Ondelettes and phase cell cluster expansions, a vindication

Y. Meyer has recently developed a particularly useful o.n. basis for L 2 ( R d ). Expansions using this basis, i.e. expansions into “ondelettes” or “wavelets,” have yielded important new results in soft and hard analysis. The expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions, a formalism already developed by the authors using other related bases. Adoption of ondelettes expansions into the phase cell program gives improvements of some extant results, and excises an early error.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46467/1/220_2005_Article_BF01206144.pd

A note on cluster expansions, tree graph identities, extra 1/ N ! factors!!!

We draw attention to a new tree graph identity which substantially improves on the usual tree graph method of proving convergence of cluster expansions in statistical mechanics and quantum field theory. We can control expansions that could not be controlled before.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43217/1/11005_2004_Article_BF00420041.pd

Navier and stokes meet the wavelet

We work in the space ℱ = ℱ ε of divergence-free measurable vector fields on R 3 complete in the norm ‖ ‖′, where for some fixed ε>0. B(x, R) is the ball of radius R centered at x . Given an initial velocity distribution (0) in ℱ, we find ( x,t ) for 0≦ t ≦ T = T (‖ v (0)‖'), T >0, such that ( x,t ) is the unique strong solution of the Navier-Stokes equations, in a suitable sense.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46484/1/220_2005_Article_BF02097391.pd

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Chiral Symmetry and the Nucleon's Vector Strangeness Form Factors

The nucleon's strange-quark vector current form factors are studied from the perspective of chiral symmetry. It is argued that chiral perturbation theory cannot yield a prediction for the strangeness radius and magnetic moment. Arrival at definite predictions requires the introduction of additional, model-dependent assumptions which go beyond the framework of chiral perturbation theory. A variety of such model predictions is surveyed, and the credibility of each is evaluated. The most plausible prediction appears in a model where the unknown chiral counterterms are identified with $t$-channel vector meson exchange amplitudes. The corresponding prediction for the mean square Dirac strangeness radius is $\langle r_s^2\rangle = 0.24$ fm$^2$, which would be observable in up-coming semileptonic determinations of the nucleon's strangeness form factors.Comment: LaTex 31 pages, four figures available from authors

1+1 dimensional QCD with fundamental bosons and fermions

We analyze the properties of mesons in 1+1 dimensional QCD with bosonic and fermionic ``quarks'' in the large \nc limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of ``mesons'' formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.Comment: 20 pages, harvmac, 5 figure

Stability and Instability of Relativistic Electrons in Classical Electro magnetic Fields

The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary classical magnetic field of finite energy. Despite the previously known facts that ordinary nonrelativistic matter with magnetic fields, or relativistic matter without magnetic fields is already unstable when the fine structure constant, is too large it is noteworthy that the combination of the two is still stable provided the projection onto the positive energy states of the Dirac operator, which defines the electron, is chosen properly. A good choice is to include the magnetic field in the definition. A bad choice, which always leads to instability, is the usual one in which the positive energy states are defined by the free Dirac operator. Both assertions are proved here.Comment: LaTeX fil

Gauge gravity duality for d-wave superconductors: prospects and challenges

We write down an action for a charged, massive spin two field in a fixed Einstein background. Despite some technical problems, we argue that in an effective field theory framework and in the context of the AdS/CFT correspondence, this action can be used to study the properties of a superfluid phase transition with a d-wave order parameter in a dual strongly interacting field theory. We investigate the phase diagram and the charge conductivity of the superfluid phase. We also explain how possible couplings between the spin two field and bulk fermions affect the fermion spectral function.Comment: 42 pages, 6 figure

Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors

Dispersion relations allow for a coherent description of the nucleon electromagnetic form factors measured over a large range of momentum transfer, $Q^2 \simeq 0 \ldots 35$ GeV$^2$. Including constraints from unitarity and perturbative QCD, we present a novel parametrisation of the absorptive parts of the various isoscalar and isovector nucleon form factors. Using the current world data, we obtain results for the electromagnetic form factors, nucleon radii and meson couplings. We stress the importance of measurements at large momentum transfer to test the predictions of perturbative QCD.Comment: 33 pp, RevTEX or plain LaTeX, 7 figures (in ffig.uu