6465693
Quantum cosmological Friedman models with an initial singularity
We consider the Wheeler–DeWitt equation Hψ = 0 in a suitable Hilbert space. It turns out that this equation has countably many solutions ψi which can be considered as eigenfunctions of a Hamilton operator implicitly defined by H. We consider two models, a bounded one, 0 < r < r0, and an unbounded, 0 < r < ∞, which represent different eigenvalue problems. In the bounded model we look for eigenvalues , where the are the values of the cosmological constant which we used in the Einstein–Hilbert functional, and in the unbounded model the eigenvalues are given by , where . Note that r is the symbol for the scale factor, usually denoted by a, or a power of it. The ψi form a basis of the underlying Hilbert space. We prove furthermore that the implicitly defined Hamilton operator is selfadjoint and that the solutions of the corresponding Schrodinger equation satisfy the Wheeler–DeWitt equation, if the initial values are superpositions of eigenstates. All solutions have an initial singularity in r = 0. Under certain circumstances a smooth transition from big crunch to big bang is possible.
9548206
On the foliation of space-time by constant mean curvature hypersurfaces
We prove that the mean curvature $\tau$ of the slices given by a constant mean curvature foliation can be used as a time function, i.e. $\tau$ is smooth with non-vanishing gradient.
15442219
Quantum cosmological Friedman models with a massive Yang–Mills field
We prove the existence of a spectral resolution of the Wheeler–DeWitt equation when the matter field is provided by a massive Yang–Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang–Mills field. In the latter case, the mass of the Yang–Mills field assumes the role of the eigenvalue.
14435367
The inverse mean curvature flow in cosmological spacetimes
We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime $N$ under the necessary and sufficent assumptions that $N$ satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter $t$ can be used to define a new physically important time function.
1745746
Branes, moduli spaces and smooth transition from big crunch to big bang
We consider branes N in a Schwarzschild-AdS(n+2) bulk, where the stress energy tensor is dominated by the energy density of a scalar fields map φ : N → S with potential V , where S is a semiRiemannian moduli space. By transforming the field equation appropriately, we get an equivalent field equation that is smooth across the singularity r = 0, and which has smooth and uniquely determined solutions which exist across the singularity in an interval (− , ). Restricting a solution to (− , 0) resp. (0, ), and assuming n odd, we obtain branes N resp. N which together form a smooth hypersurface. Thus a smooth transition from big crunch to big bang is possible both geometrically as well as physically.
13474074
An Energy Gap for Yang-Mills Connections
Consider a Yang-Mills connection over a Riemann manifold M = Mn, n ≥ 3, where M may be compact or complete. Then its energy must be bounded from below by some positive constant, if M satisfies certain conditions, unless the connection is flat.
121817998
Electroproduction cross sections in the resonance region measured at large scattering angles
To complete data on resonance electroproduction we constructed an electron spectrometer with large angular and momentum acceptance. As a first result inclusive cross sections for an invariant hadronic mass 1.2<W<1.7 GeV and a four momentum transfer squared 0.5<Q2<1.5 (GeV/c)2 and for values of the polarization parameter 0.1<ɛ<0.25 are presented. Combining our results with the SLAC 4°-data we obtain σL/σT in the specified kinematical range.