Elementary Particle Physics is the study of the structure of matter and the fundamental laws governing matter deep inside the atom. It leads to research into the incredibly small or short-lived, such as quarks inside protons, and the incredibly ancient, such as the early moments at the birth of the Universe. In the process of trying to describe physics at these very small scales and very early times, it has become evident that we also need to construct a unified theory of all the fundamental interactions of nature.
During the 1980's several hypotheses and models emerged from both the examination of the detailed structure of matter and from the theoretical progress in constructing more complete theories of interactions. These ideas and models include the possibilities of further structure inside quarks and leptons ("technicolor" or "compositeness"), greater symmetries such as "supersymmetry" that may occur at 10-17 centimeters or smaller distances, "grand unification" at 10-30 centimeters, or "supergravity" close to 10-33 centimeters. However, the most daring of these theories is "Superstring Theory" which succeeds in describing quantum gravity together with the other fundamental quantum forces of nature while describing all elementary particles as various configurations of a relativistic string. String theory has been the main focus of theoretical research since 1984.
The members of the Particle Physics group at USC have contributed to the development of the above ideas over the years, and currently their main emphasis is on superstring theory and related topics. Included in the group are Professors Itzhak Bars, Dennis Nemeschansky, Krzysztof Pilch, Hubert Saleur, and Nicholas Warner. This is a leading and very dynamic group whose work has been recognized internationally.
Professor Itzhak Bars is interested in superstring theory and quantum gauge field theory and their application to the Standard Model of elementary particles , unification of forces, and cosmology. In his work he emphasizes the role of symmetries and supersymmetries, which often leads to development of new mathematical tools. In recent years he introduced and studied exactly solvable models of string theory in curved spacetime (possibly with singularities such as black holes ). His current interests include the exploration of the duality symmetry of superstring theory. He is also interested in applying techniques of particle physics to a wide range of areas from mathematics to biology.
Professor Dennis Nemeschansky is interested in high energy physics. Currently he is working on string theory. Professor Nemeschansky is particularly interested in conformal field theory and has been studying applications of conformal field theory in string theory. Another area of current interest is the study of possible vacuum states in string theory. Professor Nemeschansky is studying viable solutions to the equations of motion of the string theory.
Professor Krzysztof Pilch is exploring string theory. Understanding string theory requires very elaborate mathematical methods which range from such classical subjects as Riemannian geometry or the theory of Riemann surfaces to the very modern ones such as algebraic topology of Calabi-Yau spaces, singularity theory or the theory of infinite dimensional spaces and groups.
The specific problems he has been recently working on are: 1) the relation between the absence of anomalies in the heterotic string theories and the topology of the underlying loop space; 2) the index theory of the Dirac operator in the loop space, and elliptic cohomology; 3) Kahler geometry of loop spaces and the representation theory of Diff S1; 4) quantization of strings in the harmonic gauge; 5) two-dimensional conformal field theory, in particular the Thirring model on higher genus Riemann surfaces and the generalized ghost Thirring models; 6) representation theory of Kac-Moody algebras, in particular the free field realizations of current algebras.
Professor Hubert Saleur's contributions to physics and mathematics range through statistical mechanics, conformal field theory, integrable models, the applications of quantum groups, knot theory and map-coloring theorems. A major underlying theme of this work has been the study of geometric phase transitions, and the role of conformal invariance. These ideas have important physical applications in the study of polymers and percolation problems, while in mathematics they provide new insight into the construction of knot invariants and into the properties of chromatic polynomials of maps. In mathematical physics pioneered research on the physical applications of quantum groups in exactly solvable lattice models, and the relationship between such lattice models and conformal field theory.
Professor Nicholas Warner is currently working in two apparently different areas: string theory and two dimensional quantum integrable systems. The underlying relationship between these two subjects is provided by conformal field theory, which can be used to construct string theories in high energy physics, and also can be used to describe second order phase transitions in two dimensional systems. His research presently centers around developing new techniques to solve problems in these two fields, and most particularly in using the perspective of either one of these two fields to gain new insight into the other. An example of this is his work that uses the ideas of mean field theory in statistical mechanics to obtain powerful new methods for investigating the structure of string theories.