On Nonperturbative Calculations in Quantum Electrodynamics

A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach allows one to take into account the gauge invariance conditions (Ward identities) and to perform the renormalization program. The iteration scheme can be realized in two versions. The first one ("perturbative vacuum") corresponds to chain summation in the diagram language. In this version in four-dimensional theory the non-physical singularity (Landau pole) arises which leads to the triviality of the renormalized theory. The second version ("nonperturbative vacuum") corresponds to ladder summation and permits one to make non-perturbative calculations of physical quantities in spite of the triviality problem. For chiral-symmetrical leading approximation two terms of the expansion of the first-step vertex function over photon momentum are calculated. A formula for anomalous magnetic moment is obtained. A problem of dynamical chiral symmetry breaking (DCSB) is considered, the calculations are performed for renormalized theory in Minkowsky space. In the strong coupling region DCSB-solutions arise. For the renormalized theory a DCSB-solution is also possible in the weak coupling region but with a subsidiary condition on the value of $\alpha$.Comment: 31 pages, Plain LaTex, no figures. Journal version: some discussion and refs. are adde

On the roots of the Poincare structure of asymptotically flat spacetimes

The analysis of vacuum general relativity by R. Beig and N. O Murchadha (Ann. Phys. vol 174, 463 (1987)) is extended in numerous ways. The weakest possible power-type fall-off conditions for the energy-momentum tensor, the metric, the extrinsic curvature, the lapse and the shift are determined, which, together with the parity conditions, are preserved by the energy-momentum conservation and the evolution equations. The algebra of the asymptotic Killing vectors, defined with respect to a foliation of the spacetime, is shown to be the Lorentz Lie algebra for slow fall-off of the metric, but it is the Poincare algebra for 1/r or faster fall-off. It is shown that the applicability of the symplectic formalism already requires the 1/r (or faster) fall-off of the metric. The connection between the Poisson algebra of the Beig-O Murchadha Hamiltonians and the asymptotic Killing vectors is clarified. The value H[K^a] of their Hamiltonian is shown to be conserved in time if K^a is an asymptotic Killing vector defined with respect to the constant time slices. The angular momentum and centre-of-mass, defined by the value of H[K^a] for asymptotic rotation-boost Killing vectors K^a, are shown to be finite only for 1/r or faster fall-off of the metric. Our center-of-mass expression is the difference of that of Beig and O Murchadha and the spatial momentum times the coordinate time. The spatial angular momentum and this centre-of-mass form a Lorentz tensor, which transforms in the correct way under Poincare transformations.Comment: 34 pages, plain TEX, misleading notations changed, discussion improved and corrected, appearing in Class. Quantum Gra

Assessment of mesoscale eddy parameterizations for coarse resolution ocean models

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 1999Climate simulation with numerical oceanic models requires a proper parameterization scheme in order to represent the effects of unresolved mesoscale eddies. Even though a munber of schemes have been proposed and some have led to improvements in the simulation of the bulk climatological properties, the success of the parameterizations in representing the mesoscale eddies has not been investigated in detail. This thesis examines the role of eddies in a 105-years long basin scale eddy resolving simulation with the MIT General Circulation Model (GCM) forced by idealized wind stress and relaxation to prescribed meridional temperature; this thesis also evaluates the Fickian diffusive, the diabatic Green-Stone (GS) and the quasi-adiabatic Gent-McWilliams (GM) parameterizations in a diagnostic study and a series of coarse resolution experiments with the same model in the same configuration. The mesoscale eddies in the reference experiment provide a significant contribution to the thermal balance in limited areas of the domain associated with the upper 1000M of the boundary regions. Specifically designed diagnostic tests of the schemes show that the horizontal and vertical components of the parameterized flux are not simultaneously downgradient to the eddy heat flux. The transfer vectors are more closely aligned with the isopycnal surfaces for deeper layers, thus demonstrating the adiabatic nature of the eddy heat flux for deeper layers. The magnitude of the coefficients is estimated to be consistent with traditionally used values. However, the transfer of heat associated with timedependent motions is identified as a complicated process that cannot be fully explained with any of the local parameterization schemes considered. The eddy parameterization schemes are implemented in the coarse resolution configuration with the same model. A series of experiments exploring the schemes' parameter space demonstrate that Fickian diffusion has the least skill in the climatological simulations because it overestimates the temperature of the deep ocean and underestimates the total heat transport. The GS and GM schemes perform better in the simulation of the bulk climatological properties of the reference solution, although the GM scheme in particular produces an ocean that is consistently colder than the reference state. Comparison of the eddy heat flux divergence with the parameterized divergences for typical parameter values demonstrates that the success of the schemes in the climatological simulation is not related to the representation of the eddy heat flux but to the representation of the overall internal mixing processes.The financial support for this research was provided by ONR grant number NOOOl4- 98-1-0881, Alliance for Global Sustainability and American Automobile Manufactures Association

Chiral-loop and vector-meson contributions to eta -> pi pi gamma gamma decays

The process eta -> pi0 pi0 gamma gamma is discussed in Chiral Perturbation Theory (ChPT) extending two recent analyses. Special attention is devoted to one-loop corrections, eta-eta' mixing effects and vector-meson dominance of ChPT counter-terms. The less interesting eta -> pi^+ pi^- gamma gamma transition is briefly discussed too.Comment: 15 pages, 3 Postscript figures, uses epsfig.st

USp(2k) Matrix Model: Nonperturbative Approach to Orientifolds

We discuss theoretical implications of the large k USp(2k) matrix model in zero dimension. The model appears as the matrix model of type IIB superstrings on a large $T^{6}/Z^{2}$ orientifold via the matrix twist operation. In the small volume limit, the model behaves four dimensional and its T dual is six-dimensional worldvolume theory of type I superstrings in ten spacetime dimensions. Several theoretical considerations including the analysis on planar diagrams, the commutativity of the projectors with supersymmetries and the cancellation of gauge anomalies are given, providing us with the rationales for the choice of the Lie algebra and the field content. A few classical solutions are constructed which correspond to Dirichlet p-branes and some fluctuations are evaluated. The particular scaling limit with matrix T duality transformation is discussed which derives the F theory compactification on an elliptic fibered K3.Comment: LaTeX, 29 pages, 3 figures. PostScript problems are fixe