renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

automatic search for fmri connectivity mapping an alternative to granger causality testing using formal equivalences among sem path modeling var and unified sem modeling the relationships among brain regions of interest rois carries unique potential to explicate how the brain orchestrates information processing however hurdles arise when using functional mri data variation in roi activity contains sequential dependencies and shared influences on synchronized activation consequently both lagged and contemporaneous relationships must be considered for unbiased statistical parameter estimation identifying these relationships using a data driven approach could guide theory building regarding integrated processing the present paper demonstrates how the unified sem attends to both lagged and contemporaneous influences on roi activity additionally this paper offers an approach akin to granger causality testing lagrange multiplier testing for statistically identifying directional influence among rois and employs this approach using an automatic search procedure to arrive at the optimal model rationale for this equivalence is offered by explicating the formal relationships among path modeling vector autoregression and unified sem when applied to simulated data biases in estimates which do not consider both lagged and contemporaneous paths become apparent finally the use of unified sem with the automatic search procedure is applied to an empirical data example

parametric representation of rank d tensorial group field theory abelian models with kinetic term sum_s p_s mu we consider the parametric representation of the amplitudes of abelian models in the so called framework of rank d tensorial group field theory these models are called abelian because their elds live on

construction of a non trivial planar field theory with ultraviolet stable fixed point we study a 4 4 planar euclidean quantum field theory with propagator 1 p 2 2 0 with the help of the tree expansion of gallavotti and nicolo 1 this non renormalizable theory is shown to have a non trivial ultraviolet stable fixed point at negative coupling constant the vicinity of the fixed point is discussed

construction of the hierarchical φ4 trajectory we study the invariant unstable manifold of the trivial renormalization group fixed point tangent to the 4 vertex in the hierarchical approximation we parametrize it by a running 4 coupling with linear step function the manifold is studied as a fixed point of the renormalization group composed with a flow of the running coupling we present a rigorous construction of it beyond perturbation theory by means of a contraction mapping starting from a perturbative approximant of order seven we obtain a convergent representation in dimensions 2 d 28 9 with certain restrictions the perturbative approximant is logarithmically divergent in d 3 dimensions

mayer expansions and the hamilton jacobi equation we review the derivation of wilson s differential equation in infinitely many variables which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal integration out is performed we show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic the resulting series solutions are generalizations of the mayer expansion in statistical mechanics the differential equation approach gives a remarkable identity for connected parts and precise estimates which include criteria for convergence of iterated mayer expansions applications include the yukawa gas in two dimensions past the 4 threshold and another derivation of some earlier results of gopfert and mack

some classes of renormalizable tensor models we identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property mainly a version of the rank 3 tensor model as defined by ben geloun and samary ann henri poincare 14 1599 2013 e print arxiv 1201 0176 hep th 10 1007 s00023 012 0225 5 and the grosse wulkenhaar model in 4d and 2d generate three different classes of renormalizable models the proof of the renormalizability is fully performed for the first reduced model the same procedure can be applied for the remaining cases interestingly we find that due to the peculiar behavior of anisotropic wave function renormalizations the rank 3 tensor model reduced to a matrix model generates a simple super renormalizable vector model

renormalizable models in rank d geq 2 tensorial group field theory classes of renormalizable models in the tensorial group field theory framework are investigated the rank d tensor fields are defined over d copies of a group manifold g d u 1 d or g d su 2 d with no symmetry and no gauge invariance assumed on the fields in particular we explore the space of renormalizable models endowed with a kinetic term corresponding to a sum of momenta of the form p 2a a in 0 1 this study is tailored for models equipped with laplacian dynamics on gd case a 1 but also for more exotic nonlocal models in quantum topology case 0 a 1 a generic model can be written dim g d phi k d a where k is the maximal valence of its interactions using a multi scale analysis for the generic situation we identify several classes of renormalizable actions including matrix model actions in this specific instance we find a tower of renormalizable matrix models parametrized by k geq 4 in a second part of this work we study the uv behavior of the models up to maximal valence of interaction k 6 all rank d geq 3 tensor models proved renormalizable are asymptotically free in the uv all matrix models with k 4 have a vanishing function at one loop and very likely reproduce the same feature of the grosse wulkenhaar model commun math phys 256 305 2005

block renormalization group for euclidean fermions block renormalization group transformations rgt for lattice and continuum euclidean fermions in d dimensions are developed using fermionic integrals with exponential and function weight functions for the free field the sequence of actionsdk generated by the rgt from d the dirac operator are shown to have exponential decay uniform ink after rescaling to the unit lattice it is shown that the two point functiond 1 admits a simple telescopic sum decomposition into fluctuation two point functions which for the exponential weight rgt have exponential decay contrary to rg intuition the sequence of rescaled actions corresponding to the function rgt do not have uniform exponential decay and we give examples of initial actions in one dimension where this phenomena occurs for the exponenential weight rgt also

dimensional regularization and renormalization of qed we give an space definition of dimensional regularization suited to the tree expansion method of renormalization we apply the dimensionally regularized tree expansion to qed obtaining sharp bounds on the size of a renormalized graph subtractions are made with the lagrangian counterterms of the tree expansion not by minimal subtraction techniques and so do not entail a knowledge of the meromorphic structure of a graph as a function of dimension this renormalization procedure respects the ward identities and the counterterms required are gauge invariant

perturbation theory and non renormalizable scalar fields we study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of p d when one does not allow any renormalization besides the usual coupling constants mass and wave function renormalizations

a renormalization group proof of perturbative renormalizability this paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean 4 4 theory its aim is partly pedagogical by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages the present version is based on the renormalized tree expansion adapted to the continuous renormalization group all detailed results are proved by induction on the size of the tree the continuous rg version presented here has one big advantage over the discrete rg version discussed elsewhere in the continuous version a tree has a more restrictive structure there is a one to one correspondence between forks of the tree and lines of feynman graphs this extra structure eliminates the need to introduce feynman graphs in the first place it also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

the hierarchicalφ4 trajectory by perturbation theory in a running coupling and its logarithmby perturbation theory in a running coupling and its logarithm we compute the hierarchical 4 in terms of perturbation theory in a running coupling in the three dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling numerical data are presented and the limits of validity explored we also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

renormalization group approach to lattice gauge field theories ii cluster expansions the fluctuation field integral constructed in part i is represented by the exponentiated cluster expansion it is proved that the terms of the expansion satisfy the inductive assumptions this completes the construction of the sequence of effective actions in the small field approximation

running coupling expansion for the renormalized φ 4 4 trajectory from renormalization invariance we formulate a renormalized running coupling expansion for the function and the potential of the renormalized 4 trajectory on four dimensional euclidean space time renormalization invariance is used as a first principle no reference is made to bare quantities the expansion is proved to be finite to all orders of perturbation theory the proof includes a large momentum bound on the connected free propagator amputated vertices

a lipatov bound for φ 4 4 euclidean field theory we bound the large order behavior of these pieces of the renormalized perturbation expansion for 4 4 which do not contain renormalons 1 the bound we obtain has the form of the leading asymptotic behavior computed by the lipatov method with the exact value of the lipatov constant therefore this paper is a step towards the rigorous study of the large order behavior of 4 4 and towards a proof of existence of the first renormalon singularity which should prevent the theory from being borel summable using the results of this paper and the techniques of 15 one can for instance improve 17 the estimate 18 on the finiteness of the radius of convergence of the borel transform of renormalized 4 4 and obtain that this radius is at least the exact value conjectured in 1

soft breaking of gauge invariance in regularized quantum electrodynamics an alternative proof of the ward takahashi identity for perturbative quantum electrodynamics is given which makes no use of a gauge invariant regularization such as the pauli villars loop subtraction or dimensional regularization instead it is shown in the presence of an arbitrary high momentum cutoff that the exact w t identity holds with an error ofo 1 e with 0 e 1 the proof involves a perturbative analysis of the euclidean functional integral for qed by the tree expansion method

the sine gordon field theory model at α2 8π the non superrenormalizable theory we study the sine gordon field theory at 2 8 we prove that the theory is renormalizable but not superrenormalizable and we show how the perturbative renormalization procedure works in this case where the interaction is not polynomial to go beyond the perturbative results we investigate the functional equation for this theory and discuss in what sense at 2 8 the theory is lacking the asymptotic freedom and how it is asymptotic free for 2 8 in a appropriate region of the coupling constants

on the convergence of planar diagram expansions renormalizable quantum field theories whose perturbation expansions are described by planar feynman diagrams only such as su gauge theory are considered in 4 dimensional euclidean space for studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs in this paper it is proved that this infinite set of diagrams when summed converges within a finite radius of convergence for the coupling constant

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model

the scaling limit of the energy correlations in non integrable ising models we obtain an explicit expression for the multipoint energy correlations of a non solvable two dimensional ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory which generalizes the one originally used by schultz mattis and lieb for the nearest neighbor ising model the interacting model is then analyzed by a multiscale method first proposed by pinson and spencer if the lattice spacing is finite then the correlations cannot be computed in closed form rather they are expressed in terms of infinite convergent power series in in the scaling limit these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable ising model up to a finite renormalization of the parameters explicit bounds on the speed of convergence to the scaling limit are derived

local existence of the borel transform in euclidean massless φ 4 4 we extend the methods of 1 to prove large order estimates on the renormalized feynman amplitudes of massless 4 4 euclidean field theory at non exceptional momenta the borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane this result is a step towards the rigorous investigation of the infra red singularities in the borel plane for theories containing massless particles like the gauge theories

analysis of fmri time series revisited abstract this paper presents a general approach to the analysis of functional mri time series from one or more subjects the approach is predicated on an extension of the general linear model that allows for correlations between error terms due to physiological noise or correlations that ensue after temporal smoothing this extension uses the effective degrees of freedom associated with the error term the effective degrees of freedom are a simple function of the number of scans and the temporal autocorrelation function a specific form for the latter can be assumed if the data are smoothed in time to accentuate hemodynamic responses with a neural basis this assumption leads to an expedient implementation of a flexible statistical framework the importance of this small extension is that in contradistinction to our previous approach any parametric statistical analysis can be implemented we demonstrate this point using a multiple regression analysis that tests for effects of interest activations due to word generation while taking explicit account of some obvious confounds

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

phase space analysis and particle structure in field theory progress in the last few years in constructive field theory has included 1 the construction of three dimensional non abelian gauge theories in a finite volume 2 the construction of models that are asymptotically free or have a nontrivial fixed point 3 a new presentation of perturbation theory yielding old and new large order estimates and 4 asymptotic completeness for renormalizable models in the two particle region the existence of multiparticle structure equations in the euclidean region provided that the coupling constant goes to zero as the energy increases these equations yield formally the asymptotic completeness in obtaining most of these results the phase space expansion pioneered by glimm and jaffe plays a crucial role the first part of this review is a description of the phase space expansion in the ecole polytechnique version the second part is devoted to the construction of models the third part treats perturbation theory and the last part deals with asymptotic completeness

convergent perturbation expansions for euclidean quantum field theory mayer perturbation theory is designed to provide computable convergent expansions which permit calculation of greens functions in euclidean quantum field theory to arbitrary accuracy including nonperturbative contributions from large field fluctuations here we describe the expansions at the example of 3 dimensional 4 theory in continuous space they are not essentially more complicated than standard perturbation theory the nth order term is expressed in terms of o n dimensional integrals and is of order k if 4k 3 n 4k

trace inequalities for completely monotone functions and bernstein functions abstract we prove a matrix trace inequality for completely monotone functions and for bernstein functions as special cases we obtain non trivial trace inequalities for the power function x x q which for certain values of q complement mccarthy s trace inequality and for others strengthen it

the temperature zero limit we prove that for a broad class of many fermion models the amplitudes of renormalized feynman diagrams converge to their temperature zero values in the limit as the temperature tends to zero

renormalization group approach to lattice gauge field theories i generation of effective actions in a small field approximation and a coupling constant renormalization in four dimensions on etudie des theories de champs de jauge pures a 4 dimensions par l approche du groupe de renormalisation on se restreint a l approximation de champ petit dans cette region on construit une suite d actions effectives localisees par des developpements en amas dans des transformations de renormalisation a un pas

the n 1 supersymmetric sine gordon model in two dimensions ii in this second paper the technical part of the results about the supersymmetricn 1 massless sine gordon field theory at finite space volume is given the proof that the theory exists and is analytic in the coupling constant and that at finite space volume its witten index is 1 is therefore completed

perturbative renormalization of composite operators via flow equations i we apply the general framework of the continuous renormalization group whose significance for perturbative quantum field theories was recognized by polchinski to investigate by new and mathematically simple methods the perturbative renormalization of composite operators in this paper we demonstrate the perturbative renormalizability of the green functions of the euclidean massive 44 theory with one insertion of a possibly oversubtracted in the bphz language composite operator moreover we show that our method admits an easy proof of the zimmermann identities and of the lowenstein rule

an algebraic birkhoff decomposition for the continuous renormalization group this paper aims at presenting the first steps towards a formulation of the exact renormalization group equation in the hopf algebra setting of connes and kreimer it mostly deals with some algebraic preliminaries allowing us to formulate perturbative renormalization within the theory of differential equations the relation between renormalization formulated as a change of boundary condition for a differential equation and an algebraic birkhoff decomposition for rooted trees is explicited

local borel summability of euclidean 311 1311 1311 1a simple proof via differential flow equations it is shown how the differential flow equation or equivalently the continous renormalization group method can be employed to give an astonishingly easy proof of the local borel summability of the renormalized perturbative euclidean massive 44