A generalized Reissner-Nordström solution

A new class of solutions to the Einstein-Maxwell equations is presented; it stands in the same relation to the Robinson & Robinson (1969) metrics as the Reissner-Nordström solution to Schwarzschild's.This work was supported in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, under Contract F33615-68-C-1675; Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR Grant No. 903-67; National Aeronautics and Space Administration under NASA Grant No. NGL 44-004-001; and National Science Foundation under Travel Grant GP-14505.     

Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV

We systematize the study of reflection positivity in statistical mechanical models, and thereby two techniques in the theory of phase transitions: the method ofinfrared bounds and the chessboard method of estimating contour probabilities in Peierls arguments. We illustrate the ideas by applying them to models with long range interactions in one and two dimensions. Additional applications are discussed in a second paper.Research partially supported by US National Science Foundation under Grant MPS-75-11864Research partially supported by Canadian National Research Council under Grant A4015Research partially supported by US National Science Foundation under Grant MCS-75-21684-A01     

A Rigorous Treatment of Energy Extraction from a Rotating Black Hole

The Cauchy problem is considered for the scalar wave equation in the Kerr geometry. We prove that by choosing a suitable wave packet as initial data, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain. We also compute the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou’s result for the Penrose process. The main mathematical tool is our previously derived integral representation of the wave propagator. Research supported in part by the Deutsche Forschungsgemeinschaft. Research supported by NSERC grant # RGPIN 105490-2004. Research supported in part by the Humboldt Foundation and the National Science Foundation, Grant No. DMS-0603754. Research supported in part by the NSF, Grant No. 33-585-7510-2-30.     

Effective action and cluster properties of the abelian Higgs model

We continue our program to establish the Higgs mechanism and mass gap for the abelian Higgs model in two and three dimensions. We develop a multiscale cluster expansion for the high frequency modes of the theory, within a framework of iterated renormalization group transformations. The expansions yield decoupling properties needed for a proof of exponential decay of correlations. The result of this analysis is a gauge invariant unit lattice theory with a deep Higgs potential of the shape required to exhibit the Higgs mechanism.Research partially supported by the National Science Foundation under Grant DMS-8602207 and by the Air Force Office of Scientific Research under Grant AFOSR-86-0229Alfred P. Sloan Research Fellow. Research partially supported by the National Science Foundation under Grants PHY-84-13285 and PHY-85-13554Research partially supported by the National Science Foundation under Grant PHY-85-13554     

Distributional limits of renormalized Feynman integrals with zero-mass denominators

It is shown that the 0 limits of renormalized Feynman integrals exist and define Lorentz invariant tempered distributions in the external momenta. The proof applies to the case where some or all particle masses vanish.Research supported in part by the National Science Foundation Grant MPS-74-21778.Research supported in part by the National Science Foundation Grant GP-43758.     

Contact transformations and conformal group. III. Finite nonrelativistic transformations

Contact conformal transformations (as defined in a previous work) are integrated giving the finite form of these transformations. Some properties of such a group of motions are pointed out.Research supported in part by the National Science Foundation under Grant No. MPS75-20427.On leave of absence from Departamento de Fisica Matematica, Universidad de Salamanca, Spain.     

A note on reflection positivity

We establish reflection positivity of covariance operators, using properties of Dirichlet or Neumann boundary data.Supported in part by National Science Foundation Grant No. PHY 78-08066.Supported in part by National Science Foundation Grant No. PHY 77-18762.     

Topology of monopole catalysis

We give the necessary mathematical conditions for strong monopole catalysis.Researach supported in part by the National Science Foundation under Grant No PHY 82-15249.     

On determinants of Laplacians on Riemann surfaces

Determinants of Laplacians on tensors and spinors of arbitrary weights on compact hyperbolic Riemann surfaces are computed in terms of values of Selberg zeta functions at half integer points.Research supported in part by the U.S. Department of EnergyResearch supported in part by the National Science Foundation under Grant DMS-84-02710     

Rigorous results for general ising ferromagnets

Several new results are given concerning the Lee-Yang theorem, the GHS inequality, and spin-1/2 approximations for general Ising ferromagnets, and the extension of these results to vector spin models is discussed.Research supported in part by National Science Foundation Grant MPS 74-04870 A01.     

There are no classical glueballs

I show that there are no finite-energy non-singular solutions of classical Yang-Mills theory in four-dimensional Minkowski space that do not radiate energy out to spatial infinity. Finite-energy non-singular solutions that are either static or periodic in time, are a fortiori non-radiant; thus this generalizes earlier theorems that state that there are no such solutions.Research supported in part by the National Science Foundation under Grant No. PHY75-20427     

Quark confinement in the two-dimensional lattice Higgs-Villain model

We prove quark confinement in the two-dimensional lattice Higgs-Villain model in the weak coupling region by using a Kirkwood-Salsburg equations for unbounded spins.Research partially supported by the National Science Foundation under Grant PHY-77-18762On leave from Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada. Research partially supported by National Research Council under Grant A4015On leave from Istituto di Fisica Teorica, Napoli, Italy     

Propagators and renormalization transformations for lattice gauge theories. II

We continue the studies of the Paper I and extend the results of this paper to operators defined by restrictions on different scales, or by renormalization transformations of different orders.Research supported in part by the National Science Foundation under Grant PHY-82-03669     

Convergence theorems for renormalized Feynman integrals with zero-mass propagators

A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions, for a wide class of theories with zero-mass propagators.Research supported in part by National Science Foundation Grant MPS-74-21778.     

Propagators for lattice gauge theories in a background field

We prove regularity and decay properties for propagators connected with the renormalization group method in lattice gauge theories. These propagators depend on an external gauge field configuration, called a background field.Research supported in part by the National Science Foundation under Grant PHY-82-0369     

Ornstein-Zernike behavior for self-avoiding walks at all noncritical temperatures

We prove that the self-avoiding walk has Ornstein-Zernike decay and some related properties for all noncritical temperatures at which the model is defined.National Science Foundation Postdoctoral Research Fellows. Work supported in part by the National Science Foundation under Grants No. PHY-82-03669 and MCS-81-20833     

An exact solution of Laplace's equation for cuspidal geometry

An exact solution of Laplace's equation is obtained for a system of conducting electrodes with cuspidal symmetry. The significance of this result in predicting and verifying the equilibrium configuration of a rotationally symmetric conducting fluid subject to electrostatic stress is discussed.This work was supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-8108829     

Group theoretical nature of Bäcklund transformations

The purpose of this paper is to establish the group theoretical nature of Bäcklund transformations admitted by evolution equations. This result can be easily extended to other types of equations.Research supported in part by the National Science Foundation, Grant MCS78-03036.     

Dark matter and inflation

I demonstrate that dark matter consisting of any type or types of stable weakly interacting elementary particle is incompatible with the minimal predictions of inflation, based on present observation of galaxy clustering, and assuming galaxies are good tracers of mass in the universe. If we wish to resolve this problem by particle physics alone, we seem to be driven to the possibility that the initial dark matter was unstable.Research supported in part by the National Science Foundation under Grant No. PHY-82-15249 and also by the NSERC (Canada).This essay received the first award from the Gravity Research Foundation for the year 1984-Ed.     

The Hartree-Fock theory for Coulomb systems

For neutral atoms and molecules and positive ions and radicals, we prove the existence of solutions of the Hartree-Fock equations which minimize the Hartree-Fock energy. We establish some properties of the solutions including exponential falloff.Research partially supported by U.S. National Science Foundation Grant MCS-75-21684Research partially supported by U.S. National Science Foundation under Grants MPS-75-11864 and MPS-75-20638. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, NJ08540, USA