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.
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.
14259478
Transition from big crunch to big bang in brane cosmology
We consider branes N = I × S0, where S0 is an n–dimensional space form, not necessarily compact, in a Schwarzschild-AdS(n+2) bulk N . The branes have a big crunch singularity. If a brane is an ARW space, then, under certain conditions, there exists a smooth natural transition flow through the singularity to a reflected brane N , which has a big bang singularity and which can be viewed as a brane in a reflected Schwarzschild-AdS(n+2) bulk N . The joint branes N ∪ N can thus be naturally embedded in R × S0, hence there exists a second possibility of defining a smooth transition from big crunch to big bang by requiring that N ∪ N forms a C∞-hypersurface in R × S0. This last notion of a smooth transition also applies to branes that are not ARW spaces, allowing a wide range of possible equations of state.
14951562
The mass of a Lorentzian manifold
We define a physically reasonable mass for an asymptotically Robertson-Walker (ARW) manifold which is uniquely defined in the case of a normalized representation.
55245277
A unified quantum theory II: gravity interacting with Yang-Mills and spinor fields
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space $(V,\om)$ and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space $\so$ of a given Riemannian metric $\rho_{ij}$. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms.
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.
123586923
A resonance analysis of electroproduction data
We determinedN* electromagnetic transition form factors using π- and η-electroproduction data in the resonance region published till December, 1978. We discuss problems with the results obtained by various experimental groups. The method of analysis is a modification of the procedure used by Devenish and Lyth. Using the new photoproduction results of Barbour and Crawford and the δ- and η-data published till 1978, we are able to parametrise all multipoles in a unique way and to describe the background without further high energy input. Thus a better description of the data with less assumptions is achieved. However, it is still not possible to determine more multipoles than previously.
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.