On Renormalization Group Flows and Polymer Algebras

In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function the RG equations are reduced to flow equations of a finite number of coupling constants. Generating functions of Greens functions are expressed by polymer activities. Polymer activities are useful for solving the large volume and large field problem in field theory. The RG flow of the polymer activities is studied by the introduction of polymer algebras. The definition of products and recursive functions replaces cluster expansion techniques. Norms of these products and recursive functions are basic tools and simplify a RG analysis for field theories. The methods will be discussed at examples of the $\Phi^4$-model, the $O(N)$ $\sigma$-model and hierarchical scalar field theory (infrared fixed points).Comment: 32 pages, LaTeX, MS-TPI-94-12, Talk presented at the conference ``Constructive Results in Field Theory, Statistical Mechanics and Condensed Matter Physics'', 25-27 July 1994, Palaiseau, Franc

Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas

With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the boundary of the dipole region in the activity-temperature phase-space.Comment: 61 pages, 2 figure

Superior Capsule Reconstruction:What Do We Know?

The management of irreparable rotator cuff tears remains challenging. Since its introduction by Mihata in 2012, superior capsule reconstruction (SCR) has grown in popularity at an astonishingly rapid rate. The aim of this article is to provide a comprehensive review of the available literature, in order to highlight what has so far been published on SCR, covering all aspects including biomechanical, clinical and radiological studies as well as descriptions of the various techniques for performing the procedure. The short-term clinical results of SCR are promising, but there is need for further long-term studies, as well as randomised controlled trials comparing SCR to other treatment modalities for irreparable rotator cuff tears. Further imaging studies looking at graft healing rates are also required as the healing rates published so far are variable. Additionally, the mechanism of action by which SCR delivers good short-term functional outcomes needs further clarification, as does the importance of the choice of graft type and thickness

Scale Invariance in disordered systems: the example of the Random Field Ising Model

We show by numerical simulations that the correlation function of the random field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this non perturbative phenomenon is not particular to the RFIM in 3-d. It is generic for disordered systems in two dimensions and may also happen in other three dimensional disordered systems

Relativistic Lee Model on Riemannian Manifolds

We study the relativistic Lee model on static Riemannian manifolds. The model is constructed nonperturbatively through its resolvent, which is based on the so-called principal operator and the heat kernel techniques. It is shown that making the principal operator well-defined dictates how to renormalize the parameters of the model. The renormalization of the parameters are the same in the light front coordinates as in the instant form. Moreover, the renormalization of the model on Riemannian manifolds agrees with the flat case. The asymptotic behavior of the renormalized principal operator in the large number of bosons limit implies that the ground state energy is positive. In 2+1 dimensions, the model requires only a mass renormalization. We obtain rigorous bounds on the ground state energy for the n-particle sector of 2+1 dimensional model.Comment: 23 pages, added a new section, corrected typos and slightly different titl

Local covariant quantum field theory over spectral geometries

A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling (possibly noncommutative) globally hyperbolic spacetimes is introduced in terms of so-called globally hyperbolic spectral triples. The concept is further generalized to a category of globally hyperbolic spectral geometries whose morphisms describe the generalization of isometric embeddings. Then a local generally covariant quantum field theory is introduced as a covariant functor between such a category of globally hyperbolic spectral geometries and the category of involutive algebras (or *-algebras). Thus, a local covariant quantum field theory over spectral geometries assigns quantum fields not just to a single noncommutative geometry (or noncommutative spacetime), but simultaneously to ``all'' spectral geometries, while respecting the covariance principle demanding that quantum field theories over isomorphic spectral geometries should also be isomorphic. It is suggested that in a quantum theory of gravity a particular class of globally hyperbolic spectral geometries is selected through a dynamical coupling of geometry and matter compatible with the covariance principle.Comment: 21 pages, 2 figure

Distal triceps rupture repair: The triceps pulley-pullover technique

Distal triceps rupture is an uncommon but debilitating injury, and surgical fixation is almost invariably warranted. A number of techniques have been described in the literature in which combinations of transosseous tunnels and bone anchors have been used. We describe a modification to existing techniques-the triceps pulley-pullover technique with all-suture anchors. This technique minimizes bone loss, while maximizing the bone-tendon contact area and creating a double-row repair to optimize strength and healing

On the Convergence to the Continuum of Finite Range Lattice Covariances

In J. Stat. Phys. 115, 415-449 (2004) Brydges, Guadagni and Mitter proved the existence of multiscale expansions of a class of lattice Green's functions as sums of positive definite finite range functions (called fluctuation covariances). The lattice Green's functions in the class considered are integral kernels of inverses of second order positive self adjoint operators with constant coefficients and fractional powers thereof. The fluctuation coefficients satisfy uniform bounds and the sequence converges in appropriate norms to a smooth, positive definite, finite range continuum function. In this note we prove that the convergence is actually exponentially fast.Comment: 14 pages. We have added further references as well as a proof of Corollary 2.2. This version submitted for publicatio

The Gravitational Demise of Cold Degenerate Stars

We consider the long term fate and evolution of cold degenerate stars under the action of gravity alone. Although such stars cannot emit radiation through the Hawking mechanism, the wave function of the star will contain a small admixture of black hole states. These black hole states will emit radiation and hence the star can lose its mass energy in the long term. We discuss the allowed range of possible degenerate stellar evolution within this framework.Comment: LaTeX, 18 pages, one figure, accepted to Physical Review