SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

On the 1/n expansion

The 1/n expansion is considered for then-component non-linear -model (classical Heisenberg model) on a lattice of arbitrary dimensions. We show that the expansion for correlation functions and free energy is asymptotic, for all temperatures above the spherical model critical temperature. Furthermore, the existence of a mass gap is established for these temperatures andn sufficiently large.Supported in part by the National Science Foundation under Grant PHY 79-16812     

Probabilistic Estimates for the Two-Dimensional Stochastic Navier–Stokes Equations

We consider the Navier–Stokes equation on a two-dimensional torus with a random force, white noise in time, and analytic in space, for arbitrary Reynolds number R. We prove probabilistic estimates for the long-time behavior of the solutions that imply bounds for the dissipation scale and energy spectrum as R.     

Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

Renormalization group and asymptotics of solutions of nonlinear parabolic equations

We present a general method for studying long-time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion-type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity. In an accompanying paper, [5], the method is applied to systems of equations where some variables are “slaved,” such as the complex Ginzburg-Landau equation. © 1994 John Wiley & Sons, Inc.