36469643
Lorentzian path integral for minisuperspace cosmology.
The path integral for minisuperspace models of cosmology is defined as a sum over Lorentzian geometries, and is a Green function for the Wheeler-DeWitt operator. It is shown to be a symmetric function of the initial and final configurations, and its real part is a solution to the Wheeler-DeWitt equation. The Lorentzian path integral is computed explicitly for the de Sitter minisuper-space model and is convergent. The resulting Green function is then related to the solutions of the Wheeler-DeWitt equation known as the Hartle-Hawking and tunneling wave functions of the Universe. The real part of this Green function is a product of Hartle-Hawking wave functions.
6269112
Action functionals for relativistic perfect fluids
Action functionals describing relativistic perfect fluids are presented. Two of these actions apply to fluids whose equations of state are specified by giving the fluid energy density as a function of particle number density and entropy per particle. Other actions apply to fluids whose equations of state are specified in terms of other choices of dependent and independent fluid variables. Particular cases include actions for isentropic fluids and pressureless dust. The canonical Hamiltonian forms of these actions are derived, symmetries and conserved charges are identified, and the boundary value and initial value problems are discussed. As in previous works on perfect fluid actions, the action functionals considered depend on certain Lagrange multipliers and Lagrangian coordinate fields. Particular attention is paid to the interpretations of these variables and to their relationships to the physical properties of the fluid.
16734842
Black Hole Thermodynamics in a Box
Simple calculations indicate that the partition function for a black hole is defined only if the temperature is fixed on a finite boundary. Consequences of this result are discussed. (Contribution to the Proceedings of the Lanczos Centenary Conference.)
16432578
Dust as a standard of space and time in canonical quantum gravity.
The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. The Hamiltonian constraint can be resolved with respect to the momentum that is canonically conjugate to the dust time. Formal imposition of the resolved constraint as an operator restriction on the quantum states yields a functional Schr\"odinger equation. The ensuing Hamiltonian density has an extraordinary feature: it depends only on the geometric variables, not on the dust coordinates or time. This has three important consequences. First, the functional Schr\"odinger equation can be solved by separating the dust time from the geometric variables. Second, disregarding the standard factor-ordering difficulties, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra. The particles of dust introduce into space a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. The Schr\"odinger equation yields a formally conserved inner product that can be written in terms of either the instantaneous state functionals or the solutions of constraints. Gravitational observables admit a similar dual representation. Examples of observables are given, though neither the intrinsic metric nor the extrinsic curvature are observables. This comes as close as one can reasonably expect to a satisfactory phenomenological quantization scheme that is free of most of the problems of time.
119986427
On the Poisson brackets of differentiable generators in classical field theory
The canonical formulation of field theory on open spaces is considered. It is proved, under appropriate assumptions, that the Poisson bracket of two differentiable generators is also a differentiable generator.
119005465
Modifying the Einstein equations off the constraint hypersurface
A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the gravitational field variables are modified by the addition of terms that are linear and nonlocal in the constraints. These terms are obtained from solutions of the linearized Einstein constraints.
11983780
Is there large weak mixing in heavy nuclei?
Recent results in parity non-conserving neutron-nucleus scattering show a tendency for the parity non-conserving effects to predominantly have the same sign. Explanations of this phenomenon all require a weak matrix element between single-particle levels in heavy nuclei to be [similar to]100 eV. This paper contains a discussion of this effect and how the same phenomenon will manifest itself in other systems. The gamma decay of [sup 207]Pb is given as an example of a system where the weak matrix element between single-particle levels in a heavy nucleus can be measured directly.
45820359
Strength of the rho meson coupling to nucleons.
In his recent publication of a [ital NN] phase shift analysis below 160 MeV, Henneck reports relatively large values for the mixing parameter [epsilon][sub 1]. Based on these results, Henneck suggests that the strength of the [rho]-meson coupling to the nucleon may be weaker than used in present day [ital NN] interactions, like the Paris, Nijmegen, or Bonn potentials. We point out that at low enegies ([approx lt] 100 MeV) there is rather little sensitivity to the strength of the [rho] coupling, due to the compensating effect of the second-order tensor term. In order to establish sensitivity, one has to go to energies [approx gt]200 MeV, where the second-order contribution has gone out. As it happens, the [epsilon][sub 1] mixing parameter is well determined in the region of energies 200--300 MeV, and there is agreement with the predictions by the Paris and Bonn potentials; the weak-[rho] model is about 50% above the data. This and additional considerations in triplet [ital P] waves reconfirm that [ital NN] scattering requires the strong [rho], consistent with the [pi][pi]-[ital N[bar N]] partial-wave analysis by Hoehler and Pietarinen.
42270711
Transition densities in 30Si studied by electron scattering and coupled-channel calculations of 650 MeV proton scattering.
Proton and neutron transition densities in $^{30}\mathrm{Si}$ are examined by a combination of intermediate energy (e,e') and (p,p') reactions and mirror electromagnetic transition rates. This analysis is performed for the ${2}_{1}^{+}$ and ${2}_{2}^{+}$ states at 2.234 and 3.499 MeV in $^{30}\mathrm{Si}$. Electron scattering data are presented for these states. Shell-model calculations for the proton and neutron transition matrix elements and proton transition densities are compared with the electromagnetic results. The proton transition densities are reasonably predicted for the ${2}_{1}^{+}$ state but are not adequately predicted for the ${2}_{2}^{+}$ state. A microscopic coupled-channel calculation of 650 MeV (p,p') is used to test the shell-model isoscalar transition densities. Given the uncertainties present in the reaction calculation and interaction, the isoscalar density for the ${2}_{1}^{+}$ state is found to be adequate, but the density for the ${2}_{2}^{+}$ state is less accurate. The coupled-channel effect is shown to be important for the ${2}_{2}^{+}$ state. This dependence increases with energy but should be taken into account for an accurate description of (p,p') reactions at all energies.
29372740
Strength functions and spreading widths of simple shell model configurations.
The exact solution of the many-body problem in the framework of the nuclear shell model with a realistic residual Hamiltonian makes it possible to study the fragmentation of simple configurations as a function of excitation energy and interaction strength. The analysis is performed for 839 states with quantum numbers {ital J}{sup {pi}}{ital T}=0{sup +}0 in a system of 12 valence particles within the {ital sd} shell. Our statistics allow us to establish the generic shape of the strength function in the region of strong mixing. For the realistic interaction, the strength function is close to Gaussian in the central part and has exponential wings. The spreading width is larger than predicted by the standard golden rule. At the artificially suppressed interaction strength, we recover the Breit-Wigner shape and the golden rule for the spreading width. The transition between these regimes agrees with theoretical considerations based on the idea of chaotic dynamics. {copyright} {ital 1996 The American Physical Society.}
25192813
Spin-flip transitions in 16O and 18O excited by inelastic proton scattering.
Inelastic proton scattering at forward angles has been carried out on /sup 16/O and /sup 18/O at a bombarding energy of 201 MeV. The (p,p') spin-flip transitions to 1/sup +/ and 2/sup -/ states are compared with (e,e'), (p,..gamma..), and charge exchange data, and with microscopic distorted-wave Born approximation calculations using shell model wave functions. The ratios of orbital to spin contributions are deduced for the known 1/sup +/ states in /sup 16/O.