SO YOU WANT TO BE A LATTICE THEORIST? Page: 3 of 8
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FIGURE 1. Lattices abound in the real world. Here is lattice of daisies.
So you want to be a lattice theorist?
Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA
Abstract. For this after dinner talk I intersperse images of real lattices with a discussion of the
motivations for lattice gauge theory and some current unresolved issues.
Keywords: lattice gauge theory
Although lattices are frequently seen in the real world, as in Figure 1, to the particle
theorist they are nothing but a mathematical trick. We constrain quarks so that rather
than following arbitrary world lines, they only move in discrete hops between lattice
sites. As they hop they get spun around in group space by the gauge fields, which are
restricted to the lattice bonds. It is a nice framework for exploring confinement, which
is related to this spinning; quarks act like kangaroos, strongly preferring to hop together
Since the vacuum is not a crystal, this seems at first sight a rather strange thing to
do. However, the lattice has several advantages, primarily in allowing calculations in
situations where other methods fail. In particular, one can go far beyond the realms of
perturbation theory or semi-classical methods. Furthermore, the predictions can have
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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/m1/3/: accessed September 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.