Today, the known laws of Physics attempt to explain natural phenomena from distance scales larger than a billion light year to distances more than a million times smaller than the typical size of an atom. Remarkably, the phenomena occurring at the shortest distances accessible experimentally can be described using the formalism of quantum field theory with local symmetries, namely gauge theory.

The best known gauge theory is Quantum Electrodynamics (QED). It describes the electromagnetic interactions of electrons and photons. This theory provides predictions in agreement with experiment with more than ten significant digits. Quantum Chromodynamics QCD describes the strong interactions of quarks and gluons. This theory has a complex large distance behavior which includes phenomena such as the confinement of quarks. Finding calculational methods for QCD having an accuracy comparable to QED is a challenge for theoretical physics. The weak interactions are described by the Glashow-Weinberg-Salam model. The predictions of this model have received spectacular confirmations with the recent discoveries of $W$ and $Z$ bosons and of the top quark. At the present time, much effort is being spent to develop experiments capable of discovering the Higgs boson. General relativity and other geometrical theories provide a description of classical gravitational phenomena. In many frameworks this may also be called a gauge theory. Finding a consistent quantum theory of gravity is an important goal for many physicists.

The members of the theoretical particle physics group are involved in a variety of problems in particle phenomenology and quantum field theory. These include perturbative predictions of the electroweak standard model and QCD for high energy colliders at Fermilab and CERN. Field theoretical aspects that are covered include lattice field theory, renormalization group techniques, classical and quantum gravity as related to string theories and various applications of the theory of group representations.

Perturbative methods are used to probe QCD. The applicability of perturbative QCD to a variety of processes in proton-proton, proton-antiproton, and electron-proton colliders as well as fixed target experiments is being tested. These theoretical tests require calculations at next-to-leading order in the perturbative expansion parameter, the strong coupling constant. A combination of analytical and numerical techniques are used, including symbolic manipulations and numerical integration on the high energy group's computers.

The renormalization group method is an essential tool to understand and describe the large distance behavior of gauge theories and spin models. The practical implementation of this method can be drastically simplified if one considers, as a first approximation, a model where the interactions are self-similar. This approximation allows the calculation of small and large coupling expansions to very large order and their comparison with numerical answers. The perturbative corrections to this approximation in self-similar models are being calculated using analytical and numerical methods. A case of particular interest is the three-dimensional Ising model which is dual to a gauge theory and has been conjectured to be equivalent to a string theory. Another important application being considered is the determination of an upper bound on the Higgs boson.

Other theoretical studies of gauge and gravitational theories in the non-perturbative regime include the use of geometry and topology. These studies include the study of two dimensional quantum gravity and its four dimensional gravity analogue, supersymmetric theories and string theory that is related to QCD. In conjunction with members of the mathematics department, relationships between representations of infinite dimensional algebras and determinants of Dirac operators on four manifolds are studied and well as anomalies in four dimensional gravity and the spectrum of certain differential operators.

Theoretical physicists and mathematicians meet weekly for a joint seminar. Topics discussed involve ergodic problems, quantum chaos and the theory of group representation. A seminar series on topics of interest to theoretical and experimental particle and nuclear physics also meets weekly.

Selected Publications:

• ``A 2D Inspired 4D Theory of Gravity,'' by V.G.J. Rodgers, Physics Letters B336, 343 (1994).
• ``A Study of Fermions on a Cylinder Coupled to Gauge and Gravitational Fields,'' by Ralph Lano and V.G.J. Rodgers, Nuclear Physics B437, 4 (1995).
• ``Precise Determination of the Energy Levels of the Anharmonic oscillator from the Quantization of the Angle Variable,'' by B. Bacus, Y. Meurice and A. Soemadi, Journal of Physics A 28, L381 (1995).
• ``The Elusive Asymptotic Behavior of the High-Temperature Expansion of the Hierarchical Ising Model,'' by Y. Meurice and G. Ordaz, Journal of Statistical Physics 82, 343 (1996).
• ``Evidence for Complex Subleading Exponents from the High-Temperature Expansion of Dyson's Hierarchical Model,'' by Y. Meurice, G. Ordaz and V.G.J. Rodgers, Physical Review Letters 7?, 4555 (1995).
• ``Ultrahigh-Energy Neutrino Interactions,'' by R. Gandhi, C. Quigg, I. Sarcevic and M.H. Reno, to be published in Astroparticle Physics.
• ``Hadron Collider Limits on Anomalous W-W-Photon Couplings,'' by K.R. Barger and M.H. Reno, Physical Review D51, 90 (1995).
• ``Relative Distributions of W's and Z's at Low Transverse Momenta,'' by M.H. Reno, Physical Review D49, 4326 (1994).