Página 1 dos resultados de 53 itens digitais encontrados em 0.019 segundos

## Perturbation splitting for more accurate eigenvalues

Ralha, Rui
Fonte: Society for Industrial and Applied Mathematics (SIAM) Publicador: Society for Industrial and Applied Mathematics (SIAM)
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.98%
Let $T$ be a symmetric tridiagonal matrix with entries and eigenvalues of different magnitudes. For some $T$, small entrywise relative perturbations induce small errors in the eigenvalues, independently of the size of the entries of the matrix; this is certainly true when the perturbed matrix can be written as $widetilde{T}=X^{T}TX$ with small $||X^{T}X-I||$. Even if it is not possible to express in this way the perturbations in every entry of $T$, much can be gained by doing so for as many as possible entries of larger magnitude. We propose a technique which consists of splitting multiplicative and additive perturbations to produce new error bounds which, for some matrices, are much sharper than the usual ones. Such bounds may be useful in the development of improved software for the tridiagonal eigenvalue problem, and we describe their role in the context of a mixed precision bisection-like procedure. Using the very same idea of splitting perturbations (multiplicative and additive), we show that when $T$ defines well its eigenvalues, the numerical values of the pivots in the usual decomposition $T-lambda I=LDL^{T}$ may be used to compute approximations with high relative precision.; Fundação para a Ciência e Tecnologia (FCT) - POCI 2010

## Building the full fermion-photon vertex of QED by imposing multiplicative renormalizability of the Schwinger-Dyson equations for the fermion and photon propagators

Kizilersu, A.; Pennington, M.
Fonte: American Physical Soc Publicador: American Physical Soc
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.93%
In principle, calculation of a full Green’s function in any field theory requires knowledge of the infinite set of multipoint Green’s functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an ansatz for the full 3-point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how these conditions imply that the 3-point vertex in the propagator equations is largely determined by the behavior of the fermion propagator itself and not by knowledge of the many higher-point functions. We give an explicit form for the fermion-photon vertex, which in the fermion and photon propagator fulfills these constraints to all orders in leading logarithms for massless QED, and accords with the weak coupling limit in perturbation theory at O(α). This provides the first attempt to deduce nonperturbative Feynman rules for strong physics calculations of propagators in massless QED that ensure a more consistent truncation of the 2-point Schwinger-Dyson equations. The generalization to next-to-leading order and masses will be described in a longer publication.; Ayse Kizilersu and Michael R. Pennington

## Multiplicative Lidskii's inequalities and optimal perturbations of frames

Massey, Pedro Gustavo; Ruiz, Mariano Andres; Stojanoff, Demetrio
Fonte: Elsevier Science Inc Publicador: Elsevier Science Inc
Tipo: info:eu-repo/semantics/article; info:ar-repo/semantics/artículo; info:eu-repo/semantics/publishedVersion Formato: application/pdf
ENG
Relevância na Pesquisa
35.88%
In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame F={fj}j∈In for Cd we compute those dual frames G of F that are optimal perturbations of the canonical dual frame for F under certain restrictions on the norms of the elements of G. On the other hand, we compute those V⋅F={Vfj}j∈In – for invertible operators V which are close to the identity – that are optimal perturbations of F. That is, we compute the optimal perturbations of F among frames G={gj}j∈In that have the same linear relations as F. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskii's inequality in terms of log-majorization and a characterization of the case of equality.; Fil: Massey, Pedro Gustavo. Universidad Nacional de la Plata. Facultad de Ciencias Exactas. Departamento de Matematicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina; Fil: Ruiz...

## Accurate solution of structured least squares problems via rank-revealing decompositions

Castro González, Nieves; Ceballos Cañón, Johan Armando; Martínez Dopico, Froilán C.; Molera, Juan M.
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Relevância na Pesquisa
66.03%
Least squares problems min(x) parallel to b - Ax parallel to(2) where the matrix A is an element of C-mXn (m >= n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems that yield highly structured matrices, but many other examples exist. Very often, structured matrices have huge condition numbers kappa(2)(A) = parallel to A parallel to(2) parallel to A(dagger)parallel to(2) (A(dagger) is the Moore-Penrose pseudoinverse of A) and therefore standard algorithms fail to compute accurate minimum 2-norm solutions of least squares problems. In this work, we introduce a framework that allows us to compute minimum 2-norm solutions of many classes of structured least squares problems accurately, i.e., with errors parallel to(x) over cap (0) - x(0)parallel to(2)/parallel to x(0)parallel to(2) = O(u), where u is the unit roundoff, independently of the magnitude of kappa(2)(A) for most vectors b. The cost of these accurate computations is O(n(2)m) flops, i.e., roughly the same cost as standard algorithms for least squares problems. The approach in this work relies in computing first an accurate rank-revealing decomposition of A, an idea that has been widely used in recent decades to compute...

## Additive and multiplicative renormalization of topological charge with improved gluon/fermion actions: A test case for 3-loop vacuum calculations, using overlap or clover fermions

Skouroupathis, A.; Panagopoulos, H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.88%
We calculate perturbative renormalization properties of the topological charge, using the standard lattice discretization given by a product of twisted plaquettes. We use the overlap and clover action for fermions, and the Symanzik improved gluon action for 4- and 6-link loops. We compute the multiplicative renormalization of the topological charge density to one loop; this involves only the gluon part of the action. The power divergent additive renormalization of the topological susceptibility is calculated to 3 loops. Our work serves also as a test case of the techniques and limitations of lattice perturbation theory, it being the first 3-loop computation in the literature involving overlap fermions.; Comment: 15 pages, 7 figures. Final version, accepted in Physical Review D

## Improved Perturbation Theory for Improved Lattice Actions

Constantinou, M.; Panagopoulos, H.; Skouroupathis, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.03%
We study a systematic improvement of perturbation theory for gauge fields on the lattice; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik coefficients, clover coefficient) by dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is significantly better as compared to results from bare perturbation theory.; Comment: 17 pages...

## Triviality of $\phi^4_4$ theory: small volume expansion and new data

Weisz, Peter; Wolff, Ulli
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.85%
We study a renormalized coupling g and mass m in four dimensional phi^4 theory on tori with finite size z=mL. Precise numerical values close to the continuum limit are reported for z=1,2,4, based on Monte Carlo simulations performed in the equivalent all-order strong coupling reformulation. Ordinary renormalized perturbation theory is found to work marginally at z=2 and and to fail at z=1. By exactly integrating over the constant field mode we set up a renormalized expansion in z and compute three nontrivial orders. These results reasonably agree with the numerical data at small z. In the new expansion, the universal continuum limit exists as expected from multiplicative renormalizability. The triviality scenario is corroborated with significant precision.; Comment: 27 pages, 7 figures, 4 tables

## Form factors and non-local Multiplicative Anomaly for fermions with background torsion

de Berredo-Peixoto, Guilherme; Maicá, Alan E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.93%
We analyse the Multiplicative Anomaly (MA) in the case of quantized massive fermions coupled to a background torsion. The one-loop Effective Action (EA) can be expressed in terms of the logarithm of determinant of the appropriate first-order differential operator acting in the spinors space. Simple algebraic manipulations on determinants must be used in order to apply properly the Schwinger-DeWitt technique, or even the covariant perturbation theory (Barvinsky and Vilkovisky, 1990), which is used in the present work. By this method, we calculate the finite non-local quantum corrections, and analyse explicitly the breakdown of those algebraic manipulations on determinants, called by MA. This feature comes from the finite non-local EA, but does not affect the results in the UV limit, in particular the beta-functions. Similar results was also obtained in previous papers but for different external fields (QED and scalar field).; Comment: LaTeX file, 12 pages, no figures

## Non-Perturbative Evaluation of the Physical Classical Velocity in the Lattice Heavy Quark Effective Theory

Mandula, Jeffrey E.; Ogilvie, Michael C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.83%
In the lattice formulation of the Heavy Quark Effective Theory, the value of the classical velocity v, as defined through the separation of the 4-momentum of a heavy quark into a part proportional to the heavy quark mass and a residual part which remains finite in the heavy quark limit (P = Mv + p) is different from its value as it appears in the bare heavy quark propagator (S(p) = 1/vp). The origin of the difference, which is effectively a lattice-induced renormalization, is the reduction of Lorentz (or O(4)) invariance to (hyper)-cubic invariance. The renormalization is finite and depends specifically on the form of the discretization of the reduced heavy quark Dirac equation. For the Forward Time - Centered Space discretization, we compute this renormalization non-perturbatively, using an ensemble of lattices at beta = 6.1 provided by the Fermilab ACP-MAPS Collaboration. The calculation makes crucial use of a variationally optimized smeared operator for creating composite heavy-light mesons. It has the property that its propagator achieves an asymptotic plateau in just a few Euclidean time steps. For comparison, we also compute the shift perturbatively, to one loop in lattice perturbation theory. The non-perturbative calculation of the leading multiplicative shift in the classical velocity is considerably different from the one-loop estimate...

## On the renormalisation group for the boundary Truncated Conformal Space Approach

Watts, Gerard
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.9%
In this paper we continue the study of the truncated conformal space approach to perturbed boundary conformal field theories. This approach to perturbation theory suffers from a renormalisation of the coupling constant and a multiplicative renormalisation of the Hamiltonian. We show how these two effects can be predicted by both physical and mathematical arguments and prove that they are correct to leading order for all states in the TCSA system. We check these results using the TCSA applied to the tri-critical Ising model and the Yang-Lee model. We also study the TCSA of an irrelevant (non-renormalisable) perturbation and find that, while the convergence of the coupling constant and energy scales are problematic, the renormalised and rescaled spectrum remain a very good fit to the exact result, and we find a numerical relationship between the IR and UV couplings describing a particular flow. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points.; Comment: 27 pages, 19 figures

## Non-Fermi liquid theory of a compactified Anderson single-impurity model

Zhang, Guang-Ming; Hewson, A. C.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36%
We consider a version of the symmetric Anderson impurity model (compactified) which has a non-Fermi liquid weak coupling regime. We find that in the Majorana fermion representation, perturbation theory can be conveniently developed in terms of Pfaffian determinants and we use this formalism to calculate the impurity free energy, self energies, and vertex functions. In the second-order perturbation theory, a linear temperature dependence of electrical resistivity is obtained, and the leading corrections to the impurity specific heat are found to behave as $T\ln T$. The impurity susceptibilities have terms in $\ln T$ to zero, first, and second order, and corrections of $\ln^2 T$ to second order as well. The singlet superconducting paired susceptibility at the impurity site, is found to have second-order corrections $\ln T$, which we interpret as an indication that a singlet conduction electron pairing resonance forms at the Fermi level. When the perturbation theory is extended to third order logarithmic divergences are found in the vertex function $\Gamma_{0,1,2,3}(0,0,0,0)$. Multiplicative renormalization-group method is then used to sum all the leading order logarithmic contributions, giving rise to a new weak-coupling low-temperature energy scale $T_c=\Delta{\rm exp}\left[-\frac{1}{9}\left(\frac{\pi\Delta}{U} \right )^{2}\right]$. The scaling equation shows the dimensionless coupling constant $\frac{U}{\pi\Delta}$ is increased as the energy scale $\Delta$ reduces. Our perturbational results can be justified only in the regime $T>T_c$.; Comment: 40 pages...

## Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model

Makino, Hiroki; Suzuki, Hiroshi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.93%
It is known that the gauge field and its composite operators evolved by the Yang--Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As application of the UV finiteness of the gradient flow, we construct the energy--momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.; Comment: 32 pages, 15 figures, the tittle has been changed, the final version to appear in PTEP

## Building the Full Fermion-Photon Vertex of QED by Imposing Multiplicative Renormalizability of the Schwinger-Dyson Equations for the Fermion and Photon Propagators

Kizilersu, A.; Pennington, M. R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.96%
In principle, calculation of a full Green's function in any field theory requires knowledge of the infinite set of multi-point Green's functions, unless one can find some way of truncating the corresponding Schwinger-Dyson equations. For the fermion and boson propagators in QED this requires an {\it ansatz} for the full three point vertex. Here we illustrate how the properties of gauge invariance, gauge covariance and multiplicative renormalizability impose severe constraints on this fermion-boson interaction, allowing a consistent truncation of the propagator equations. We demonstrate how these conditions imply that the 3-point vertex {\bf in the propagator equations} is largely determined by the behaviour of the fermion propagator itself and not by knowledge of the many higher point functions. We give an explicit form for the fermion-photon vertex, which in the fermion and photon propagator fulfills these constraints to all orders in leading logarithms for massless QED, and accords with the weak coupling limit in perturbation theory at ${\cal O}(\alpha)$. This provides the first attempt to deduce non-perturbative Feynman rules for strong physics calculations of propagators in massless QED that ensures a more consistent truncation of the 2-point Schwinger-Dyson equations. The generalisation to next-to-leading order and masses will be described in a longer publication.; Comment: 57 pages...

## Functional integral approach for multiplicative stochastic processes

Arenas, Zochil González; Barci, Daniel G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.96%
We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green functions in the Grassman sector of the theory. We also study non-perturbative constraints imposed by BRS symmetry and supersymmetry on correlation functions. We show that the specific prescription to define the stochastic process is wholly contained in tadpole diagrams. Therefore, in a supersymmetric theory the stochastic process is uniquely defined since tadpole contributions cancels at all order of perturbation theory.; Comment: 9 pages, no figures, appendix added, references added, final version as will appear in PRE.

## Improving perturbation theory with cactus diagrams

Constantinou, Martha; Panagopoulos, Haralambos; Skouroupathis, Apostolos
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.04%
We study a systematic improvement of perturbation theory for gauge fields on the lattice [hep-lat/0606001]; the improvement entails resumming, to all orders in the coupling constant, a dominant subclass of tadpole diagrams. This method, originally proposed for the Wilson gluon action, is extended here to encompass all possible gluon actions made of closed Wilson loops; any fermion action can be employed as well. The effect of resummation is to replace various parameters in the action (coupling constant, Symanzik and clover coefficient) by dressed'' values; the latter are solutions to certain coupled integral equations, which are easy to solve numerically. Some positive features of this method are: a) It is gauge invariant, b) it can be systematically applied to improve (to all orders) results obtained at any given order in perturbation theory, c) it does indeed absorb in the dressed parameters the bulk of tadpole contributions. Two different applications are presented: The additive renormalization of fermion masses, and the multiplicative renormalization Z_V (Z_A) of the vector (axial) current. In many cases where non-perturbative estimates of renormalization functions are also available for comparison, the agreement with improved perturbative results is consistently better as compared to results from bare perturbation theory.; Comment: 7 pages...

## Cumulant Dynamics of a Population under Multiplicative Selection, Mutation and Drift

Rattray, Magnus; Shapiro, Jonathan L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
36.06%
We revisit the classical population genetics model of a population evolving under multiplicative selection, mutation and drift. The number of beneficial alleles in a multi-locus system can be considered a trait under exponential selection. Equations of motion are derived for the cumulants of the trait distribution in the diffusion limit and under the assumption of linkage equilibrium. Because of the additive nature of cumulants, this reduces to the problem of determining equations of motion for the expected allele distribution cumulants at each locus. The cumulant equations form an infinite dimensional linear system and in an authored appendix Adam Prugel-Bennett provides a closed form expression for these equations. We derive approximate solutions which are shown to describe the dynamics well for a broad range of parameters. In particular, we introduce two approximate analytical solutions: (1) Perturbation theory is used to solve the dynamics for weak selection and arbitrary mutation rate. The resulting expansion for the system's eigenvalues reduces to the known diffusion theory results for the limiting cases with either mutation or selection absent. (2) For low mutation rates we observe a separation of time-scales between the slowest mode and the rest which allows us to develop an approximate analytical solution for the dominant slow mode. The solution is consistent with the perturbation theory result and provides a good approximation for much stronger selection intensities.; Comment: Minor changes and authored appendix by Adam Prugel-Bennett. To appear in Theoretical Population Biology...

## Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms

Ahmady, M. R.; Elias, V.; McKeon, D. G. C.; Squires, A.; Steele, T. G.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
35.85%
Invariance of the effective action under changes of the renormalization scale $\mu$ leads to relations between those (presumably calculated) terms independent of $\mu$ at a given order of perturbation theory and those higher order terms dependent on logarithms of $\mu$. This relationship leads to differential equations for a sequence of functions, the solutions of which give closed form expressions for the sum of all leading logs, next to leading logs and subsequent subleading logarithmic contributions to the effective action. The renormalization group is thus shown to provide information about a model beyond the scale dependence of the model's couplings and masses. This procedure is illustrated using the $\phi_6^3$ model and Yang-Mills theory. In the latter instance, it is also shown by using a modified summation procedure that the $\mu$ dependence of the effective action resides solely in a multiplicative factor of $g^2 (\mu)$ (the running coupling). This approach is also shown to lead to a novel expansion for the running coupling in terms of the one-loop coupling that does not require an order-by-order redefinition of the scale factor $\Lambda_{QCD}$. Finally, logarithmic contributions of the instanton size to the effective action of an SU(2) gauge theory are summed...

## Gauge transformations in relativistic two-particle constraint theory

Jallouli, H.; Sazdjian, H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.86%
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in $x$-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli-Schr\"odinger type eigenvalue equation has the gauge invariant attractive singularity $\alpha^2/r^2$, leading to a gauge invariant critical coupling constant $\alpha_c =1/2$.; Comment: 32 pages, latex file with 3 figures, uses epsfile.sty for figures

## Ultraviolet divergences and factorization for coordinate-space amplitudes

Erdoğan, Ozan; Sterman, George