Theoretical Particle Physics
Richard Brower,
Andrew Cohen,
Liam Fitzpatrick,
Emanuel Katz,
Kenneth Lane,
SoYoung Pi,
Claudio Rebbi,
Martin Schmaltz
The goal of particle physics is to understand the fundamental constituents of matter and their mutual interactions. Particle theorists attempt to reach this goal in a variety of ways, but they depend on close contact with the results of their experimental colleagues to test theoretical ideas. The "standard model" of particle physics is that the fundamental constituents are quarks, leptons, gauge bosons and the graviton, interacting via the strong, electroweak and gravitational interactions. At Boston University, this picture and its possible extensions are investigated by a wide range of approaches including:

attempts to determine the physical origin of electroweak symmetry and the breaking of quark and lepton flavor symmetries;

numerical simulations of complex physical situations such as Quantum Chromodynamics and critical phenomena in Statistical Mechanics;

the impact of particle physics on cosmology;

the application of mathematics to quantum field theory, especially with the hope of developing a consistent, unified theory of all interactions, including gravity.
Research
 Electroweak Symmetry Breaking
Andrew Cohen, Emanuel Katz, Kenneth Lane
The problems of the breakdown of electroweak and flavor symmetries are among the most pressing facing particle physics today. Electroweak symmetry breaking is manifested by the nonzero masses of the weak W and Z bosons, and requires the existence of a Higgs boson or some other yet unseen mechanism. To solve the problem of flavor, one must understand why there are six quarks and six leptons forming three families, and why these particles exhibit such a peculiar pattern of masses and mixing. This question has become especially acute with the recent experimental proof that neutrinos have mass and experience oscillations. Several theoretical approaches to electroweak and flavor symmetry breaking, as well as the related question of CP violation, are being investigated actively. All of them require that there be new particles and new interactions at soontobe accessible energies. In particular, experiments at the Large Hadron Collider are currently accumulating data which should clarify the origins of electroweak symmetry breaking. The highenergy theorists are interacting closely with their experimental colleagues who will be working on these experiments. Research is aimed at formulating consistent theoretical models and exploring their observable consequences.
 Quantum Chromodynamics
Claudio Rebbi
A crucial component of the scientific process consists of deriving quantitative predictions from assumed theoretical models. The power of modern computers has added a new dimension to this aspect of research. Today, physicists can use advanced numerical techniques to simulate the behavior of very complex systems and thus solve problems that defy the more traditional methods of mathematical analysis. Scientists in the particle theory group have been applying forefront computational methods to the study of quantum chromodynamics (QCD, the theory of interacting quarks and gluons) and to other particle models. Spacetime is approximated by a lattice of points, and the fundamental fields, defined over this lattice, are represented by an extremely large collection of numbers stored in the memory of a supercomputer. Calculating at the rate of billions of operations per second, the computer simulates the effects of quantum fluctuations of the fields. From such techniques, one can calculate fundamental observables such as particle masses or the temperature at which quarks and gluons become unbound and evaluate matrix elements crucial for the interpretation of collider experiments. Students, research staff, and faculty working on these problems avail themselves of the supercomputer resources and support structure of the Center for Computational Science. While doing research in the fascinating and challenging field of subatomic particles, students also acquire invaluable expertise in the use of the most modern and powerful supercomputer technologies.
 The Big Bang, Dark Matter, and Cosmology
Andrew Cohen, SoYoung Pi
Many of the questions of current theoretical interest are beyond the energy reach of existing accelerators. However, extremely high energies were once realized in the largest natural particle accelerator, the Big Bang. Shortly after the Big Bang, the universe was composed of a hot plasma of elementary particles. The nature of this plasma, which depends on the properties of the constituent elementary particles, determined the subsequent evolution of the universe. By observing the universe today, we can obtain information about its state shortly after the Big Bang and obtain information about the interactions of these particles at high energy. Several cosmological problems are presently being considered, among them: Is there a consistent inflationary model of the early universe? What is the nature of "dark matter" and what role does it play in the development of largescale structure? What mechanism produced the baryon excess in the universe?
 Topological Effects in Quantum Field Theories
SoYoung Pi
Topology, the mathematical description of the robustness of form, appears in many branches of physics and provides strong constraints on physical systems. Topologically interesting field theories predict various hypothetical objects and mathematical constructs. Although many of the fascinating objects have not been seen in particle physics, they demonstrate possible phenomena that quantum field theory can support.
A significant deformation of the Dirac equation is achieved when the constant mass term is replaced by topologically nontrivial profiles. Examples of interesting profiles are: kink in one dimension, vortex in two and magnetic monopole in three.
Dirac equation in the presence of such topological entities possesses an isolated zeroenergy solution. The existence of zeroenergy solution does not require a speciﬁc form for the inhomogeneous mass proﬁle; all that matters is that it belongs to a nontrivial topological class. It has been shown that they give rise to fermion fractionalization and isolated Majorana fermion bound states depending on the absence or presence of superconductivity in the system. The difference between the two situations results in the presence or absence of a conserved fermion number.