of particle and nuclear
physics, from extracting weak matrix elements in processes involving large hadronic
corrections, to understanding the behavior of matter under the extreme conditions of
heavy ion collisions, and to detailed studies of hadronic structure.
And of course we get to have fun playing with big computers. Indeed, these them-
selves are large lattices of processors, such as the six dimensional torus that makes up
the QCDOC supercomputer dedicated to lattice gauge theory. There are also more ab-
stract reasons to study lattice gauge theory. As shown in Figure 2, lattices can have
good flavors. However one should be careful of any harmful lurking tastes. Lattices are
frequently seen in cities, such as the lattice of trees seen in Figure 3.
One of the fun things about lattice gauge theory is the addictive power it gives over
the system. Entire lattice configurations are stored in the computer memory, and you
are free to measure anything you want. In the process uncertainties can arise, and the
theorist is in the unusual situation of having error bars. First of all, since we are using.
Monte Carlo methods, there will be statistical errors. These can be reduced by massive
applications of computer time. There are also several sources of systematic error, some
of which we have control over. These include finite volume and finite lattice spacing
corrections, which can also be reduced by increased computer time. In practice using
quarks with physical masses is quite computer intensive; so, we usually simulate with
heavier than normal quarks and then do an extrapolation.
There are also some sources of error that are basically uncontrolled. One is the so-
called "valence" or "quenched" approximation, wherein the feedback of internal quark
loops is ignored. This is a tempting approximation since it saves a couple of orders of
magnitude of computer time. But fortunately the continuing growth in computer power
is now alleviating the need for this inexact approach.
Another uncontrolled source of error comes from extrapolations in the number of
quark flavors. Again to save computer time, it is popular, mainly in the US, to start with
a fermion formulation that has some of the naive doubling issues remaining and then do
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CREUTZ, M. SO YOU WANT TO BE A LATTICE THEORIST?, article, September 2, 2006; [Upton, New York]. (digital.library.unt.edu/ark:/67531/metadc885344/m1/4/: accessed February 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.