Donald Marolf

This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this context, on the uniqueness of the construction. While in general the results depend heavily on the choices made for certain auxiliary structures, an additional physical argument leads to a unique result for typical cases. We also discuss the `superselection laws' that result from this scheme and how their existence also depends on the choice of auxiliary structures. Again, when these structures are chosen in a physically motivated way, the resulting superselection laws are physically reasonable.

We consider a family of solutions to string theory which depend on arbitrary functions and contain regular event horizons. They describe six dimensional extremal black strings with traveling waves and have an inhomogeneous distribution of momentum along the string. The structure of these solutions near the horizon is studied and the horizon area computed. We also count the number of BPS string states at weak coupling whose macroscopic momentum distribution agrees with that of the black string. It is shown that the number of such states is given by the Bekenstein-Hawking entropy of the black string with traveling waves.

We extend our recent analysis of the entropy of extremal black strings with traveling waves. We previously considered waves carrying linear momentum on black strings in six dimensions. Here we study waves carrying angular momentum on these strings, and also waves carrying linear momentum on black strings in five dimensions. In both cases, we show that the horizon remains homogeneous and compute its area. We also count the number of BPS states at weak string coupling with the same distribution of linear and angular momentum, and find complete agreement with the black string entropy.

This work closes certain gaps in the literature on material reference systems in general relativity. It is shown that perfect fluids are a special case of DeWitt's relativistic elastic media and that the velocity--potential formalism for perfect fluids can be interpreted as describing a perfect fluid coupled to a fleet of clocks. A Hamiltonian analysis of the elastic media with clocks is carried out and the constraints that arise when the system is coupled to gravity are studied. When the Hamiltonian constraint is resolved with respect to the clock momentum, the resulting true Hamiltonian is found to be a functional only of the gravitational variables. The true Hamiltonian is explicitly displayed when the medium is dust, and is shown to depend on the detailed construction of the clocks.

It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string solution. In these spacetimes, the dynamics of quantum particles is well defined and uniquely determined.

Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test cases. Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse.

We investigate conservation laws in the quantum mechanics of closed systems. We review an argument showing that exact decoherence implies the exact conservation of quantities that commute with the Hamiltonian including the total energy and total electric charge. However, we also show that decoherence severely limits the alternatives which can be included in sets of histories which assess the conservation of these quantities when they are not coupled to a long-range field arising from a fundamental symmetry principle. We then examine the realistic cases of electric charge coupled to the electromagnetic field and mass coupled to spacetime curvature and show that when alternative values of charge and mass decohere, they always decohere exactly and are exactly conserved as a consequence of their couplings to long-range fields. Further, while decohering histories that describe fluctuations in total charge and mass are also subject to the limitations mentioned above, we show that these do not, in fact, restrict {\it physical} alternatives and are therefore not really limitations at all.

We consider a quantization of the Bianchi IX cosmological model based on taking the constraint to be a self-adjoint operator in an auxiliary Hilbert space. Using a WKB-style self-consistent approximation, the constraint chosen is shown to have only continuous spectrum at zero. Nevertheless, the auxiliary space induces an inner product on the zero-eigenvalue generalized eigenstates such that the resulting physical Hilbert space has countably infinite dimension. In addition, a complete set of gauge-invariant operators on the physical space is constructed by integrating differential forms over the spacetime. The behavior of these operators indicates that this quantization preserves Wald's classical result that the Bianchi IX spacetimes expand to a maximum volume and then recollapse.