The research that falls into this group of topics addresses questions about the basic laws of nature, as well as about the ultimate structure of both microscopic matter and the macroscopic universe. A number of investigations in this field of theoretical inquiry, many of them funded by the Department of Energy, are currently being carried out in the Physics Department.
One of the important questions in particle theory is how basic constituents of matter -- quarks and gluons -- are fused into the nucleons and mesons that we observe in nature. Quantum chromodynamics (QCD) is currently the accepted theory of the strong interactions, and it is generally believed that QCD can be used to understand how quarks and gluons are combined to form these stable groupings. QCD is a gauge theory that resembles the familiar quantum electrodynamics (QED) in many respects, but differs from it in that the underlying gauge group, SU(3), is a non-commutative (non-Abelian) Lie group. We still do not know how satisfactory QCD is in the long-range (non-perturbative) domain, because the consequences for that regime are difficult to work out. Even the short-range (perturbative) consequences of QCD, which are generally well-confirmed by high energy scattering data, are often obscured by long-range effects, so that much remains to be done to clarify its implications for phenomenology. Even the lowest energy state -- the QCD vacuum -- is not well understood.
One project in our Department that addresses this question is based on the construction of states that obey the non-Abelian Gauss's law that applies in QCD. To maintain consistency with canonical equal-time commutation rules, the operator that expresses Gauss's law cannot be required to vanish identically. Instead, quantum states are constructed that are annihilated by this operator, which is called the ``Gauss's law operator''. This Gauss's law operator also implements a class of gauge transformations, so that the imposition of Gauss's law enables us to construct gauge-invariant spinor (quark) and gauge (gluon) fields. It is generally recognized that unless quark and gluon fields are gauge-invariant, they cannot describe the physical quarks and glue that constitute hadrons. The results of this work have been used to transform the QCD Hamiltonian to a form that refers only to gauge-invariant quark and gluon fields. In this transformed representation, the QCD Hamiltonian has a structure strongly reminiscent of the form characteristic of a gauge theory in the Coulomb gauge -- for example, its commutation rules are in very good agreement with corresponding ones in Schwinger's work on Coulomb-gauge QCD. In this formulation, the QCD Hamiltonian includes a nonlocal interaction between color-bearing matter -- quarks, groupings of quarks, and glue -- which is the analog, in QCD, of the nonlocal Coulomb interaction in QED; but in QCD, there is a very different kind of charge density -- an ``effective color-charge density'' -- appearing as the non-Abelian analog of the electric charge density in QED. For technical reasons related to the role of the ``color charge'' as a generator of a global transformation in an SU(3) ``color'' space, this non-Abelian analog of the Coulomb interaction weakens significantly or even vanishes for ``colorless'' color singlet configurations. Further work has demonstrated topological characteristics of the gauge-invariant fields, among them non-integer values of a topological charge. A connection has also been shown between the implementation of the non-Abelian Gauss's law and the appearance of Gribov copies of gauge fields. The purpose of this approach is to develop an effective tool for representing QCD in terms of physical variables -- which must be gauge-invariant -- and thereby to provide a new avenue for exploring a variety of dynamical questions including the confinement of quarks and of color-bearing groupings of quarks.
Another project is an effort to understand the structure of the nucleon, based on analyses of high energy elastic proton-proton and proton-antiproton scattering. Research along this direction has led to the development of a model of the nucleon as a ``topological soliton'' embedded in a condensed ground state of quarks and antiquarks. The condensed ground state is found to be analogous to a superconducting ground state and has important implications regarding the nucleon mass, the confinement of quarks, and the nucleon-nucleon interaction. Future measurements of elastic proton-proton scattering at the Large Hadron Collider (LHC) at CERN will test many aspects of this model, which include the prediction of a chiral phase transition at short distances (or large momentum transfer). Furthermore, the model provides a framework for an effective description to study the behavior of nuclear matter at high energy density and high temperature - behavior that can now be investigated experimentally at the Relativistic Heavy Ion Collider ( RHIC ) at Brookhaven National Laboratory. The model indicates that a chiral phase transition from nuclear matter to quark matter occurs.
Chern-Simons theories, which are special gauge theories in 2+1 dimensional space-time, have provided (amongst other things) new insights into anomalous symmetries in particle physics. This is particularly true of some of our recent work on Chern-Simons theories at finite temperature. This work has led to a new understanding of the interplay between finite temperature effects and large gauge invariance. This was a long-standing puzzle that has now been partially resolved, but which has also raised other fundamental questions about finite temperature perturbation theory. Most recently these ideas have been extended to systems in four dimensional space-time. Another research program concerns the so-called derivative expansion which is a widely-used approximation technique in theoretical physics; used for example in computing effective actions to describe the physically relevant degrees of freedom below a certain energy scale. Our work has investigated the convergence properties of derivative expansions in quantum electrodynamics, building on our earlier exact results (the only ones known so far) for the QED effective action in inhomogeneous electric or magnetic background fields. This has applications in both particle physics and laser physics.
Studies of 2+1-dimensional electrodynamics with an Abelian Chern-Simons term -- the so-called topologically massive QED -- have explored the consequences of constructing gauge-invariant charged states that implement Gauss's law. A gauge-invariant description of charged particle states eliminates the pure gauge degrees of freedom as transmitters of interactions, and replaces them by explicit non-local interactions between charged states -- in a sense, planar analogs of the Coulomb force in electrodynamics. This work has shown that ``anyonic'' rotational phases (i.e. spin) attach to charged particles in this planar geometry, but that this model does not develop any exotic multi-particle statistics. Charged fermions and bosons, after they have been rendered gauge-invariant, retain fermionic and bosonic statistics respectively.
One investigation in astroparticle theory reexamines a metric theory of gravitation based on an idea due to Weyl, which is fourth-order rather than second-order, and is conformal, so that it possesses no dimensionful constants which could impart any intrinsic length scales to the theory. One consequence of this theory is that the gravitational potential has a component linear in the distance, which is insignificant on solar distance scales, but important on galactic scales. This fact is of interest because one of the major puzzles of contemporary astrophysics is that the stars on the periphery of spiral galaxies rotate far too quickly to be consistent with the Newtonian limit of Einstein's general theory of relativity when applied to the observed galactic distribution of stars. This inconsistency has led many astrophysicists to believe that non-luminous or ``dark'' matter must exist in these galaxies in amounts copious enough to avoid this paradox. This reexamination of the conformal theory suggests that it might be possible to account for observed galactic rotation curves without requiring the postulation of dark matter. Further application of this same conformal theory has been found to successfully address the other two major puzzles of contemporary cosmolgy, with the theory naturally explaining the recently discovered unexpected fact that the universe appears to be accelerating rather than decelerating, while also naturally explaining why the cosmological constant is as small as the data apparently require.
Another research program deals with the gravitational field produced by a single continuously circulating beam of light in a unidirectional ring laser. It is predicted that a spinning neutral particle, when placed in the ring, is dragged around by the resulting gravitational field. Calculations show that, for light circulating in a transparent dielectric medium, the gravitational frame dragging-precession rate is inversely proportional to the velocity of light in the medium. This opens up the possibility that slow-light experiments may be used to detect this gravitational effect. Another aspect of this research explores the effect on time of a circulating unidirectional light beam. It can also be shown that, by the proper adjustment of beam intensity and location, closed loops in time can be formed.
In other work, a general relativistically covariant theory of a self-coupled scalar field has been developed as a possible solution of the missing mass problem. It has been shown that spontaneous symmetry breaking of a neutral scalar field coupled to gravity leads directly to ultra-low mass bosons, with a critical temperature far above the temperature of the universe, for most of its duration. The particles are therefore expected to condense into a degenerate Bose Einstein gas, providing a potential candidate for nonbaryonic nonluminous matter.
Other work continues on an ongoing research program that focuses on the use of path integrals in the calculation of quantum mechanical quantities such as transition elements and partition functions. There are four areas of particular interest. The first is in the role of classical configurations in evaluating the path integral, ranging from the WKB approximation to the use of monopole solutions to develop the ground state of quantum chromodynamics and related supersymmetric theories. The second, related to the first, is in understanding the localization of path integrals onto the zero modes of its variables and the associated issues regarding the measure of path integrals. The third is in developing path integral techniques for redefining actions in terms of new variables and their relationship to the first two areas. The fourth is in understanding the role that geometry and topology play in the first three areas, such as the identification of moduli spaces, induced metrics on quantum mechanical phase space, classical solutions, and the implementation of constraints.
The computational methods and conceptual framework developed for work in Particle and Field Theory often have had implications for physics as a whole. Similarly, particle theorists have benefitted from insights gained in theoretical studies in other parts of physics. In our Department such cross-fertilization occurs in the application of gauge theories to nuclear physics and to quantum optics, and in common underlying principles that govern non-perturbative vacuum states in quantum field theories and in superconductivity. In recent years, these relationships have been intensified by the connection between Chern-Simons theory and the Quantum Hall Effect, and by anyonic models of high-Tc superconductivity. Such contributions by one research specialty to another have always enriched all of physics.