Renormalization Research Articles

Approximately Einstein ACH metrics, volume renormalization, and an invariant for contact manifolds

(Metriques presque d'Einstein ACH, renormalisation de volume, et un invariant pour les varietes de contact) Pour toute variete lisse compacte M munie d'une structure de contact H et d'une structure presque CR partiellement integrable J, nous demontrons l'existence et l'unicite, a des termes d'erreur de degre superieur et action de diffeomorphisme pres, d'une metrique presque d'Einstein ACH (asymptotiquement complexe hyperbolique) g sur M x (-1,0). Nous considerons le developpement asymptotique, en des puissances d'une fonction definissante speciale, du volume de M x (-1,0) par rapport a g. Nous demontrons que le coefficient du terme logarithmique est independant de J (et du choix de la forme de contact θ); par consequent, c'est un invariant de la structure de contact H. La metrique presque d'Einstein ACH g est une generalisation de la metrique presque d'Einstein kahlerienne complete g + de Fefferman sur les domaines strictement pseudoconvexes. Elle a egalement un comportement asymptotique similaire au bord. Le present travail demontre que le coefficient du terme logarithmique CR-invariant dans le developpement asymptotique du volume de g + est, en fait, un invariant de contact. Nous traitons egalement quelques implications possibles pour la Q-courbure CR. La methode de trouver g par le biais de series formelles comporte une obstruction d'ordre fini. Nous demontrons que cette obstruction est partiellement donnee par une 1-forme sur H*. Ceci est un resultat nouveau particulier au contexte partiellement integrable.

The etiology and treatment of significant societal problems: Behaviorists diving into murky Waters with Strangers.

In January of 2007, I edited an issue of the International Journal of Behavior Consultation and Therapy (IJBCT) (see Golden, 2007) encouraging behavior analysts to consider the problems of children who are non-responders to the typical behavioral techniques and suggested that behavior analysts consider literature and clinical approaches from other sources. Specifically, these children included those with attachment problems, exhibiting difficulties with and behaviors. In this issue, I am again appealing to behavior analysts to broaden their focus to include populations that are not normally the purview of these professionals. In the 2007 issue of the Behavior Analyst, Kangas and Vaidya presented data on the number of presentations that dealt with each of the applied categories of topic areas at the annual conventions of the Association for Behavior Analysis (ABA) from 1980 to 2007. At the 2007 annual convention of the ABA, in the combined categories of Clinical, Family, and Behavioral Medicine (C/F/BM) there were a total of 107 presentations compared to 325 presentations in the combined categories of Developmental Disabilities and Autism (DD/AUT). That means that there were three times as many presentations at the 2007 convention about DD/AUT than there were about C/F/BM. At the 2009 convention, I chaired a symposium in which I outlined likely reasons why behaviorists more frequently deal with individuals with DD/AUT than with other types of disorders or problems. They are as follows: 1. The black box (Uttal, 1999) of their inner world is much less complicated to study. When clinicians deal with individuals with emotional and moral behavioral issues, they have to contend with the possibility of complex underlying psychological constructs such as: higher level cognitions, ambivalent emotions, nuances of social interaction, consciousness, a conscience, and sense of self- and other-perspectives. 2. The identification and delivery of reinforcers and punishers are much easier to identify and control. Clinicians and parents can control computer or TV access, preferred toys or items, social reinforcers and tokens, to name a few reinforcers that work well with children with DD/AUT. It is a lot more difficult (not to mention, unethical) to deliver contingently and/or limit access to tobacco, sexual activity, drugs/alcohol, gambling, prostitution, on-line pornography, the excitement of an ambulance arriving when cut your wrist, charging over your credit card limit, criminal behavior, etc. The point is, the clinician cannot use these as reinforcers, but if these are the individuals' most reinforcing activities, how do you compete with them? 3. The ramifications of following through and being consistent are much less drastic. When individuals with DD/AUT escalate their behavior during a tantrum, the worst ensuing consequences are usually either: aggression toward others, self-injurious behavior or running away to no particular destination. Not to minimize the seriousness of these behaviors, but they can be easily handled through environmental manipulation. However, when individuals with behavioral or problems escalate their behavior, the clinician is faced with consequences such as: threats/hurtful verbal statements, suicide/homicide or threats of these, running away to a life of homelessness, alcohol/substance abuse, elicit sexual activity, false allegations of abuse, triangulation of caregivers, and physical/sexual assault. 4. There exists a much narrower network of negative influences and there are more limited environments. Clinicians helping children with DD/AUT become frustrated when they must change the behavior of family members and school personnel in order help the children they serve. With individuals who have and behavior problems, there is a much wider sphere of influences and there are many more environments that impact behaviors. …

Automatic generation of Feynman rules in the Schrödinger functional

We provide an algorithm to generate vertices for the Schrödinger functional with an abelian background gauge field. The background field has a non-trivial color structure, therefore we mainly focus on a manipulation of the color matrix part. We propose how to implement the algorithm especially in python code. By using python outputs produced by the code, we also show how to write a numerical expression of vertices in the time-momentum as well as the coordinate space into a Feynman diagram calculation code. As examples of the applications of the algorithm, we provide some one-loop results, ratios of the Λ parameters between the plaquette gauge action and the improved gauge actions composed from six-link loops (rectangular, chair and parallelogram), the determination of the O( a) boundary counter term to this order, and the perturbative cutoff effects of the step scaling function of the Schrödinger functional coupling constant.

Cardy–Verlinde formula in Taub–NUT/Bolt–(A)dS space

We consider a finite action for a higher dimensional Taub–NUT/Bolt–(A)dS space via the so-called counter term subtraction method. In the limit of high temperature, we show that the Cardy–Verlinde formula holds for the Taub–Bolt–AdS metric and for the specific dimensional Taub–NUT–(A)dS metric, except for the Taub–Bolt–dS metric.

Eighth-order vacuum-polarization function formed by two light-by-light-scattering diagrams and its contribution to the tenth-order electrong−2

We have evaluated the contribution to the anomalous magnetic moment of the electron from six tenth-order Feynman diagrams which contain eighth-order vacuum-polarization function formed by two light-by-light-scattering diagrams connected by three photons. The integrals are constructed by two different methods. In the first method the subtractive counter terms are used to deal with ultraviolet (UV) singularities together with the requirement of gauge invariance. In the second method, the Ward-Takahashi identity is applied to the light-by-light-scattering amplitudes to eliminate UV singularities. Numerical evaluation confirms that the two methods are consistent with each other within their numerical uncertainties. Combining the two results statistically and adding small contribution from the muons and/or tau leptons, we obtain 0.000 399 9 (18) $(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$. We also evaluated the contribution to the muon $g\ensuremath{-}2$ from the same set of diagrams and found $\ensuremath{-}1.263\text{ }44\text{ }(14)$ $(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$.

Spatial Pattern of an Epidemic Model with Cross-diffusion

Pattern formation of a spatial epidemic model with both self- and cross-diffusion is investigated. From the Turing theory, it is well known that Turing pattern formation cannot occur for the equal self-diffusion coefficients. However, combined with cross-diffusion, the system will show emergence of isolated groups, i.e., stripe-like or spotted or coexistence of both, which we show by both mathematical analysis and numerical simulations. Our study shows that the interaction of self- and cross-diffusion can be considered as an important mechanism for the appearance of complex spatiotemporal dynamics in epidemic models.

Divergence-free nonrenormalizable models

A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of exhibiting a divergence-free perturbation analysis. To achieve this desirable goal it is necessary to reexamine the meaning of the free theory about which such a perturbation takes place.

The Evangelical Conversion Narrative: Spiritual Autobiography in Early Modern England (review)

Reviewed by: The Evangelical Conversion Narrative: Spiritual Autobiography in Early Modern England Carrie Hintz D. Bruce Hindmarsh . The Evangelical Conversion Narrative: Spiritual Autobiography in Early Modern England. Oxford University Press 2005. x, 384. US $110.00 The Evangelical Conversion Narrative offers a stimulating 'biography of a genre' from its seventeenth-century origins through its decline in the nineteenth century, with emphasis on the conversion narratives of the eighteenth-century evangelical revival. Drawing on hitherto unexplored archival sources, D. Bruce Hindmarsh offers critical insight into the way that laity and clergy alike framed their spiritual lives in narrative form. The book traces the cultural changes that shaped the conversion narratives of this period, including technological and social change, [End Page 246] and the reasons why individuals turned to religious community as a means of shaping their lives. After a brief exploration of the early modern origins of the conversion narrative, Hindmarsh offers a useful exploration of the transatlantic evangelical revival in the 1730s, with an emphasis on 'how plastic religious identity had become by the mid-eighteenth century.' This chapter also argues for the social dimensions of conversion 'to stimulate parallel experience and allow the formation of a narrative community.' Much of the book is given over to a consideration of how the doctrinal, cultural, and social differences between religious groups might have shaped the kinds of narratives produced by individual believers, whether the evangelical Presbyterians of the Cambuslang revival in Scotland, moderate Calvinists within the Church of England, or Moravians. Hindmarsh's rich account covers a wide cross-section of people in the period, in large part because of his impressive work with archives and primary sources. As one example among many, he recognizes the 'special significance' of a collection of letters to Charles Wesley in the John Rylands Library, which contains 'the diverse testimony of women and men, those literate and barely literate, and persons of higher and lower ranks in society.' Hindmarsh offers powerful analysis of the interaction of self and community in the period, noting that conversion narratives were 'located at the cusp of modernity but also sharing all the assumptions of a fading Christian hegemony,' thus involving 'both creativity and discovery, both individuation and discovery.' With this expansive understanding of life narratives, it is regrettable that Hindmarsh does not draw on contemporary life-writing theorists who work on 'relational autobiography' (such as Paul John Eakins, Richard Freadman, and Nancy K. Miller), although he uses classic theorists of individualistic autobiography (such as Georges Gusdorf and James Olney) very effectively. Any scholar of the eighteenth century might productively consult this book as an alternative to secular Enlightenment models of the self. In writing the 'biography of a genre' Hindmarsh takes on a challenging task. With historical sensitivity, deep research, and engaging writing he brings to life not just the conversion narrative genre but the thousands of people who turned to it to recount their experiences. Carrie Hintz Queens College, CUNY Copyright © 2008 University of Toronto Press Incorporated

Wilson lines and transverse-momentum dependent parton distribution functions: A renormalization-group analysis

The renormalization-group properties of gauge-invariant transverse-momentum dependent (TMD) parton distribution functions (PDF) in QCD are addressed. We perform an analysis of their leading-order anomalous dimensions, which are local quantities, making use of the renormalization properties of contour-dependent composite operators in QCD. We argue that attaching individual gauge links with transverse segments to quark fields in the light-cone gauge, the associated gauge contours are joined at light-cone infinity through a cusp-like junction point. We find that the renormalization effect on the junction point creates an anomalous dimension which has to be compensated in order to recover the results in a covariant gauge. To this end, we include in the definition of the TMD PDF an additional soft counter term (gauge link) along that cusped contour. We show that the eikonal factors entering this counter term are peculiar to the Mandelstam field formalism and are absent when one uses a direct gauge contour.

Bridgingp-wave π production and weak processes in few-nucleon systems with chiral perturbation theory

I study an aspect of chiral perturbation theory (\ensuremath{\chi}PT) that enables one to ``bridge'' different reactions. That is, an operator fixed in one of the reactions can then be used to predict the other. For this purpose, I calculate the partial-wave amplitude for the $p$-wave pion production ($\mathit{pp}\ensuremath{\rightarrow}\mathit{pn}{\ensuremath{\pi}}^{+}$) using the pion production operator from the lowest and the next nonvanishing orders. The operator includes a contact operator whose coupling has been fixed using a matrix element of a low-energy weak process ($\mathit{pp}\ensuremath{\rightarrow}{\mathit{de}}^{+}{\ensuremath{\nu}}_{e}$). I find that this operator does not reproduce the partial-wave amplitude extracted from experimental data, showing that the bridging over the reactions with significantly different kinematics is not necessarily successful. I study the dependence of the amplitude on the various inputs such as the $\mathit{NN}$ potential, the $\ensuremath{\pi}N\ensuremath{\Delta}$ coupling, and the cutoff. I argue the importance of a higher-order calculation. To gain an insight into a higher-order calculation, I add a higher-order counter term to the operator used above and fit the couplings to both the low-energy weak process and the pion production. The energy dependence of the partial-wave amplitude for the pion production is described by the operator consistently with the data. However, I find a result that tells us to be careful about the convergence of the chiral expansion for the $\mathit{pp}\ensuremath{\rightarrow}\mathit{pn}{\ensuremath{\pi}}^{+}$ reaction.

Renormalization, Wilson lines, and transverse-momentum-dependent parton-distribution functions

We perform an analysis of transverse-momentum dependent parton-distribution functions, making use of their renormalization properties in terms of their leading-order anomalous dimensions. We show that the appropriate Wilson line in the light cone gauge, associated with such quantities, is a cusped one at light cone infinity. To cancel the ensuing cusp anomalous dimension, we include in the definition of the transverse-momentum dependent parton-distribution functions an additional soft counter term (gauge link) along that cusped transverse contour. We demonstrate that this is tantamount to an ``intrinsic (Coulomb) phase,'' which accumulates the full gauge history of the color-charged particle.

Asymptotics and Hamiltonians in a first-order formalism

We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the spacetime. We address the subtle but important problems that arise because of logarithmic translations and super translations both in the Lagrangian and Hamiltonian frameworks. As a forthcoming paper will show, the treatment of higher dimensions is considerably simpler. Our first-order framework also suggests a new direction for generalizing the spectral action of non-commutative geometry.

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in finite volume. The resulted formula is very close to the known expression of the measure term in infinite volume with a single parameter integration, and would be useful in practical implementations.

A priori bounds for some infinitely renormalizable quadratics: II. Decorations

Une décoration de l’ensemble de Mandelbrot M est une partie de M découpée par deux rayons externes aboutissant à la pointe d’une petite copie de M attachée à la cardioïde principale. Dans cet article nous considérons des polynômes quadratiques infiniment renormalisables qui satisfont à la condition de décoration, à savoir que la combinatoire des opérateurs de renormalisation mis en jeu est sélectionnée à partir d’une famille finie de décorations. Pour cette classe d’applications, nous donnons des bornes a priori. Ces bornes impliquent la connexité locale des ensembles de Julia correspondants et celle de l'ensemble de Mandelbrot aux paramètres correspondants.

Renormalized solution for nonlinear degenerate problems in the whole space

Nous considerons l'equation parabolique degeneree general: u t - Δb(u) + div F(u) = f dans Q = ]0, T[xR N , T > 0. Nous supposons que le flux F est continu, b est continue et croissante au sens large et les deux fonctions ne sont pas necessairement lipschitziennes. Nous prouvons l'existence de solution renormalisee du probleme de Cauchy associe a cette equation avec des donnees (terme source et condition initiale) dans L 1 . Nous etablissons l'unicite de cette solution sous une condition dite de structure du type F(r) = F(b(r)) et sous une hypothese sur le module de continuite de b. La nouveaute dans le travail vient du fait que Ω = R N , u 0 , f ∈ L 1 , b, F ne sont pas des fonctions necessairement lipschitziennes et les techniques sont differentes de celles developpees dans les travaux anterieurs.

Physical register reference counting

Several proposed techniques including CPR (checkpoint processing and recovery) and NoSQ (no store queue) rely on reference counting to manage physical registers. However, the register reference counting mechanism itself has received surprisingly little attention. This paper fills this gap by describing potential register reference counting schemes for NoSQ, CPR, and a hypothetical NoSQ/CPR hybrid. Although previously described in terms of binary counters, we find that reference counts are actually more naturally represented as matrices. Binary representations can be used as an optimization in specific situations.

Renormalization Proof for Massive $$\phi_4^4$$ Theory on Riemannian Manifolds

In this paper we present an inductive renormalizability proof for massive $\vp_4^4$ theory on Riemannian manifolds, based on the Wegner-Wilson flow equations of the Wilson renormalization group, adapted to perturbation theory. The proof goes in hand with bounds on the perturbative Schwinger functions which imply tree decay between their position arguments. An essential prerequisite are precise bounds on the short and long distance behaviour of the heat kernel on the manifold. With the aid of a regularity assumption (often taken for granted) we also show, that for suitable renormalization conditions the bare action takes the minimal form, that is to say, there appear the same counter terms as in flat space, apart from a logarithmically divergent one which is proportional to the scalar curvature.

Giant magnons under NS-NS and Melvin fields

The giant magnon is a rotating spiky string configuration which has the same dispersion relation between the energy and angular momentum as that of a spin magnon. In this paper we investigate the effects of the NS-NS and Melvin fields on the giant magnon. We first analyze the energy and angular momenta of the two-spin spiky D-string moving on the $AdS_3\times S^1$ with the NS-NS field. Due to the infinite boundary of the AdS spacetime the D-string solution will extend to infinity and it appears the divergences. After adding the counter terms we obtain the dispersion relation of the corresponding giant magnon. The result shows that there will appear a prefactor before the angular momentum, in addition to some corrections in the sine function. We also see that the spiky profile of a rotating D-string plays an important role in mapping it to a spin magnon. We next investigate the energy and angular momentum of the one-spin spiky fundamental string moving on the $R \times S^2$ with the electric or magnetic Melvin field. The dispersion relation of the corresponding deformed giant magnon is also obtained. We discuss some properties of the correction terms and their relations to the spin chain with deformations.

Sharp interface tracking using the phase-field equation

A general interface tracking method based on the phase-field equation is presented. The zero phase-field contour is used to implicitly track the sharp interface on a fixed grid. The phase-field propagation equation is derived from an interface advection equation by expressing the interface normal and curvature in terms of a hyperbolic tangent phase-field profile across the interface. In addition to normal interface motion driven by a given interface speed or by interface curvature, interface advection by an arbitrary external velocity field is also considered. In the absence of curvature-driven interface motion, a previously developed counter term is used in the phase-field equation to cancel out such motion. Various modifications of the phase-field equation, including nonlinear preconditioning, are also investigated. The accuracy of the present method is demonstrated in several numerical examples for a variety of interface motions and shapes that include singularities, such as sharp corners and topology changes. Good convergence with respect to the grid spacing is obtained. Mass conservation is achieved without the use of separate re-initialization schemes or Lagrangian marker particles. Similarities with and differences to other interface tracking approaches are emphasized.

A holographic dual of CFT with flavor on de Sitter space

We introduce a D7-brane probe in AdS_5 x S^5 background in a way that the 4d part of the induced metric on D7-brane becomes 4d de-Sitter space (dS_4) inside AdS_5 instead of 4d Minkowski space. Although supersymmetry is completely broken, we obtain a static configuration and show the absence of dynamical tachyonic modes. Following holographic renormalization we renormalize the Dirac-Born-Infeld action of D7-brane and we completely fix the counter terms including finite contributions from the consistency under various limits. Through the AdS/CFT correspondence we study the chiral condensate and meson spectrum of CFT dual theory on dS_4 where the energy scale is identified with the direction normal to dS_4 space in AdS_5. We identify and properly reproduce the finite temperature effects on dS_4. Our results support the holographic interpretation of the Randall-Sundrum model with non fine-tuned dS_4 brane(s) and the holography between AdS_p (or dS_p) bulk gravity and CFT on dS_{p-1} called the (A)dS/dS correspondence.