The goal of elementary particle physics is to discover the constituents of the universe and the forces through which they interact. Our present understanding of this problem is summarized in the Standard Model of high energy physics. It says that the fundamental particles of matter are the leptons and the quarks. The four fundamental forces through which they interact are described by gauge theories, which are a generalization of Maxwell's theory of electrodynamics. Associated with the forces are particles: the photon for electromagnetism, the gluon for strong interactions, and the W and Z bosons for weak interactions. There is also the graviton for gravity, but quantum gravity is not included within the framework of the Standard Model. The part of the Standard Model that describes the strong interactions among the quarks is a non-Abelian gauge theory called Quantum Chromodynamics (QCD). It is a particularly simple and elegant theory. Simple to state, that is, but not at all simple to solve. Nature has told us that quarks are confined within hadrons and cannot be separated to macroscopic distances. Is this a consequence of QCD? Although the answer is most likely "yes", we have not yet extracted that result from QCD.

It appears that the forces in QCD are weak at short distances but strong at large distances! For those physical processes that are controlled by short-distance interactions, the results of perturbative calculations and experiments can be compared quantitatively. For most reactions, this is not the case because large-distance, nonperturbative effects are important. Confinement is only the most dramatic example, but there are others.

The general goal of my research is to further the understanding of non-Abelian gauge fields in nonperturbative regions. I am particularly interested in the interplay of gauge symmetry, vacuum structure, and hadron structure. The perturbative calculations that are valid at short distance where the effective coupling is weak require a gauge fixing that obscures to some considerable extent the fundamental role of gauge symmetry. We would like an approximation that is complementary to continuum perturbation theory in that it maintains manifest gauge invariance. Lattice gauge theory is able to do this, However, the price is that space-time is discretized and reduced to a lattice of points. Nevertheless, it is a good framework in which to apply nonperturbative methods. This has been my main research speciality in recent years.

Within the framework of lattice gauge theory, one can employ either approximate, analytical methods or a direct attack by numerical simulation. My work has exploited both approaches. Recently it has been mostly analytical although much of the motivation is from my previous numerical results.

The zero-temperature pure gauge theory has no adjustable parameters. This is part of the reason that it is so difficult to approximate. A study of the theory at finite temperature introduces a parameter T that can be varied in a controlled way so as to probe different aspects of the theory. In particular, confinement, which is apparently present at low temperature, is absent at sufficiently high temperature. A study of the theory as the temperature is changed can yield useful information about the features that distinguish these two phases and thus contribute to an understanding of the vacuum state. Most of my current work is related to finite temperature gauge theory.

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Joseph E. Kiskis

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