54221487
The quantization of gravity in globally hyperbolic spacetimes
We apply the ADM approach to obtain a Hamiltonian description of the Einstein-Hilbert action. In doing so we add four new ingredients: (i) We eliminate the diffeomorphism constraints. (ii) We replace the densities $\sqrt g$ by a function $\f(x,g_{ij})$ with the help of a fixed metric $\chi$ such that the Lagrangian and hence the Hamiltonian are functions. (iii) We consider the Lagrangian to be defined in a fiber bundle with base space $\so$ and fibers F(x) which can be treated as Lorentzian manifolds equipped with the Wheeler-DeWitt metric. It turns out that the fibers are globally hyperbolic. (iv) The Hamiltonian operator $H$ is a normally hyperbolic operator in the bundle acting only in the fibers and the Wheeler-DeWitt equation $Hu=0$ is a hyperbolic equation in the bundle. Since the corresponding Cauchy problem can be solved for arbitrary smooth data with compact support, we then apply the standard techniques of QFT which can be naturally modified to work in the bundle.
54629664
A unified quantum theory I: Gravity interacting with a Yang-Mills field
Using the results and techniques of a previous paper where we proved the quantization of gravity we extend the former result by adding a Yang-Mills functional and a Higgs term to the Einstein-Hilbert action.
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.
16464322
The inverse mean curvature flow in ARW spaces--transition from big crunch to big bang
We consider spacetimes $N$ satisfying some structural conditions, which are still fairly general, and prove convergence results for the leaves of an inverse mean curvature flow. Moreover, we define a new spacetime $\hat N$ by switching the light cone and using reflection to define a new time function, such that the two spacetimes $N$ and $\hat N$ can be pasted together to yield a smooth manifold having a metric singularity, which, when viewed from the region $N$ is a big crunch, and when viewed from $\hat N$ is a big bang. The inverse mean curvature flows in $N$ \resp $\hat N$ correspond to each other via reflection. Furthermore, the properly rescaled flow in $N$ has a natural smooth extension of class $C^3$ across the singularity into $\hat N$. With respect to this natural, globally defined diffeomorphism we speak of a transition from big crunch to big bang.
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.
119713081
A unified field theory I: The quantization of gravity
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two possible modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system. 
\nd In the second model the resulting equation is a wave equation in $\so \times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions for each fixed $\xi$. This set of equations contains as a special case the equation of a quantized cosmological Friedmann universe without matter but with a cosmological constant, when we look for solutions which only depend on $t$. Moreover, in case $\so$ is compact we prove a spectral resolution of the equation.
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.