Charge renormalization in nominally apolar colloidal dispersions
Evans, Daniel J.; Hollingsworth, Andrew D.; Grier, David G.
2016-04-01
We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.
Anomalous Kinetics of Hard Charged Particles Dynamical Renormalization Group Resummation
Boyanovsky, D
1999-01-01
We study the kinetics of the distribution function for charged particles of hard momentum in scalar QED. The goal is to understand the effects of infrared divergences associated with the exchange of quasistatic magnetic photons in the relaxation of the distribution function. We begin by obtaining a kinetic transport equation for the distribution function for hard charged scalars in a perturbative expansion that includes hard thermal loop resummation. Solving this transport equation, the infrared divergences arising from absorption and emission of soft quasi-static magnetic photons are manifest in logarithmic secular terms. We then implement the dynamical renormalization group resummation of these secular terms in the relaxation time approximation. The distribution function (in the linearized regime) is found to approach equilibrium as $\\delta n_k(t) =\\delta n_k(t_o) e^{-2\\alpha T (t-t_o) and $\\alpha =e^2/4\\pi$. This anomalous relaxation is recognized to be the square of the relaxation of the single particle p...
Energy Technology Data Exchange (ETDEWEB)
Alvaro Calle Cordon,Manuel Pavon Valderrama,Enrique Ruiz Arriola
2012-02-01
We study the interplay between charge symmetry breaking and renormalization in the NN system for S-waves. We find a set of universality relations which disentangle explicitly the known long distance dynamics from low energy parameters and extend them to the Coulomb case. We analyze within such an approach the One-Boson-Exchange potential and the theoretical conditions which allow to relate the proton-neutron, proton-proton and neutron-neutron scattering observables without the introduction of extra new parameters and providing good phenomenological success.
Renormalization group flow and fixed point of the lattice topological charge in the 2D O(3) σ model
International Nuclear Information System (INIS)
We study the renormalization group evolution up to the fixed point of the lattice topological susceptibility in the 2D O(3) nonlinear σ model. We start with a discretization of the continuum topological charge by a local charge density polynomial in the lattice fields. Among the different choices we propose also a Symanzik-improved lattice topological charge. We check step by step in the renormalization group iteration the progressive dumping of quantum fluctuations, which are responsible for the additive and multiplicative renormalizations of the lattice topological susceptibility with respect to the continuum definition. We find that already after three iterations these renormalizations are negligible and an excellent approximation of the fixed point is achieved. We also check by an explicit calculation that the assumption of slowly varying fields in iterating the renormalization group does not lead to a good approximation of the fixed point charge operator. copyright 1997 The American Physical Society
Charge renormalization and phase separation in colloidal suspensions
Diehl, Alexandre; Barbosa, Marcia C.; Levin, Yan
2000-01-01
We explore the effects of counterion condensation on fluid-fluid phase separation in charged colloidal suspensions. It is found that formation of double layers around the colloidal particles stabilizes suspensions against phase separation. Addition of salt, however, produces an instability which, in principle, can lead to a fluid-fluid separation. The instability, however, is so weak that it should be impossible to observe a fully equilibrated coexistence experimentally.
International Nuclear Information System (INIS)
Highlights: → One-step renormalization approach to describe the DBL-DNA molecule. → Electronic tight-binding Hamiltonian model. → A quasiperiodic sequence to mimic the DNA nucleotides arrangement. → Electronic transmission spectra. → I-V characteristics. -- Abstract: We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.
Energy Technology Data Exchange (ETDEWEB)
Sarmento, R.G. [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Fulco, U.L. [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Albuquerque, E.L., E-mail: eudenilson@gmail.com [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Caetano, E.W.S. [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara, 60040-531 Fortaleza, CE (Brazil); Freire, V.N. [Departamento de Fisica, Universidade Federal do Ceara, 60455-760 Fortaleza, CE (Brazil)
2011-10-31
Highlights: → One-step renormalization approach to describe the DBL-DNA molecule. → Electronic tight-binding Hamiltonian model. → A quasiperiodic sequence to mimic the DNA nucleotides arrangement. → Electronic transmission spectra. → I-V characteristics. -- Abstract: We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.
Nonperturbative Description Of The Mass And Charge Renormalization In Quantum Electrodynamics
Feranchuk, I D
2003-01-01
In this paper the nonperturbative analysis of the spectrum for one-particle excitations of the electron-positron field (EPF) is considered in the paper. A standard form of the quantum electrodynamics (QED) is used but the charge of the "bare" electron $e_0$ is supposed to be of a large value. It is shown that in this case the quasi-particle can be formed with a non-zero averaged value of the scalar component of the electromagnetic field (EMF). Self-consistent equations for the distribution of charge density in the "physical" electron (positron) are derived. A variational solution of these equations is obtained and it defines the finite renormalization of the charge and mass of the electron (positron). It is found that the coupling constant between EPF and EMF and mass of the "bare" electron can be connected with the observed values of the fine structure constant and the mass of the "physical" electron. It is also shown that although the non-renormalized QED corresponds to the strong coupling between EPF and E...
Directory of Open Access Journals (Sweden)
V. Bacsó
2015-12-01
Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.
Combinatorial Hopf algebras from renormalization
Brouder, Christian; Menous, Frederic
2009-01-01
In this paper we describe the right-sided combinatorial Hopf structure of three Hopf algebras appearing in the context of renormalization in quantum field theory: the non-commutative version of the Fa\\`a di Bruno Hopf algebra, the non-commutative version of the charge renormalization Hopf algebra on planar binary trees for quantum electrodynamics, and the non-commutative version of the Pinter renormalization Hopf algebra on any bosonic field. We also describe two general ways to define the associative product in such Hopf algebras, the first one by recursion, and the second one by grafting and shuffling some decorated rooted trees.
Bianchi, M; Skenderis, K; Bianchi, Massimo; Freedman, Daniel Z.; Skenderis, Kostas
2002-01-01
We systematically develop the procedure of holographic renormalization for RG flows dual to asymptotically AdS domain walls. All divergences of the on-shell bulk action can be cancelled by adding covariant local boundary counterterms determined by the near-boundary behavior of bulk fields. This procedure defines a renormalized action from which correlation functions are obtained by functional differentiation. The correlators are finite and well behaved at coincident points. Ward identities, corrected for anomalies, are satisfied. The correlators depend on parts of the solution of the bulk field equations which are not determined by near-boundary analysis. In principle a full nonlinear solution is required, but one can solve linearized fluctuation equations to define a bulk-to-boundary propagator from which 2-point correlation functions are easily obtained. We carry out the procedure explicitly for two known RG flows obtained from the maximal gauged D=5 supergravity theory, obtaining new results on correlators...
Holographic Renormalization in Dense Medium
International Nuclear Information System (INIS)
The holographic renormalization of a charged black brane with or without a dilaton field, whose dual field theory describes a dense medium at finite temperature, is investigated in this paper. In a dense medium, two different thermodynamic descriptions are possible due to an additional conserved charge. These two different thermodynamic ensembles are classified by the asymptotic boundary condition of the bulk gauge field. It is also shown that in the holographic renormalization regularity of all bulk fields can reproduce consistent thermodynamic quantities and that the Bekenstein-Hawking entropy is nothing but the renormalized thermal entropy of the dual field theory. Furthermore, we find that the Reissner-Nordström AdS black brane is dual to a theory with conformal matter as expected, whereas a charged black brane with a nontrivial dilaton profile is mapped to a theory with nonconformal matter although its leading asymptotic geometry still remains as AdS space
The renormalization of the electroweak standard model
International Nuclear Information System (INIS)
A renormalization scheme for the electroweak standard model is presented in which the electric charge and the masses of the gauge bosons, Higgs particle and fermions are used as physical parameters. The photon is treated such that quantum electrodynamics is contained in the usual form. Field renormalization respecting the gauge symmetry gives finite Green functions. The Ward identities between the Green functions of the unphysical sector allow a renormalization that maintains the simple pole structure of the propagators. Explicit results for the renormalization self energies and vertex functions are given. They can be directly used as building blocks for the evaluation of l-loop radiative corrections. (orig.)
Freire, Hermann; de Carvalho, Vanuildo
2015-03-01
The two-loop renormalization group (RG) calculation is considerably extended here for a two-dimensional (2D) fermionic effective field theory model, which includes only the so-called ``hot spots'' that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t -t' Hubbard model at low hole doping. We compute the Callan-Symanzik RG equation up to two loops describing the flow of the single-particle Green's function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that - in addition to clearly dominant SDW correlations - an approximate (pseudospin) symmetry relating a short-range incommensurate d-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates. We acknowledge financial support from CNPq under Grant No. 245919/2012-0 and FAPEG under Grant No. 201200550050248 for this project.
Gover, A Rod
2016-01-01
For any conformally compact manifold with hypersurface boundary we define a canonical renormalized volume functional and compute an explicit, holographic formula for the corresponding anomaly. For the special case of asymptotically Einstein manifolds, our method recovers the known results. The anomaly does not depend on any particular choice of regulator, but the coefficients of divergences do. We give explicit formulae for these divergences valid for any choice of regulating hypersurface; these should be relevant to recent studies of quantum corrections to entanglement entropies. The anomaly is expressed as a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. We show that the variation of these energy functionals is exactly the obstruction to solving a singular Yamabe type problem with boundary data along the...
Renormalized entanglement entropy
Taylor, Marika
2016-01-01
We develop a renormalization method for holographic entanglement entropy based on area renormalization of entangling surfaces. The renormalized entanglement entropy is derived for entangling surfaces in asymptotically locally anti-de Sitter spacetimes in general dimensions and for entangling surfaces in four dimensional holographic renormalization group flows. The renormalized entanglement entropy for disk regions in $AdS_4$ spacetimes agrees precisely with the holographically renormalized action for $AdS_4$ with spherical slicing and hence with the F quantity, in accordance with the Casini-Huerta-Myers map. We present a generic class of holographic RG flows associated with deformations by operators of dimension $3/2 < \\Delta < 5/2$ for which the F quantity increases along the RG flow, hence violating the strong version of the F theorem. We conclude by explaining how the renormalized entanglement entropy can be derived directly from the renormalized partition function using the replica trick i.e. our re...
Entanglement Renormalization: an introduction
Vidal, Guifre
2009-01-01
We present an elementary introduction to entanglement renormalization, a real space renormalization group for quantum lattice systems. This manuscript corresponds to a chapter of the book "Understanding Quantum Phase Transitions", edited by Lincoln D. Carr (Taylor & Francis, Boca Raton, 2010)
Renormalization of Dirac's Polarized Vacuum
Lewin, Mathieu
2010-01-01
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\\Lambda$. We then discuss the limit $\\Lambda\\to\\infty$ in detail, by resorting to charge renormalization.
Renormalization of the vector current in QED
International Nuclear Information System (INIS)
It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false (b) how to obtain the renormalization of the current to all orders of perturbation theory, and (c) how to correctly define an electron number operator. The current mixes with the four-divergence of the electromagnetic field-strength tensor. The true electron number operator is the integral of the time component of the electron number density, but only when the current differs from the MS-renormalized current by a definite finite renormalization. This happens in such a way that Gauss's law holds: the charge operator is the surface integral of the electric field at infinity. The theorem extends naturally to any gauge theory
Renormalization: an advanced overview
Gurau, Razvan; Sfondrini, Alessandro
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.
Entanglement Renormalization and Wavelets
Evenbly, Glen; White, Steven R.
2016-04-01
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Renormalization of the QEMD of a dyon field
International Nuclear Information System (INIS)
A renormalized quantum electromagnetodynamics (QEMD) of a dyon field is defined. Finite and n independent answers can be obtained in each order of the loop expansion for all processes. The electric and magnetic charges are not constrained with the Dirac condition and therefore perturbation theory can be made reliable. The renormalized theory is found to possess exact dual invariance. Comparisons with the general QEMD of electric and magnetic charges are made. (author)
Renormalization of Wilson Operators in Minkowski space
Andraši, A.; Taylor, J. C.
1996-01-01
We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge renormalization does not work in a simple graph-by-graph way; but does work when certain graphs are added together. We also verify that, in a simple example of a smooth loop in Minkowski space, the existence of pairs of points which are light-like separated ...
Renormalization in supersymmetric models
Fonseca, Renato M
2013-01-01
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the instability of the Higgs boson mass under radiative corrections. In this thesis, some topics related to the renormalization of supersymmetric models are analyzed. One of them is the automatic computation of the Lagrangian and the renormalization group equations of these models, which is a hard and error-prone process if carried out by hand. The generic renormalization group equations themselves are extended so as to include those models which have more than a single abelian gauge factor group. Such situations can occur in grand unified theories, for example. For a wide range of SO(10)-inspired supersymmetric models, we also show that the renormalization group imprints on sparticle masses some information on the higher energies behavior of the models. Finally, in some cases these the...
Loop structure of renormalizations
International Nuclear Information System (INIS)
Asymptotics in the internal momenta p and q is obtained for renormalized Feynman amplitudes recurrently to a number of loops. The asymptotics has the form of a polynomial in powers of these momenta. The renormalization method implies the exclusion of UV-''bad'' asymptotics which provides the p and q convergence of the integral (UV - ultraviolet divergences). It is pointed out the regularization of the integral performed here may be convenient for combined analysis of UV and infrared problem
Renormalization of fermion mixing
International Nuclear Information System (INIS)
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Renormalization of fermion mixing
Energy Technology Data Exchange (ETDEWEB)
Schiopu, R.
2007-05-11
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Geometry, Renormalization, And Supersymmetry
Berg, G M
2001-01-01
This thesis is about understanding, applying and improving quantum field theory. We compute renormalization group flows as the evolution of a “coarse-graining” operator without the need for a Euclidean formulation. Renormalization is cast in the form of a Lie algebra of (in general infinite) matrices that generate, by exponentiation, counterterms for diagrams with subdivergences. These results may shed light on noncommutative geometry. We check our results in a scalar three-loop example. Then, we consider the renormalization of a certain supersymmetric gauge theory, the low-energy limit of a string model. We compare results to those computed directly in the string model and find agreement. Finally, we discuss the possibility of detecting quantum-mechanical phases distinguishing the two Pin groups, double covers of the full Lorentz group. Majorana fermions, if detected, would provide an important testing ground; such particles can restrict the choice of Pin group.
Renormalization and plasma physics
International Nuclear Information System (INIS)
A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields
On renormalization of axial anomaly
International Nuclear Information System (INIS)
It is shown that multiplicative renormalization of the axial singlet current results in renormalization of the axial anomaly in all orders of perturbation theory. It is a necessary condition for the Adler - Bardeen theorem being valid. 10 refs.; 2 figs
Renormalization of QED at low temperature and high density
International Nuclear Information System (INIS)
The results of the calculation of charge renormalization constant in QED at low temperature and high value of the chemical potential is presented. It completes the discussion of renormalization of QED in different limits of temperature and chemical potential. As a simple illustration of this procedure the scalar Higgs decay (H→e+e-) rate is corrected for this limit showing that the KLN theorem of QED is correct for this region of temperatures and chemical potential also. (author). 12 refs, 2 figs
International Nuclear Information System (INIS)
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t′ Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates
Teaching the renormalization group
International Nuclear Information System (INIS)
The renormalization group theory of continuous phase transitions is described with the use of a hands on model suitable for presentation as part of an undergraduate thermal physics course. It is an extension of the work of Maris and Kadanoff in that key concepts such as universality fixed points and critical surface are introduced
Nonequilibrium Renormalization Group
International Nuclear Information System (INIS)
Thermal equilibrium properties of many-body or field theories are known to be efficiently classified in terms of renormalization group fixed points. A particularly powerful concept is the notion of infrared fixed points, which are characterized by universality. These correspond to critical phenomena in thermal equilibrium, where a characteristic large correlation length leads to independence of long-distance properties from details of the underlying microscopic theory. In contrast, a classification of properties of theories far from thermal equilibrium in terms of renormalization group fixed points is much less developed. The notion of universality or critical phenomena far from equilibrium is to a large extent unexplored, in particular, in relativistic quantum field theories. Here the strong interest is mainly driven by theoretical and experimental advances in our understanding of early universe cosmology as well as relativistic collision experiments of heavy nuclei in the laboratory. In these lectures I will introduce the functional renormalization group for the effective average action out of equilibrium. While in equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems a generating functional for nonequilibrium correlation functions with given density matrix at initial time can be written down using the Schwinger-Keldysh closed time path contour. In principle, this can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. However, important differences include the absence of time-translation invariance for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, since it becomes independent of the initial density matrix. I will discuss some simple examples for which I derive a hierarchy of fixed point solutions
Renormalizing Entanglement Distillation
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens
2016-01-01
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
Renormalization of current algebra
Mickelsson, J
1993-01-01
In this talk I want to explain the operator substractions needed to renormalize gauge currents in a second quantized theory. The case of space-time dimensions $3+1$ is considered in detail. In presence of chiral fermions the renormalization effects a modification of the local commutation relations of the currents by local Schwinger terms. In $1+1$ dimensions on gets the usual central extension (Schwinger term does not depend on background gauge field) whereas in $3+1$ dimensions one gets an anomaly linear in the background potential. We extend our method to the spatial components of currents. Since the bose-fermi interaction hamiltonian is of the form $j^k A_k$ (in the temporal gauge) we get a new renormalization scheme for the interaction. The idea is to define a field dependent conjugation for the fermi hamiltonian in the one-particle space such that after the conjugation the hamiltonian can be quantized just by normal ordering prescription.
Entanglement renormalization and integral geometry
Huang, Xing; Lin, Feng-Li
2015-01-01
We revisit the applications of integral geometry in AdS$_3$ and argue that the metric of the kinematic space can be realized as the entanglement contour, which is defined as the additive entanglement density. From the renormalization of the entanglement contour, we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz. Furthermore, a renormalization group equation of the long-distance entanglement contour is then derived....
Fisher Renormalization for Logarithmic Corrections
Kenna, Ralph; Hsu, Hsiao-Ping; Von Ferber, Christian
2008-01-01
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at t...
Renormalization on noncommutative torus
D'Ascanio, D; Vassilevich, D V
2016-01-01
We study a self-interacting scalar $\\varphi^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the nonlocal counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points towards the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $\\theta$.
Renormalization on noncommutative torus
Energy Technology Data Exchange (ETDEWEB)
D' Ascanio, D.; Pisani, P. [Universidad Nacional de La Plata, Instituto de Fisica La Plata-CONICET, La Plata (Argentina); Vassilevich, D.V. [Universidade Federal do ABC, CMCC, Santo Andre, SP (Brazil); Tomsk State University, Department of Physics, Tomsk (Russian Federation)
2016-04-15
We study a self-interacting scalar φ{sup 4} theory on the d-dimensional noncommutative torus. We determine, for the particular cases d = 2 and d = 4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ. (orig.)
Renormalizing Entanglement Distillation.
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens
2016-01-15
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow. PMID:26824532
Infrared troubles of differential renormalization
International Nuclear Information System (INIS)
The possibility of generalizing differential renormalization of D.Z. Freedman, K.Jonnson and J.I.Latorre in an invariant fashion to theories with infrared divergencies is investigated. It is concluded that the calculations on infrared differential renormalization lead to incorrect result. 16 refs.; 7 figs
On mass and charge renormalization in OED
International Nuclear Information System (INIS)
It is shown that Quantum Electrodynamics is a consistent theory, without ultraviolet or vacuum-vacuum singularities, when proper care is taken of operator contractions evaluated at coalescing points. (author)
Some lessons of renormalization theory
International Nuclear Information System (INIS)
The term renormalization has a variety of associations both mathematical and physical. On the one hand, renormalization in one broad sense has often come to include any procedure by which infinite or ambiguous expressions in quantum field theory are replaced by well defined mathematical objects. A more precise definition would here distinguish renormalization and regularization, the latter being any rule that produces finite answers while the former is reserved for the special case in which the rule gives answers associated with a self-consistent field theory. On the other hand, renormalization is often used as a catch word for a family of methods of analyzing the significant parameters labeling the states of a theory and of their relations to the parameters actually appearing in the Hamiltonian. The author examines some of the significant developments in the history of renormalization theory for the light they can throw on present unsolved problems. (Auth.)
Gutzwiller renormalization group
Lanatà, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Wang, Cai-Zhuang; Ho, Kai-Ming; Kotliar, Gabriel
2016-01-01
We develop a variational scheme called the "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.
Chaotic renormalization-group trajectories
DEFF Research Database (Denmark)
Damgaard, Poul H.; Thorleifsson, G.
1991-01-01
regions where the renormalization-group flow becomes chaotic. We present some explicit examples of these phenomena for the case of a Lie group valued spin-model analyzed by means of a variational real-space renormalization group. By directly computing the free energy of these models around the parameter......Under certain conditions, the renormalization-group flow of models in statistical mechanics can change dramatically under just very small changes of given external parameters. This can typically occur close to bifurcations of fixed points, close to the complete disappearance of fixed points, or in...... regions in which such nontrivial modifications of the renormalization-group flow occur, we can extract the physical consequences of these phenomena....
KAM Theorem and Renormalization Group
E. Simone; Kupiainen, A.
2007-01-01
We give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a PDE with quadratic nonlinearity, the so called Polchinski renormalization group equation studied in quantum field theory.
Differential renormalization of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab
The analytic renormalization group
Ferrari, Frank
2016-08-01
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k ∈ Z, associated with the Matsubara frequencies νk = 2 πk / β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk | < μ (with the possible exception of the zero mode G0), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk | ≥ μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.
Renormalization group analysis of graphene with a supercritical Coulomb impurity
Nishida, Yusuke
2016-01-01
We develop a field theoretical approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.
Holographic renormalization group
International Nuclear Information System (INIS)
The holographic renormalization group (RG) is reviewed in a self-contained manner. The holographic RG is based on the idea that the radial coordinate of a space-time with asymptotically AdS geometry can be identified with the RG flow parameter of boundary field theory. After briefly discussing basic aspects of the AdS/CFT correspondence, we explain how the concept of the holographic GR emerges from this correspondence. We formulate the holographic RG on the basis of the Hamilton-Jacobi equations for bulk systems of gravity and scalar fields, as introduced by de Boer, Verlinde and Verlinde. We then show that the equations can be solved with a derivative expansion by carefully extracting local counterterms from the generating functional of the boundary field theory. The calculational methods used to obtain the Weyl anomaly and scaling dimensions are presented and applied to the RG flow from the N = 4 SYM to an N = 1 superconformal fixed point discovered by Leigh and Straussler. We further discuss the relation between the holographic RG and the noncritical string theory and show that the structure of the holographic RG should persist beyond the supergravity approximation as a consequence of the renormalizability of the nonlinear σ-model action of noncritical strings. As a check, we investigate the holographic RG structure of higher-derivative systems. We show that such systems can also be analyzed based on the Hamilton-Jacobi equations and that the behavior of bulk fields are determined solely by their boundary values. We also point out that higher-derivative gravity systems give rise to new multicritical points in the parameter space of boundary field theories. (author)
An exact, finite, gauge-invariant, non-perturbative approach to QCD renormalization
International Nuclear Information System (INIS)
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway
An Exact, Finite, Gauge-Invariant, Non-Perturbative Model of QCD Renormalization
Fried, H M; Gabellini, Y; Grandou, T; Sheu, Y -M
2014-01-01
A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no 'self-energy' to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion's chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to HE elastic pp scattering is now underway.
Lecture notes on holographic renormalization
International Nuclear Information System (INIS)
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime
Functional and Local Renormalization Groups
Codello, Alessandro; Pagani, Carlo
2015-01-01
We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example. We show that away from criticality the Wess-Zumino action is described by a derivative expansion with coefficients naturally related to RG quantities. We then demonstrate that the Weyl consistency conditions derived in the LRG approach are equivalent to the RG equation for the $c$-function available in the FRG scheme. This allows us to give an explicit FRG representation of the Zamolodchikov-Osborn metric, which in principle can be used for computations.
Renormalization in Coulomb gauge QCD
International Nuclear Information System (INIS)
Research highlights: → The Hamiltonian in the Coulomb gauge of QCD contains a non-linear Christ-Lee term. → We investigate the UV divergences from higher order graphs. → We find that they cannot be absorbed by renormalization of the Christ-Lee term. - Abstract: In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.
Renormalization of the nonlinear O(3) model with θ-term
Energy Technology Data Exchange (ETDEWEB)
Flore, Raphael, E-mail: raphael.flore@uni-jena.de [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-07743 Jena (Germany)
2013-05-11
The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.
Renormalization of the nonlinear O(3) model with θ-term
Flore, Raphael
2013-05-01
The renormalization of the topological term in the two-dimensional nonlinear O(3) model is studied by means of the Functional Renormalization Group. By considering the topological charge as a limit of a more general operator, it is shown that a finite multiplicative renormalization occurs in the extreme infrared. In order to compute the effects of the zero modes, a specific representation of the Clifford algebra is developed which allows to reformulate the bosonic problem in terms of Dirac operators and to employ the index theorem.
The Wilson renormalization group for low x physics towards the high density regime
Marian, J J; Leonidov, A V; Weigert, H; Marian, Jamal Jalilian -; Kovner, Alex; Leonidov, Andrei; Weigert, Heribert
1999-01-01
We continue the study of the effective action for low $x$ physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of $x$. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small $x$.
Lecture Notes on Holographic Renormalization
Skenderis, K
2002-01-01
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime.
Fixed point of the parabolic renormalization operator
Lanford III, Oscar E
2014-01-01
This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishi...
Renormalization group theory for fluids
International Nuclear Information System (INIS)
Some extensions of renormalization group methods to fluids are discussed that may facilitate the development of a general renormalization group theory for real fluids that is capable of predicting their thermodynamic properties globally, including both at the critical point and away from the critical point, from a specification solely of the microscopic interactions among the constituent molecules. The extensions include application to virial series and free energies for freely moving molecules (as contrasted with Hamiltonian methods used for fixed lattices of molecules); inclusion of contributions from fluctuations of very short wavelengths, comparable to the range of the attractive forces; and evaluation of the scale factor for fluctuation amplitudes. An approximate theory incorporating these new features is formulated and illustrated in a simple application to the thermal behavior of n-pentane in a large extended neighborhood of its critical point
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic lattices in QFT renormalization
Borinsky, Michael
2015-01-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the Standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, the lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Perturbative renormalization in quantum mechanics
International Nuclear Information System (INIS)
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theory, but much simpler, regularization and renormalization lead to finite physical results, which compare correctly to the exact ones. The Dirac delta potential, because of its relevance to triviality, and the Aharonov-Bohm potential, because of its relevance to anyons, are used as examples here. ((orig.))
Renormalization programme for effective theories
Vereshagin, Vladimir; Semenov-Tyan-Shanskiy, Kirill; Vereshagin, Alexander
2004-01-01
We summarize our latest developments in perturbative treating the effective theories of strong interactions. We discuss the principles of constructing the mathematically correct expressions for the S-matrix elements at a given loop order and briefly review the renormalization procedure. This talk shall provide the philosophical basement as well as serve as an introduction for the material presented at this conference by A. Vereshagin and K. Semenov-Tian-Shansky.
Renormalization aspects of chaotic strings
International Nuclear Information System (INIS)
Chaotic strings are a class of non-hyperbolic coupled map lattices, exhibiting a rich structure of complex dynamical phenomena with a surprising correspondence to physical contents. In this paper we introduce different types and models for chaotic strings, where 2B-strings with finite length are considered in detail. We demonstrate possibilities to extract renormalized quantities, which are expected to describe essential properties of the string.
Renormalized RPA at finite temperature
International Nuclear Information System (INIS)
A method taking account of a deviation of state occupation numbers from the thermal RPA prescriptions is elaborated to study collective excitations in hot nuclei. The main idea of this Thermal Renormalized Random Phase Approximation goes back to Ken-Ji Hara and D.J.Rowe. In developing the TRRPA, a formalism of the thermofield dynamics (TFD) is used. Some numerical results are given for the SU(2) model. 15 refs., 1 fig
Concepts of Renormalization in Physics
Alexandre, Jean
2005-01-01
A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, and then show how similar ideas appear in Particle Physics. This short review is written for non-particle physicists and/or students aiming at studying Particle Physics.
Renormalization and asymptotic expansion of Dirac's polarized vacuum
Gravejat, Philippe; Séré, Eric
2010-01-01
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\\alphaph$, provided that the ultraviolet cut-off behaves as $\\Lambda\\sim e^{3\\pi(1-Z_3)/2\\alphaph}\\gg1$. The renormalization parameter $0
Renormalization of Multiple q-Zeta Values
Institute of Scientific and Technical Information of China (English)
Jianqiang ZHAO
2008-01-01
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV)which are special values of multiple q-zeta functions ζq(S1,..., sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv:math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(S1,..., Sd) (i.e., S1≤1). Moreover, when q 1 our renormalizations agree with those of Guo and Zhang.
Renormalization of Loop Functions in QCD
Berwein, Matthias; Brambilla, Nora; Vairo, Antonio
2013-01-01
We give a short overview of the renormalization properties of rectangular Wilson loops, the Polyakov loop correlator and the cyclic Wilson loop. We then discuss how to renormalize loops with more than one intersection, using the simplest non-trivial case as an illustrative example. Our findings expand on previous treatments. The generalized exponentiation theorem is applied to the Polyakov loop correlator and used to renormalize linear divergences in the cyclic Wilson loop.
Introduction to the functional renormalization group
International Nuclear Information System (INIS)
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)
LETTER: Fisher renormalization for logarithmic corrections
Kenna, Ralph; Hsu, Hsiao-Ping; von Ferber, Christian
2008-10-01
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogues. The scheme is tested in lattice animals and the Yang-Lee problem at their upper critical dimensions, where predictions for logarithmic corrections are made.
Runge-Kutta methods and renormalization
International Nuclear Information System (INIS)
Rooted trees have been used to calculate the solution of nonlinear flow equations and Runge-Kutta methods. More recently, rooted trees have helped systematizing the algebra underlying renormalization in quantum field theories. The Butcher group and B-series establish a link between these two approaches to rooted trees. On the one hand, this link allows for an alternative representation of the algebra of renormalization, leading to nonperturbative results. On the other hand, it helps to renormalize singular flow equations. The usual approach is extended here to nonlinear partial differential equations. A nonlinear Born expansion is given, and renormalization is used to partly remove the secular terms of the perturbative expansion. (orig.)
Renormalization Method and Mirror Symmetry
Directory of Open Access Journals (Sweden)
Si Li
2012-12-01
Full Text Available This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental's symplectic loop space formalism in the context of B-model geometry on Calabi-Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. We also give a physics interpretation of the Virasoro constraints as the symmetry of the classical BCOV action functional, and discuss the Virasoro constraints in the quantum theory.
Scale invariance and renormalization group
International Nuclear Information System (INIS)
Scale invariance enabled the understanding of cooperative phenomena and the study of elementary interactions, such as phase transition phenomena, the Curie critical temperature and spin rearrangement in crystals. The renormalization group method, due to K. Wilson in 1971, allowed for the study of collective phenomena, using an iterative process from smaller scales to larger scales, leading to universal properties and the description of matter state transitions or long polymer behaviour; it also enabled to reconsider the quantum electrodynamic theory and its relations to time and distance scales
Renormalization in few body nuclear physics
International Nuclear Information System (INIS)
Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the 3Sl -3 D1 states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three-body halo nuclei is also
Wavelet view on renormalization group
Altaisky, M V
2016-01-01
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier described in {\\em Phys.Rev.D} 81(2010)125003, 88(2013)025015, is finite by construction. The space of scale-dependent functions $\\{ \\phi_a(x) \\}$ is more relevant to physical reality than the space of square-integrable functions $\\mathrm{L}^2(R^d)$, because, due to the Heisenberg uncertainty principle, what is really measured in any experiment is always defined in a region rather than point. The effective action $\\Gamma_{(A)}$ of our theory turns to be complementary to the exact renormalization group effective action. The role of the regulator is played by the basic wavelet -- an "aperture function" of a measuring device used to produce the snapshot of a field $\\phi$ at the point $x$ with the resolution $a$. The standard RG results for $\\phi^4$ model are reproduced.
Directory of Open Access Journals (Sweden)
V.Janiš
2006-01-01
Full Text Available The ways of introducing and handling renormalizations in the many-body perturbation theory are reviewed. We stress the indispensable role the technique of Green functions plays in extrapolating the weak-coupling perturbative approaches to intermediate and strong couplings. We separately discuss mass and charge renormalizations. The former is incorporated in a self-consistent equation for the self-energy derived explicitly from generating Feynman diagrams within the Baym and Kadanoff approach. The latter amounts to self-consistent equations for two-particle irreducible vertices. We analyze the charge renormalization initiated by De Dominicis and Martin and demonstrate that its realization via the parquet approach may become a powerful and viable way of using the many-body diagrammatic approach reliably in non-perturbative regimes with cooperative phenomena induced by either strong interaction or strong static randomness.
Combinatorics of renormalization as matrix calculus
International Nuclear Information System (INIS)
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first principles, to wit, the 'Birkhoff decomposition' in the Hopf-algebraic description of renormalization by Connes and Kreimer
On the renormalization of the Polyakov loop
Zantow, F.
2003-01-01
We discuss a non-perturbative renormalization of n-point Polyakov loop correlation functions by explicitly introducing a renormalization constant for the Polyakov loop operator on a lattice deduced from the short distance properties of 2-point correlators. We calculate this constant for the SU(3)gauge theory.
Renormalization of dimension 6 gluon operators
Directory of Open Access Journals (Sweden)
HyungJoo Kim
2015-09-01
Full Text Available We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.
Renormalization of dimension 6 gluon operators
Energy Technology Data Exchange (ETDEWEB)
Kim, HyungJoo, E-mail: hugokm0322@gmail.com; Lee, Su Houng, E-mail: suhoung@yonsei.ac.kr
2015-09-02
We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.
Renormalization and Effective Actions for General Relativity
Neugebohrn, Falk
2007-01-01
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Eucl...
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Energy Technology Data Exchange (ETDEWEB)
Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)
2013-08-01
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).
Perturbative entanglement thermodynamics for AdS spacetime: Renormalization
Mishra, Rohit
2015-01-01
We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that `boosted' AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately `renormalized' at the second order due to the corrections. We work in the perturbative regime where $T_{thermal}\\ll T_E$.
Current-induced phonon renormalization in molecular junctions
Bai, Meilin; Cucinotta, Clotilde S.; Jiang, Zhuoling; Wang, Hao; Wang, Yongfeng; Rungger, Ivan; Sanvito, Stefano; Hou, Shimin
2016-07-01
We explain how the electrical current flow in a molecular junction can modify the vibrational spectrum of the molecule by renormalizing its normal modes of oscillations. This is demonstrated with first-principles self-consistent transport theory, where the current-induced forces are evaluated from the expectation value of the ionic momentum operator. We explore here the case of H2 sandwiched between two Au electrodes and show that the current produces stiffening of the transverse translational and rotational modes and softening of the stretching modes along the current direction. Such behavior is understood in terms of charge redistribution, potential drop, and elasticity changes as a function of the current.
Coupling constant renormalization due to instantons in the O(3) non-linear sigma model
International Nuclear Information System (INIS)
The renormalized lattice coupling constant for the O(3) non-linear sigma model is calculated, including instanton effects, and the correlation length estimated. The results are in good agreement with the Monte Carlo simulation of Shenker and Tobochnik. The topological charge density is also discussed in the light of recent Monte Carlo simulations. (orig.)
Gauge invariance and holographic renormalization
Directory of Open Access Journals (Sweden)
Keun-Young Kim
2015-10-01
Full Text Available We study the gauge invariance of physical observables in holographic theories under the local diffeomorphism. We find that gauge invariance is intimately related to the holographic renormalization: the local counter terms defined in the boundary cancel most of gauge dependences of the on-shell action as well as the divergences. There is a mismatch in the degrees of freedom between the bulk theory and the boundary one. We resolve this problem by noticing that there is a residual gauge symmetry (RGS. By extending the RGS such that it satisfies infalling boundary condition at the horizon, we can understand the problem in the context of general holographic embedding of a global symmetry at the boundary into the local gauge symmetry in the bulk.
Quantum renormalization group and holography
International Nuclear Information System (INIS)
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the Einstein gravity emerges as a holographic description upto two derivative order for a matrix field theory which has no other operator with finite scaling dimension except for the energy-momentum tensor. We also point out that holographic actions for general large N matrix field theories respect the inversion symmetry along the radial direction in the bulk if the beta functions of single-trace operators are gradient flows with respect to the target space metric set by the beta functions of double-trace operators
Renormalization group in MHD turbulence
International Nuclear Information System (INIS)
The Renormalization Group (RNG) theory is applied to magnetohydrodynamic (MHD) equations written in Elsaesser variables, as done by Yakhot and Orszag. As a result, a system of coupled nonlinear differential equations for the 'effective' or turbulent 'viscosities' is obtained. Without solving this system, it is possible to prove their exponential behaviour at the 'fixed-point' and also determine the effective viscosity and resistivity. Our results do not allow negative effective viscosity or resistivity, but in certain cases the system tends to zero viscosity or resistivity. The range of possible values of the turbulent Prandtl number is also determined; the system tends to different values of this number, depending on the initial values of the viscosity and resistivity and the way the system is excited. (orig.)
Polyakov loop renormalization with gradient flow
Petreczky, Peter; Schadler, Hans-Peter
2015-01-01
We propose to use the gradient flow for the renormalization of Polyakov loops in various representations. We study Polyakov loops in 2+1 flavor QCD using the HISQ action and lattices with temporal extents $N_\\tau$=6, 8, 10 and 12 in various representations, including fundamental, sextet, adjoint, decuplet, 15-plet and 27-plet. This alternative renormalization procedure allows for the renormalization over a large temperature range from $T$=100 MeV - 800 MeV, with small errors not only for the ...
Polyakov loop renormalization with gradient flow
Petreczky, Peter
2015-01-01
We propose to use the gradient flow for the renormalization of Polyakov loops in various representations. We study Polyakov loops in 2+1 flavor QCD using the HISQ action and lattices with temporal extents $N_\\tau$=6, 8, 10 and 12 in various representations, including fundamental, sextet, adjoint, decuplet, 15-plet and 27-plet. This alternative renormalization procedure allows for the renormalization over a large temperature range from $T$=100 MeV - 800 MeV, with small errors not only for the fundamental, but also for the higher representations of the Polyakov loop. We discuss the results of this procedure and Casimir scaling of the Polyakov loop.
Aspects of Galileon Non-Renormalization
Goon, Garrett; Joyce, Austin; Trodden, Mark
2016-01-01
We discuss non-renormalization theorems applying to galileon field theories and their generalizations. Galileon theories are similar in many respects to other derivatively coupled effective field theories, including general relativity and $P(X)$ theories. In particular, these other theories also enjoy versions of non-renormalization theorems that protect certain operators against corrections from self-loops. However, we argue that the galileons are distinguished by the fact that they are not renormalized even by loops of other heavy fields whose couplings respect the galileon symmetry.
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
Brodsky, Stanley J
2012-01-01
It is often argued that the principal ambiguity in fixed-order perturbative QCD calculations lies in the choice of the renormalization scale. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the extended RG equations for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. In particular, we show that the Principle of Minimal Sensitivity (PMS) does not satisfy these requirements. The PMS requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity pro...
Wieczerkowski, C
1996-01-01
We formulate a renormalized running coupling expansion for the beta-function and the potential of the renormalized $\\phi^4$-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.
Hopf-algebraic Renormalization of QED in the linear covariant Gauge
Kißler, Henry
2016-01-01
In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green's functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.
Wilson renormalization group for low {bold {ital x}} physics: Towards the high density regime
Energy Technology Data Exchange (ETDEWEB)
Jalilian-Marian, J. [Physics Department, University of Minnesota, Minneapolis, Minnesota, 55455 (United States); Kovner, A. [Physics Department, University of Minnesota, Minneapolis, Minnesota, 55455 (United States)]|[Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, (United Kingdom); Leonidov, A. [Theoretical Physics Department, P.N. Lebedev Physics Institute, Leninsky pr. 53 Moscow, (Russia); Weigert, H. [University of Cambridge, Cavendish Laboratory, HEP, Madingley Road, Cambridge CB3 0HE, (United Kingdom)
1999-01-01
We continue the study of the effective action for low {ital x} physics based on a Wilson renormalization group approach. We express the full nonlinear renormalization group equation in terms of the average value and the average fluctuation of extra color charge density generated by integrating out gluons with intermediate values of x. This form clearly exhibits the nature of the phenomena driving the evolution and should serve as the basis of the analysis of saturation effects at high gluon density at small x. {copyright} {ital 1998} {ital The American Physical Society}
Changes of Variables and the Renormalization Group
Caticha, Ariel
2016-01-01
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a saddle point approximation is more accurate, becoming, in some cases asymptotically exact as the transformations are iterated. The formalism provides a simplified and unified approach to several known renormalization groups. It also suggests some new ways in which renormalization group methods might successfully be applied. In particular, an exact gauge covariant renormalization group transformation is constructed. Solutions for a scalar field theory are obtained both as an expansion in {\\epsilon}=4-d and as an expansion in a single coupling constant.
On the renormalization of quasi parton distribution
Ji, Xiangdong
2015-01-01
Recent developments showed that light-cone parton distributions can be studied by investigating the large momentum limit of the hadronic matrix elements of spacelike correlators, which are known as quasi parton distributions. Like a light-cone parton distribution, a quasi parton distribution also contains ultraviolet divergences and therefore needs renormalization. The renormalization of non-local operators in general is not well understood. However, in the case of quasi quark distribution, the bilinear quark operator with a straight-line gauge link appears to be multiplicatively renormalizable by the quark wave function renormalization in the axial gauge. We first show that the renormalization of the self energy correction to the quasi quark distribution is equivalent to that of the heavy-light quark vector current in heavy quark effective theory at one-loop order. Assuming this equivalence at two-loop order, we then show that the multiplicative renormalizability of the quasi quark distribution is true at tw...
Numerical renormalization group study of a dissipative quantum dot
Glossop, M. T.; Ingersent, K.
2007-03-01
We study the quantum phase transition (QPT) induced by dissipation in a quantum dot device at the degeneracy point. We employ a Bose-Fermi numerical renormalization group approach [1] to study the simplest case of a spinless resonant-level model that couples the charge density on the dot to a dissipative bosonic bath with density of states B(φ)ŝ. In anticipation of future experiments [2] and to assess further the validity of theoretical techniques in this rapidly developing area, we take the conduction-electron leads to have a pseudogap density of states: ρ(φ) |φ|^r, as considered in a very recent perturbative renormalization group study [3]. We establish the conditions on r and s such that a QPT arises with increasing dissipation strength --- from a delocalized phase, where resonant tunneling leads to large charge fluctuations on the dot, to a localized phase where such fluctuations are frozen. We present results for the single-particle spectrum and the response of the system to a local electric field, extracting critical exponents that depend in general on r and s and obey hyperscaling relations. We make full comparison with results of [3] where appropriate. Supported by NSF Grant DMR-0312939. [1] M. T. Glossop and K. Ingersent, PRL 95, 067202 (2005); PRB (2006). [2] L. G. G. V. Dias da Silva, N. P. Sandler, K. Ingersent, and S. E. Ulloa, PRL 97, 096603 (2006). [3] C.-H. Chung, M. Kir'can, L. Fritz, and M. Vojta (2006).
Hopf algebra of ribbon graphs and renormalization
International Nuclear Information System (INIS)
Connes and Kreimer have discovered a Hopf algebra structure behind renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined in terms of surfaces corresponding to ribbon graphs. As an example, we discuss renormalization of Φ4 theory and the 1/N expansion. (author)
Renormalization-group improved inflationary scenarios
Pozdeeva, E O
2016-01-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
Remarks on Renormalization of Black Hole Entropy
Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
1996-01-01
We elaborate the renormalization process of entropy of a nonextremal and an extremal Reissner-Nordstr\\"{o}m black hole by using the Pauli-Villars regularization method, in which the regulator fields obey either the Bose-Einstein or Fermi-Dirac distribution depending on their spin-statistics. The black hole entropy involves only two renormalization constants. We also discuss the entropy and temperature of the extremal black hole.
Vacuum Polarization Renormalization and the Geometric Phase
Langmann, E; Langmann, Edwin; Mickelsson, Jouko
1996-01-01
As an application of the renormalization method introduced by the second author we give a causal definition of the phase of the quantum scattering matrix for fermions in external Yang-Mills potentials. The phase is defined using parallel transport along the path of renormalized time evolution operators. The time evolution operators are elements of the restricted unitary group $U_{res}$ of Pressley and Segal. The central extension of $U_{res}$ plays a central role.
Relativistic causality and position space renormalization
Todorov, Ivan
2016-01-01
We survey the causal position space renormalization with a special attention to the role of Raymond Stora in the development of the subject. Renormalization is effected by subtracting pole terms in analytically regularized amplitudes. Residues are identified with periods whose relation to recent development in number theory is emphasized. We demonstrate the possibility of integration over internal vertices in the case of a (massless) conformal theory and display the dilation and the conformal anomaly.
Mass renormalization in cavity QED
International Nuclear Information System (INIS)
We show that the presence of a background medium and a boundary surface or surfaces in cavity QED produces no change in the energy shift of a free charged particle due to its coupling to the fluctuating electromagnetic field of the vacuum. This clarifies that the electromagnetic and the observed mass of the charged particle are not affected by the modification of the field of the vacuum. The calculations are nonrelativistic and restricted to the dipole approximation but are otherwise based on the general requirements of causality.
Renormalization of the weak hadronic current in the nuclear medium
Siiskonen, T; Suhonen, J
2001-01-01
The renormalization of the weak charge-changing hadronic current as a function of the reaction energy release is studied at the nucleonic level. We have calculated the average quenching factors for each type of current (vector, axial vector and induced pseudoscalar). The obtained quenching in the axial vector part is, at zero momentum transfer, 19% for the sd shell and 23% in the fp shell. We have extended the calculations also to heavier systems such as $^{56}$Ni and $^{100}$Sn, where we obtain stronger quenchings, 44% and 59%, respectively. Gamow--Teller type transitions are discussed, along with the higher order matrix elements. The quenching factors are constant up to roughly 60 MeV momentum transfer. Therefore the use of energy-independent quenching factors in beta decay is justified. We also found that going beyond the zeroth and first order operators (in inverse nucleon mass) does not give any substantial contribution. The extracted renormalization to the ratio $C_P/C_A$ at q=100 MeV is -3.5%, -7.1$%, ...
CIRM Workshop on Renormalization and Galois Theory
Fauvet, Frédéric; Ramis, Jean-Pierre
2009-01-01
This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes...
Introduction to the nonequilibrium functional renormalization group
Berges, Jürgen
2012-01-01
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity ...
Renormalized vacuum polarization of rotating black holes
Ferreira, Hugo R C
2015-01-01
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2+1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization (and, more importantly, the renormalized stress-energy tensor), for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.
Wilsonian renormalization, differential equations and Hopf algebras
Thomas, Krajewski
2008-01-01
In this paper, we present an algebraic formalism inspired by Butcher's B-series in numerical analysis and the Connes-Kreimer approach to perturbative renormalization. We first define power series of non linear operators and propose several applications, among which the perturbative solution of a fixed point equation using the non linear geometric series. Then, following Polchinski, we show how perturbative renormalization works for a non linear perturbation of a linear differential equation that governs the flow of effective actions. Finally, we define a general Hopf algebra of Feynman diagrams adapted to iterations of background field effective action computations. As a simple combinatorial illustration, we show how these techniques can be used to recover the universality of the Tutte polynomial and its relation to the $q$-state Potts model. As a more sophisticated example, we use ordered diagrams with decorations and external structures to solve the Polchinski's exact renormalization group equation. Finally...
Perturbatively improving RI-MOM renormalization constants
Energy Technology Data Exchange (ETDEWEB)
Constantinou, M.; Costa, M.; Panagopoulos, H. [Cyprus Univ. (Cyprus). Dept. of Physics; Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [Edinburgh Univ. (United Kingdom). School of Physics; Perlt, H.; Schiller, A. [Leipzig Univ. (Germany). Inst. fuer Theoretische Physik; Rakow, P.E.L. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Schhierholz, G. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2013-03-15
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Perturbatively improving RI-MOM renormalization constants
Constantinou, M; Gockeler, M; Horsley, R; Panagopoulos, H; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
2013-01-01
The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. In this paper we investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.
Three Topics in Renormalization and Improvement
Vladikas, A
2011-01-01
This is an expanded version of lecture notes, delivered at the XCIII Les Houches Summer School (August 2009). Our aim is to present three very specific topics: (i) The consequences of the loss of chiral symmetry in the Wilson lattice regularization of the fermionic action and its recovery in the continuum limit. The treatment of these arguments involves lattice Ward identities. (ii) The definition and properties of mass independent renormalization schemes, which are suitable for a non-perturbative computation of various operator renormalization constants. (iii) The modification of the Wilson fermion action, by the introduction of a chirally twisted mass term (known as twisted mass QCD - tmQCD), which results to improved (re)normalization and scaling properties for physical quantities of interest.
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wu, Xing-Gang [Chongqing Univ. (China); SLAC National Accelerator Lab., Menlo Park, CA (United States)
2012-08-07
In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {β^{R}_{i}}-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.
Perturbative renormalization of the electric field correlator
Christensen, C.; Laine, M.
2016-04-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ∼ 12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
Directory of Open Access Journals (Sweden)
C. Christensen
2016-04-01
Full Text Available The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3 gauge theory, finding a ∼12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Perturbative renormalization of the electric field correlator
Christensen, C
2016-01-01
The momentum diffusion coefficient of a heavy quark in a hot QCD plasma can be extracted as a transport coefficient related to the correlator of two colour-electric fields dressing a Polyakov loop. We determine the perturbative renormalization factor for a particular lattice discretization of this correlator within Wilson's SU(3) gauge theory, finding a ~12% NLO correction for values of the bare coupling used in the current generation of simulations. The impact of this result on existing lattice determinations is commented upon, and a possibility for non-perturbative renormalization through the gradient flow is pointed out.
Novel formulations of CKM matrix renormalization
Kniehl, B A
2009-01-01
We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.
Regularization independent renormalization for theories with nontrivial internal symmetry
International Nuclear Information System (INIS)
A renormalization scheme for theories with nontrivial internal symmetry is proposed. This scheme respects automatically symmetry of renormalized theory independently on a regularization used. The general scheme is illustrated by the example of QED
Directory of Open Access Journals (Sweden)
Durães F.O.
2010-04-01
Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral eﬀective ﬁeld theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a ﬁxed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoﬀ through the SRG transformation.
International Nuclear Information System (INIS)
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)
Enhancement of field renormalization in scalar theories via functional renormalization group
Zappalà, Dario
2012-01-01
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, to determine the effective potential and the renormalization function of the field in the broken phase. The flow equations of these quantities are derived from a reduction of the full flow of the effective action onto a set of equations for the n-point vertices of the theory. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.
Renormalization Group Equations for the CKM matrix
Kielanowski, P; Montes de Oca Y, J H
2008-01-01
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs extension and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle $\\alpha$ of the unitarity triangle. For the special case of the Standard Model and its extensions with $v_{1}\\approx v_{2}$ we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters $\\bar{\\rho}=(1-{1/2}\\lambda^{2})\\rho$ and $\\bar{\\eta}=(1-{1/2}\\lambda^{2})\\eta$ are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix mi...
Renormalization of the Neutrino Mass Matrix
Chiu, S H
2015-01-01
In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.
Renormalization of the Quark Mass Matrix
Chiu, S H
2016-01-01
Using a set of rephasing invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We also found approximate solutions to these equations if the quark masses are hierarchical or nearly degenerate.
Renormalized quark-anti-quark free energy
Zantow, F.; Kaczmarek, O.; Karsch, F.; Petreczky, P.
2003-01-01
We present results on the renormalized quark-anti-quark free energy in SU(3) gauge theory at finite temperatures. We discuss results for the singlet, octet and colour averaged free energies and comment on thermal relations which allow to extract separately the potential energy and entropy from the free energy.
Finite volume renormalization scheme for fermionic operators
Energy Technology Data Exchange (ETDEWEB)
Monahan, Christopher; Orginos, Kostas [JLAB
2013-11-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
Monte Carlo Renormalization Group: a review
International Nuclear Information System (INIS)
The logic and the methods of Monte Carlo Renormalization Group (MCRG) are reviewed. A status report of results for 4-dimensional lattice gauge theories derived using MCRG is presented. Existing methods for calculating the improved action are reviewed and evaluated. The Gupta-Cordery improved MCRG method is described and compared with the standard one. 71 refs., 8 figs
Large Neutrino Mixing from Renormalization Group Evolution
Balaji, K R S; Parida, M K; Paschos, E A
2001-01-01
The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of $\
Density Matrix Renormalization Group for Dummies
G. De Chiara; Rizzi, M; Rossini, D.; Montangero, S.
2006-01-01
We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch.
The Similarity Renormalization Group with Novel Generators
Li, W.; Anderson, E. R.; Furnstahl, R. J.
2011-01-01
The choice of generator in the Similarity Renormalization Group (SRG) flow equation determines the evolution pattern of the Hamiltonian. The kinetic energy has been used in the generator for most prior applications to nuclear interactions, and other options have been largely unexplored. Here we show how variations of this standard choice can allow the evolution to proceed more efficiently without losing its advantages.
Gravitational Stability and Renormalization-Group Flow
Skenderis, K; Skenderis, Kostas; Townsend, Paul K.
1999-01-01
First-order `Bogomol'nyi' equations are found for dilaton domain walls of D-dimensional gravity with the general dilaton potential admitting a stable anti-de Sitter vacuum. Implications for renormalization group flow in the holographically dual field theory are discussed.
Renormalization of the neutrino mass matrix
Chiu, S. H.; Kuo, T. K.
2016-09-01
In terms of a rephasing invariant parametrization, the set of renormalization group equations (RGE) for Dirac neutrino parameters can be cast in a compact and simple form. These equations exhibit manifest symmetry under flavor permutations. We obtain both exact and approximate RGE invariants, in addition to some approximate solutions and examples of numerical solutions.
Lectures on renormalization and asymptotic safety
International Nuclear Information System (INIS)
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method
Finite volume renormalization scheme for fermionic operators
Monahan, Christopher; Orginos, Kostas
2013-01-01
We propose a new finite volume renormalization scheme. Our scheme is based on the Gradient Flow applied to both fermion and gauge fields and, much like the Schr\\"odinger functional method, allows for a nonperturbative determination of the scale dependence of operators using a step-scaling approach. We give some preliminary results for the pseudo-scalar density in the quenched approximation.
de Meux, Albert de Jamblinne; Leconte, Nicolas; Charlier, Jean-Christophe; Lherbier, Aurélien
2015-01-01
The electronic properties of one-dimensional graphene superlattices strongly depend on the atomic size and orientation of the 1D external periodic potential. Using a tight-binding approach, we show that the armchair and zigzag directions in these superlattices have a different impact on the renormalization of the anisotropic velocity of the charge carriers. For symmetric potential barriers, the velocity perpendicular to the barrier is modified for the armchair direction while remaining unchan...
Improved Epstein-Glaser renormalization in $x$-space. III. Versus differential renormalization
Gracia-Bondía, José M; Várilly, Joseph C
2014-01-01
Renormalization of massless Feynman amplitudes in $x$-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for vertex functions at several-loop order. The approach has much in common with differential renormalization, but differs in important details. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions.
International Nuclear Information System (INIS)
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, are discussed in part III where numerical results, e.g. for the complex poles of the unstable gauge bosons, are shown. An attempt is made to define the running of the electromagnetic coupling constant at the two-loop level. (orig.)
Renormalization and effective actions for general relativity
Energy Technology Data Exchange (ETDEWEB)
Neugebohrn, F.
2007-05-15
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)
Renormalization and effective actions for general relativity
International Nuclear Information System (INIS)
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)
International Nuclear Information System (INIS)
We introduce and analyze d-dimensional Coulomb gases with random charge distribution and general external confining potential. We show that these gases satisfy a large-deviation principle. The analysis of the minima of the rate function (which is the leading term of the energy) reveals that, at equilibrium, the particle distribution is a generalized circular law (i.e. with spherical support but not necessarily uniform distribution). In the classical electrostatic external potential, there are infinitely many minimizers of the rate function. The most likely macroscopic configuration is a disordered distribution in which particles are uniformly distributed (for d = 2, the circular law), and charges are independent of the positions of the particles. General charge-dependent confining potentials unfold this degenerate situation: in contrast, the particle density is not uniform, and particles spontaneously organize according to their charge. In this picture the classical electrostatic potential appears as a transition at which order is lost. Sub-leading terms of the energy are derived: we show that these are related to an operator, generalizing the Coulomb renormalized energy, which incorporates the heterogeneous nature of the charges. This heterogeneous renormalized energy informs us about the microscopic arrangements of the particles, which are non-standard, strongly dependent on the charges, and include progressive and irregular lattices. (paper)
Renormalization Methods - A Guide For Beginners
International Nuclear Information System (INIS)
The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard φ4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
Black hole entropy and the renormalization group
Satz, Alejandro
2013-01-01
Four decades after its first postulation by Bekenstein, black hole entropy remains mysterious. It has long been suggested that the entanglement entropy of quantum fields on the black hole gravitational background should represent at least an important contribution to the total Bekenstein-Hawking entropy, and that the divergences in the entanglement entropy should be absorbed in the renormalization of the gravitational couplings. In this talk, we describe how an improved understanding of black hole entropy is obtained by combining these notions with the renormalization group. By introducing an RG flow scale, we investigate whether the total entropy of the black hole can be partitioned in a "gravitational" part related to the flowing gravitational action, and a "quantum" part related to the unintegrated degrees of freedom. We describe the realization of this idea for free fields, and the complications and qualifications arising for interacting fields.
Temperature dependent quasiparticle renormalization in nickel metal
Energy Technology Data Exchange (ETDEWEB)
Ovsyannikov, Ruslan; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann A. [Helmholtz Zentrum Berlin (Germany). BESSY II
2009-07-01
One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed', i.e. they acquire an increased effective mass and a lifetime. We studied the spin dependent quasiparticle band structure of Ni(111) with high resolution angle resolved photoemission spectroscopy. At low temperatures (50 K) a renormalization of quasiparticle energy and lifetime indicative of electron-phonon coupling is observed in agreement with literature. With increasing temperature we observe a decreasing quasiparticle lifetime at the Fermi level for all probed minority spin bands as expected from electron phonon coupling. Surprisingly the majority spin states behave differently. We actually observe a slightly increased lifetime at room temperature. The corresponding increase in Fermi velocity points to a temperature dependent reduction of the majority spin quasiparticle renormalization.
Renormalized vacuum polarization of rotating black holes
Ferreira, Hugo R. C.
2015-04-01
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.
Information loss along the renormalization flow
International Nuclear Information System (INIS)
Our ability to probe the real world is always limited by experimental constraints such as the precision of our instruments. It is remarkable that the resulting imperfect data nevertheless contains regularities which can be understood in terms of effective laws. The renormalization group (RG) aims to formalize the relationship between effective theories summarizing the behaviour of a single system probed at different length scales. An important feature of the RG is its tendency to converge to few universal effective field theories at large scale. We explicitly model the change of resolution at which a quantum lattice system is probed as a completely positive semigroup on density operators, i.e., a family of quantum channels, and derive from it a renormalization ''group'' on effective theories. This formalism suggests a family of finite distinguishability metrics which contract under the RG, hence identifying the information that is lost on the way to universal RG fixed points.
Information loss along the renormalization flow
Energy Technology Data Exchange (ETDEWEB)
Beny, Cedric; Osborne, Tobias [Leibniz Universitaet Hannover (Germany)
2013-07-01
Our ability to probe the real world is always limited by experimental constraints such as the precision of our instruments. It is remarkable that the resulting imperfect data nevertheless contains regularities which can be understood in terms of effective laws. The renormalization group (RG) aims to formalize the relationship between effective theories summarizing the behaviour of a single system probed at different length scales. An important feature of the RG is its tendency to converge to few universal effective field theories at large scale. We explicitly model the change of resolution at which a quantum lattice system is probed as a completely positive semigroup on density operators, i.e., a family of quantum channels, and derive from it a renormalization ''group'' on effective theories. This formalism suggests a family of finite distinguishability metrics which contract under the RG, hence identifying the information that is lost on the way to universal RG fixed points.
Renormalized Resonance Quartets in Dispersive Wave Turbulence
Lee, Wonjung; Kovačič, Gregor; Cai, David
2009-07-01
Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distribution is in excellent agreement with the simulation of the full wave system in equilibrium.
Renormalization of two-dimensional XQCD
Fukaya, Hidenori
2015-01-01
Recently, Kaplan proposed an interesting extension of QCD named Extended QCD or XQCD with bosonic auxiliary fields [1]. While its partition function is kept exactly the same as that of QCD, XQCD naturally contains properties of low-energy hadrons. We apply this extension to the two-dimensional QCD in the large $N_c$ limit ('t Hooft model) [2]. In this solvable model, it is possible to directly examine the hadronic picture of the 2d XQCD and analyze its renormalization group flow to understand how the auxiliary degrees of freedom behave in the low energy region. We confirm that the additional scalar fields can become dynamical acquiring the kinetic term, and its parity-odd part becomes dominant in the low energy region. This renomalization of XQCD provides an "extension" of the renormalization scheme of QCD, inserting different field variables from those in the original theory, without any changes in physical observables.
Renormalization of gauge theories without cohomology
Anselmi, Damiano
2013-07-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
Renormalization of gauge theories without cohomology
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa (Italy)
2013-07-15
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)
Renormalization Group and Problem of Radiation
Sigal, I M
2011-01-01
The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and techniques in the theory of radiation. We describe the key technique in this area - the spectral renormalization group. Our review is based on joint works with Volker Bach and Juerg Froehlich and with Walid Abou Salem, Thomas Chen, Jeremy Faupin and Marcel Griesemer. Brief discussion of related contributions is given at the end of these lectures. This review will appear in "Quantum Theory from Small to Large Scales", Lecture Notes of the Les Houches Summer Schools, volume 95, Oxford University Press, 2011. Key words: quantum electrodynamics, photons and electrons, renormalization group, quantum resonances, spectral theory, Schroedinger operators, ground state, quantum dynamics, non-relativistic theory.
Renormalization of Magnetic Excitations in Praseodymium
DEFF Research Database (Denmark)
Lindgård, Per-Anker
1975-01-01
The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...... and the ratio between the exchange interaction and d is very close to unity. However, zero-point motion prevents the system from ordering....
New Dynamic Monte Carlo Renormalization Group Method
Lacasse, Martin-D.; Vinals, Jorge; Grant, Martin
1992-01-01
The dynamical critical exponent of the two-dimensional spin-flip Ising model is evaluated by a Monte Carlo renormalization group method involving a transformation in time. The results agree very well with a finite-size scaling analysis performed on the same data. The value of $z = 2.13 \\pm 0.01$ is obtained, which is consistent with most recent estimates.
Renormalization of Gravity and Gravitational Waves
Pardy, Miroslav
2001-01-01
Strictly respecting the Einstein equations and supposing space-time is a medium, we derive the deformation of this medium by gravity. We derive the deformation in case of infinite plane, Robertson-Walker manifold, Schwarzschild manifold and gravitational waves. Some singularities are removed or changed. We call this procedure renormalization of gravity. We show that some results following from the classical gravity must be modified.
Gauge coupling renormalization in orbifold field theories
Choi, Kiwoon; Kim, Hyung Do; Kim, Ian-Woo
2002-01-01
We investigate the gauge coupling renormalization in orbifold field theories preserving 4-dimensional N=1 supersymmetry in the framework of 4-dimensional effective supergravity. As a concrete example, we consider the 5-dimensional Super-Yang-Mills theory on a slice of AdS_5. In our approach, one-loop gauge couplings can be determined by the loop-induced axion couplings and the tree level properties of 4-dimensional effective supergravity which are much easier to be computed.
Renormalization of null Wilson lines in EQCD
International Nuclear Information System (INIS)
Radiation and energy loss of a light, high-energy parton in a perturbative Quark-Gluon Plasma is controlled by transverse momentum exchange. The troublesome infrared contributions to transverse momentum exchange can be computed on the lattice using dimensional reduction to EQCD. However a novel extended operator, the Null Wilson Line of EQCD, is involved. We compute the renormalization properties of this object’s lattice implementation to next-to-leading order, which should facilitate its efficient calculation on the lattice
Renormalized field theory of resistor diode percolation
Stenull, Olaf; Janssen, Hans-Karl
2001-01-01
We study resistor diode percolation at the transition from the non-percolating to the directed percolating phase. We derive a field theoretic Hamiltonian which describes not only geometric aspects of directed percolation clusters but also their electric transport properties. By employing renormalization group methods we determine the average two-port resistance of critical clusters, which is governed by a resistance exponent $\\phi$. We calculate $\\phi$ to two-loop order.
Two-loop renormalization of gaugino masses
International Nuclear Information System (INIS)
We calculate the two-loop renormalization group equations for the running gaugino masses in general SUSY gauge models. We also study its consequence to the unification of the gaugino masses in the SUSY SU(5) model. The two-loop correction to the one-loop relation mi(μ) ∝ αi(μ) is found to be of the order of a few %. (author)
Quarkonia from charmonium and renormalization group equations
International Nuclear Information System (INIS)
A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
Extreme value distributions and Renormalization Group
Calvo, Iván; Cuchí Oterino, J. C.; Esteve, J. G.; Falceto, Fernando
2011-01-01
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. So far, only affine rescalings have been considered. We show, however, that more general rescalings are natural and lead to new limit distributions, apart from the Gumbel, Weibull, and Fr\\'echet families. The problem is approached using the language of Renormalization Group transformations in the space of probability densit...
Entanglement renormalization and two dimensional string theory
Molina-Vilaplana, J.
2016-04-01
The entanglement renormalization flow of a (1 + 1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.
Generalized Hubbard Hamiltonian: renormalization group approach
Energy Technology Data Exchange (ETDEWEB)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-12-31
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs.
RENORM tensor-Pomeron diffractive predictions
Goulianos, K
2016-01-01
Predictions of the elastic scattering, total-inetastic, and total proton-proton cross sections, based on a Regge theory inspired tensor-Pomeron implementation of the RENORM model for hadronic diffraction, are compared to the latest experimental measurements at the LHC. The measured cross sections are in good agreement within the experimental uncertainties of the data and the theoretical uncertainties of the model, reaching down to the ~1% level.
Gravitational Renormalization Group Flow, Astrophysics and Cosmology
Moffat, J W
2015-01-01
A modified gravitational theory is developed in which the gravitational coupling constants $G$ and $Q$ and the effective mass $m_\\phi$ of a repulsive vector field run with momentum scale $k$ or length scale $\\ell =1/k$, according to a renormalization group flow. The theory can explain cosmological early universe data with a dark hidden photon and late time galaxy and cluster dynamics without dark matter. The theory agrees with solar system and binary pulsar observations.
Quark mass renormalization and family unification
International Nuclear Information System (INIS)
We have explored the possibility that the observed fermion mass ratios arise purely because of renormalization effects, andthat in the extended GUTs which unify the families non-trivially, these ratios evolve differently and in the correct direction. The analysis indicates that it is sometimes premature to try to rule out some GUTs which do not contain family unification, because of their wrong predictions for some mass ratios. (orig.)
Renormalization and Interaction in Quantum Field Theory
International Nuclear Information System (INIS)
This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory.
A shape dynamical approach to holographic renormalization
Energy Technology Data Exchange (ETDEWEB)
Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2015-01-01
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)
Renormalization group flows and continual Lie algebras
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches...
A shape dynamical approach to holographic renormalization
International Nuclear Information System (INIS)
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)
The renormalization group via statistical inference
Bény, Cédric; Osborne, Tobias J.
2015-08-01
In physics, one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure to identify the corresponding equivalence classes of states, and argue that the renormalization group (RG) arises from the inherent ambiguities associated with the classes: one encounters flow parameters as, e.g., a regulator, a scale, or a measure of precision, which specify representatives in a given equivalence class. This provides a unifying framework and reveals the role played by information in renormalization. We validate this idea by showing that it justifies the use of low-momenta n-point functions as statistically relevant observables around a Gaussian hypothesis. These results enable the calculation of distinguishability in quantum field theory. Our methods also provide a way to extend renormalization techniques to effective models which are not based on the usual quantum-field formalism, and elucidates the relationships between various type of RG.
Renormalization group domains of the scalar Hamiltonian
Bagnuls, C
2000-01-01
Using the local potential approximation of the exact renormalization group(RG) equation, we show the various domains of values of the parameters of theO(1)-symmetric scalar hamiltonian. In three dimensions, in addition to theusual critical surface $S_{\\text{c}}$ (attraction domain of the Wilson-Fisherfixed point), we explicitly show the existence of a first-order phasetransition domain $S_{\\text{f}}$ separated from $S_{\\text{c}}$ by thetricritical surface $S_{\\text{t}}$ (attraction domain of the Gaussian fixedpoint). $S_{\\text{f}}$ and $S_{\\text{c}}$ are two distinct domains of repulsionfor the Gaussian fixed point, but $S_{\\text{f}}$ is not the basin of attractionof a fixed point. $S_{\\text{f}}$ is characterized by an endless renormalizedtrajectory lying entirely in the domain of negative values of the $\\phi^{4}$-coupling. This renormalized trajectory exists also in four dimensionsmaking the Gaussian fixed point ultra-violet stable (and the $\\phi_{4}^{4}$renormalized field theory asymptotically free but with...
Renormalization, Hopf algebras and Mellin transforms
Panzer, Erik
2014-01-01
This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like to point out properties of the kinematic subtraction scheme which is also widely used in physics (under the names of MOM or BPHZ). In particular we relate renormalized Feynman rules $\\phi_R$ in this scheme to the universal property of the Hopf algebra $H_R$ of rooted trees, exhibiting a refined renormalization group equation which is equivalent to $\\phi_R: H_R \\rightarrow K[x]$ being a morphism of Hopf algebras to the polynomials in one indeterminate. Upon introduction of analytic regularization this results in efficient combinatorial recursions to calculate $\\phi_R$ in terms of the Mellin transform. We find that different Feynman rules are related by a distinguished class of Hopf algebra automorphisms of $H_R$ that arise naturally from Hochschild cohomology. Also we recall...
Renormalization-Scale Uncertainty in the Decay Rate of False Vacuum
Endo, Motoi; Nojiri, Mihoko M; Shoji, Yutaro
2015-01-01
We study radiative corrections to the decay rate of false vacua, paying particular attention to the renormalization-scale dependence of the decay rate. The decay rate exponentially depends on the bounce action. The bounce action itself is renormalization scale dependent. To make the decay rate scale-independent, radiative corrections, which are due to the field fluctuations around the bounce, have to be included. We show quantitatively that the inclusion of the fluctuations suppresses the scale dependence, and hence is important for the precise calculation of the decay rate. We also apply our analysis to a supersymmetric model and show that the radiative corrections are important for the Higgs-stau system with charge breaking minima.
Hilbert space renormalization for the many-electron problem
Li, Zhendong
2015-01-01
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wav...
What can we learn from the finite temperature renormalization group?
International Nuclear Information System (INIS)
The renormalization group for finite temperature quantum field theories is studied, in particular for λφ4. It is shown that the ''high'' temperature limit can only be discussed perturbatively if T dependent renormalization schemes are implemented. Zero temperature renormalization schemes or renormalization at some fixed reference temperature T0 are both inadequate as they imply perturbative expansions about fixed points of the renormalization group which are associated with a zero temperature system and a system at temperature T0 respectively. T dependent schemes give rise to the expansion about the true fixed point of the system, the resulting renormalization group allows the entire crossover between high and low temperature behaviour to be investigated. (orig.)
The Renormalization Scale-Setting Problem in QCD
Wu, Xing-Gang; Mojaza, Matin
2013-01-01
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this {\\it ad hoc} procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale- independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the s...
Improved Epstein–Glaser renormalization in x-space versus differential renormalization
Directory of Open Access Journals (Sweden)
José M. Gracia-Bondía
2014-09-01
Full Text Available Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
Renormalization Group Approach to Einstein Equation in Cosmology
Iguchi, Osamu; Hosoya, Akio; Koike, Tatsuhiko
1997-01-01
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the present work we apply the renormalization group to the Einstein equation in cosmology and carry out detailed analysis of renormalization group flow in the vicinity of the scale invariant fixed point in the spherically symmetric and inhomogeneous dust filled uni...
Renormalization of the Polyakov loop with gradient flow
Petreczky, P.; Schadler, H. -P.
2015-01-01
We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2+1 flavor QCD with highly improved staggered quarks and lattices with temporal extents of $N_\\tau=6$, $8$, $10$ and $12$ we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from $T=116$ Me...
Generalized geometry, T-duality, and renormalization group flow
Streets, Jeffrey
2013-01-01
We interpret the physical $B$-field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural "Ricci flow" for generalized geometry. Next we show that the $B$-field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain new long time existence results for the $B$-field renormalization group flow.
Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly
Nikolov, Nikolay M; Todorov, Ivan
2013-01-01
Configuration (x-)space renormalization of Euclidean Feynman amplitudes in a massless quantum field theory is reduced to the study of local extensions of associate homogeneous distributions. Primitively divergent graphs are renormalized, in particular, by subtracting the residue of an analytically regularized expression. Examples are given of computing residues that involve zeta values. The renormalized Green functions are again associate homogeneous distributions of the same degree that transform under indecomposable representations of the dilation group.
Renormalization group and fixed points in quantum field theory
International Nuclear Information System (INIS)
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
Adiabatic renormalization in theories with modified dispersion relations
Nacir, D. Lopez; Mazzitelli, F. D.; Simeone, C.
2007-01-01
We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale $M_C$. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may c...
Renormalization theory of Feynman amplitudes on configuration spaces
Nikolov, Nikolay M
2009-01-01
In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This approach is aimed to serve for developing an algebraic algorithm for computing the Gell--Mann--Low renormalization group action. In the present work we introduce a modification of the theory of renormalization maps for the case of Minkowski space and we give the way how it is combined with the causal perturbation theory.
The two-loop renormalization of general quantum field theories
International Nuclear Information System (INIS)
This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)
Renormalization of the Periodic Scalar Field Theory by Polchinski's Renormalization Group Method
Nandori, I; Jentschura, U D; Soff, G
2002-01-01
The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this work we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas.
Renormalization of the periodic scalar field theory by Polchinski's renormalization group method
International Nuclear Information System (INIS)
The renormalization group (RG) flow for the two-dimensional sine-Gordon model is determined by means of Polchinski's RG equation at next-to-leading order in the derivative expansion. In this paper, we have two different goals, (i) to consider the renormalization scheme-dependence of Polchinski's method by matching Polchinski's equation with the Wegner-Houghton equation and with the real space RG equations for the two-dimensional dilute Coulomb-gas, (ii) to go beyond the local potential approximation in the gradient expansion in order to clarify the supposed role of the field-dependent wave-function renormalization. The well-known Coleman fixed point of the sine-Gordon model is recovered after linearization, whereas the flow exhibits strong dependence on the choice of the renormalization scheme when non-linear terms are kept. The RG flow is compared to those obtained in the Wegner-Houghton approach and in the dilute gas approximation for the two-dimensional Coulomb-gas. (author)
Renormalization schemes: Where do we stand?
International Nuclear Information System (INIS)
We consider the status of the current approaches to the application of the renormalization program to the standard SU2L x U1 theory from the standpoint of the interplay of the scheme chosen for such an application and the attendant high-precision tests of the respective loop effects. We thus review the available schemes and discuss their theoretical relationships. We also show how such schemes stand in numerical relation to one another in the context of high-precision Z0 physics, as an illustration. 15 refs., 2 figs., 2 tabs
Functional renormalization group approach to neutron matter
Directory of Open Access Journals (Sweden)
Matthias Drews
2014-11-01
Full Text Available The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter.
de Sitter Vacua, Renormalization and Locality
Banks, T
2003-01-01
We analyze the renormalization properties of quantum field theories in de Sitter space and show that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. One is the Euclidean vacuum, and the other can be viewed as an analytic continuation of Euclidean functional integrals on $RP^d$. The corresponding Lorentzian manifold is the future half of global de Sitter space with boundary conditions on fields at the origin of time. We argue that the perturbation series in this case has divergences at the origin, which render the future evolution of the system indeterminate without a better understanding of high energy physics.
Perturbative and nonperturbative renormalization in lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, M. [Regensburg Univ. (Germany). Institut fuer Theoretische Physik; Horsley, R. [University of Edinburgh (United Kingdom). School of Physics and Astronomy; Perlt, H. [Leipzig Univ. (DE). Institut fuer Theoretische Physik] (and others)
2010-03-15
We investigate the perturbative and nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields (quark-antiquark operators). These include operators which are relevant to the calculation of moments of hadronic structure functions. The nonperturbative computations are based on Monte Carlo simulations with two flavors of clover fermions and utilize the Rome-Southampton method also known as the RI-MOM scheme. We compare the results of this approach with various estimates from lattice perturbation theory, in particular with recent two-loop calculations. (orig.)
The exact renormalization group and approximation solutions
Morris, T R
1994-01-01
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\\lambda \\varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
Renormalization group domains of the scalar Hamiltonian
Bagnuls, C.; Bervillier, C.
2000-01-01
Using the local potential approximation of the exact renormalization group (RG) equation, we show the various domains of values of the parameters of the O(1)-symmetric scalar Hamiltonian. In three dimensions, in addition to the usual critical surface $S_{c}$ (attraction domain of the Wilson-Fisher fixed point), we explicitly show the existence of a first-order phase transition domain $S_{f}$ separated from $S_{c}$ by the tricritical surface $S_{t}$ (attraction domain of the Gaussian fixed poi...
Extreme-value distributions and renormalization group.
Calvo, Iván; Cuchí, Juan C; Esteve, J G; Falceto, Fernando
2012-10-01
In the classical theorems of extreme value theory the limits of suitably rescaled maxima of sequences of independent, identically distributed random variables are studied. The vast majority of the literature on the subject deals with affine normalization. We argue that more general normalizations are natural from a mathematical and physical point of view and work them out. The problem is approached using the language of renormalization-group transformations in the space of probability densities. The limit distributions are fixed points of the transformation and the study of its differential around them allows a local analysis of the domains of attraction and the computation of finite-size corrections. PMID:23214531
Renormalization group and the ideal Bose gas
International Nuclear Information System (INIS)
Critical behaviour of a d-dimensional ideal Bose gas is investigated from the point of view of the renormalization group approach. Rescaling of quantum field amplitudes is avoided by introducing a scaling variable inversely proportional to the thermal momentum of the particles. The scaling properties of various thermodynamic quantities are seen to emerge as a consequence of the irrelevant nature of this variable. Critical behaviour is discussed at fixed particle density as well as at fixed pressure. Connection between susceptibility and correlation function of the order-parameter for a quantum system is elucidated. (author)
Optimal renormalization scales and commensurate scale relations
International Nuclear Information System (INIS)
Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which satisfy a transitivity rule which ensures that predictions are independent of the choice of an intermediate renormalization scheme. QCD can thus be tested in a new and precise way by checking that the observables track both in their relative normalization and in their commensurate scale dependence. For example, the radiative corrections to the Bjorken sum rule at a given momentum transfer Q can be predicted from measurements of the e+e- annihilation cross section at a corresponding commensurate energy scale √s ∝ Q, thus generalizing Crewther's relation to non-conformal QCD. The coefficients that appear in this perturbative expansion take the form of a simple geometric series and thus have no renormalon divergent behavior. The authors also discuss scale-fixed relations between the threshold corrections to the heavy quark production cross section in e+e- annihilation and the heavy quark coupling αV which is measurable in lattice gauge theory
Optimal renormalization scales and commensurate scale relations
Energy Technology Data Exchange (ETDEWEB)
Brodsky, S.J. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Lu, H.J. [Univ. of Arizona, Tucson, AZ (United States). Dept. of Physics
1996-01-01
Commensurate scale relations relate observables to observables and thus are independent of theoretical conventions, such as the choice of intermediate renormalization scheme. The physical quantities are related at commensurate scales which satisfy a transitivity rule which ensures that predictions are independent of the choice of an intermediate renormalization scheme. QCD can thus be tested in a new and precise way by checking that the observables track both in their relative normalization and in their commensurate scale dependence. For example, the radiative corrections to the Bjorken sum rule at a given momentum transfer Q can be predicted from measurements of the e+e{sup {minus}} annihilation cross section at a corresponding commensurate energy scale {radical}s {proportional_to} Q, thus generalizing Crewther`s relation to non-conformal QCD. The coefficients that appear in this perturbative expansion take the form of a simple geometric series and thus have no renormalon divergent behavior. The authors also discuss scale-fixed relations between the threshold corrections to the heavy quark production cross section in e+e{sup {minus}} annihilation and the heavy quark coupling {alpha}{sub V} which is measurable in lattice gauge theory.
Holographic Entanglement Renormalization of Topological Insulators
Wen, Xueda; Lopes, Pedro L S; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei
2016-01-01
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA do...
Singlet Free Energies and Renormalized Polyakov Loop in full QCD
Petrov, K.
2006-01-01
We calculate the free energy of a static quark anti-quark pair and the renormalized Polyakov loop in 2+1- and 3- flavor QCD using $16^3 \\times 4$ and $16^3 \\times 6$ lattices and improved staggered p4 action. We also compare the renormalized Polyakov loop with the results of our earlier studies.
Symmetries of renormalized theories. 1. Non-gauge theories
International Nuclear Information System (INIS)
The symmetry properties of the renomalized filed theories the classical actions of which have symmetry properties are studied in the general form, when the jacobian of change of variables in the functional integral is not ignored. It is shown that to any symmetry of classical action corresponds a certain symmetry of renormalized quantum action and renormalized generating functional of proper vertices
Renormalized and entropy solutions of nonlinear parabolic systems
Directory of Open Access Journals (Sweden)
Lingeshwaran Shangerganesh
2013-12-01
Full Text Available In this article, we study the existence of renormalized and entropy solutions of SIR epidemic disease cross-diffusion model with Dirichlet boundary conditions. Under the assumptions of no growth conditions and integrable data, we establish that the renormalized solution is also an entropy solution.
Renormalization of Yukawa theory with a kernel in stochastic quantization
International Nuclear Information System (INIS)
In this paper, renormalization of massive fermionic theory with a kernel, when fermions are coupled to bosons via Yukawa coupling is studied. It is shown that the theory is indeed renormalizable by proving that no new counterterms appear in the renormalized action
Renormalization of EFT for nucleon-nucleon scattering
Yang, J. -F.
2004-01-01
The renormalization of EFT for nucleon-nucleon scattering in nonperturbative regimes is investigated in a compact parametrization of the $T$-matrix. The key difference between perturbative and nonperturbative renormalization is clarified. The underlying theory perspective and the 'fixing' of the prescriptions for the $T$-matrix from physical boundary conditions are stressed.
A new consistent renormalization concept involving bound-state problems
International Nuclear Information System (INIS)
Full text: A new consistent renormalization procedure, based on the self-consistent projection operator method (guaranteeing the consistency of the applied approximation to any order), developed by J. Seke, has been elaborated. The new complete renormalization, unlike the conventional one, removes completely the experimentally unobservable free-electron Dyson self-energy from the fermion propagator. (author)
Renormalized stress tensor for massive fields in Kerr-Newman spacetime
Belokogne, Andrei
2014-01-01
In a four-dimensional spacetime, the DeWitt-Schwinger expansion of the effective action associated with a massive quantum field reduces, after renormalization and in the large mass limit, to a single term involving the purely geometrical Gilkey-DeWitt coefficient $a_3$ and its metric variation provides a good analytical approximation for the renormalized stress-energy tensor of the quantum field. Here, from the general expression of this tensor, we obtain analytically the renormalized stress-energy tensors of the massive scalar field, the massive Dirac field and the Proca field in Kerr-Newman spacetime. It should be noted that, even if, at first sight, the expressions obtained are complicated, their structure is in fact rather simple, involving naturally spacetime coordinates as well as the mass $M$, the charge $Q$ and the rotation parameter $a$ of the Kerr-Newman black hole and permitting us to recover rapidly the results already existing in the literature for the Schwarzschild, Reissner-Nordstr\\"om and Kerr...
Temperature dependent quasiparticle renormalization in nickel and iron
Energy Technology Data Exchange (ETDEWEB)
Ovsyannikov, Ruslan; Thirupathaiah, Setti; Sanchez-Barriga, Jaime; Fink, Joerg; Duerr, Hermann [Helmholtz Zentrum Berlin, BESSY II, Albert-Einstein-Strasse 15, D-12489 Berlin (Germany)
2010-07-01
One of the fundamental consequences of electron correlation effects is that the bare particles in solids become 'dressed' with an excitation cloud resulting in quasiparticles. Such a quasiparticle will carry the same spin and charge as the original particle, but will have a renormalized mass and a finite lifetime. The properties of many-body interactions are described with a complex function called self energy which is directly accessible to modern high-resolution angle resolved photoemission spectroscopy (ARPES). Ferromagnetic metals like nickel or iron offers the exciting possibility to study the spin dependence of quasiparticle coupling to bosonic modes. Utilizing the exchange split band structure as an intrinsic 'spin detector' it is possible to distinguish between electron-phonon and electron-magnon coupling phenomena. In this contribution we will report a systematic investigation of the k- and temperature dependence of the electron-boson coupling in nickel and iron metals as well as discuss origin of earlier observed anomalous lifetime broadening of majority spin states of nickel at Fermi level.
International Nuclear Information System (INIS)
The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived
Kazinski, P. O.; Lyakhovich, S. L.; Sharapov, A. A.
2002-07-01
The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.
Kazinski, P O; Sharapov, A A
2002-01-01
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.
International Nuclear Information System (INIS)
The connection between renormalization schemes (RS's) and the renormalization group (RG) functions for a massive Yang--Mills theory is investigated. The RS's are defined in a manner independent of the regularization procedure. The RS transformations are defined in such a way that it is clear that they form a group. It is shown that to a given set of RG functions corresponds an infinite number of RS's. The subgroup of RS transformations which leave invariant the (mass-shell) MS-RG functions is carefully described. Gauge invariance, regularity of the theory when m→0 and mass decoupling are imposed and the corresponding indeterminations of RS's are given. It is seen that a RS which fulfills simultaneously the above conditions does not exist
Well funneled nuclear structure landscape: renormalization
Idini, A; Barranco, F; Vigezzi, E; Broglia, R A
2015-01-01
A complete characterization of the structure of nuclei can be obtained by combining information arising from inelastic scattering, Coulomb excitation and $\\gamma-$decay, together with one- and two-particle transfer reactions. In this way it is possible to probe the single-particle and collective components of the nuclear many-body wavefunction resulting from their mutual coupling and diagonalising the low-energy Hamiltonian. We address the question of how accurately such a description can account for experimental observations. It is concluded that renormalizing empirically and on equal footing bare single-particle and collective motion in terms of self-energy (mass) and vertex corrections (screening), as well as particle-hole and pairing interactions through particle-vibration coupling allows theory to provide an overall, quantitative account of the data.
Renormalization group flow for noncommutative Fermi liquids
International Nuclear Information System (INIS)
Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding B-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS' and BCS are discussed in detail. It is shown that while the Gaussian fixed-point remains unchanged, the BCS instability is modified due to the space noncommutativity.
On renormalization group flow in matrix model
International Nuclear Information System (INIS)
The renormalization group flow recently found by Brezin and Zinn-Justin by integrating out redundant entries of the (N+1)x(N+1) Hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding suitable counter terms to the matrix potential of the one matrix model, we deduce some interesting properties of the RG trajectories. In particular, the string equation for the general massive model interpolating between the UV and IR fixed points turns out to be a consequence of RG flow. An ambiguity in the UV region of the RG trajectory is remarked to be related to the large order behaviour of the one matrix model. (author). 7 refs
Renormalization group theory impact on experimental magnetism
Köbler, Ulrich
2010-01-01
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...
Spin connection and renormalization of teleparallel action
Energy Technology Data Exchange (ETDEWEB)
Krssak, Martin; Pereira, J.G. [Universidade Estadual Paulista, Instituto de Fisica Teorica, Sao Paulo, SP (Brazil)
2015-11-15
In general relativity, inertia and gravitation are both included in the Levi-Civita connection. As a consequence, the gravitational action, as well as the corresponding energy-momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented. (orig.)
Renormalization of QED near Decoupling Temperature
Masood, Samina S
2014-01-01
We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron selfmass, {\\delta}m/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.
Holographic Trace Anomaly and Local Renormalization Group
Rajagopal, Srivatsan; Zhu, Yechao
2015-01-01
The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.
Holographic trace anomaly and local renormalization group
Rajagopal, Srivatsan; Stergiou, Andreas; Zhu, Yechao
2015-11-01
The Hamilton-Jacobi method in holography has produced important results both at a renormalization group (RG) fixed point and away from it. In this paper we use the Hamilton-Jacobi method to compute the holographic trace anomaly for four- and six-dimensional boundary conformal field theories (CFTs), assuming higher-derivative gravity and interactions of scalar fields in the bulk. The scalar field contributions to the anomaly appear in CFTs with exactly marginal operators. Moving away from the fixed point, we show that the Hamilton-Jacobi formalism provides a deep connection between the holographic and the local RG. We derive the local RG equation holographically, and verify explicitly that it satisfies Weyl consistency conditions stemming from the commutativity of Weyl scalings. We also consider massive scalar fields in the bulk corresponding to boundary relevant operators, and comment on their effects to the local RG equation.
Renormalization methods for higher order differential equations
International Nuclear Information System (INIS)
We adapt methodology of statistical mechanics and quantum field theory to approximate solutions to an arbitrary order ordinary differential equation boundary value problem by a second-order equation. In particular, we study equations involving the derivative of a double-well potential such as u − u3 or − u + 2u3. Using momentum (Fourier) space variables we average over short length scales and demonstrate that the higher order derivatives can be neglected within the first cumulant approximation, once length is properly renormalized, yielding an approximation to solutions of the higher order equation from the second order. The results are confirmed using numerical computations. Additional numerics confirm that the main role of the higher order derivatives is in rescaling the length. (paper)
Semihard processes with BLM renormalization scale setting
Energy Technology Data Exchange (ETDEWEB)
Caporale, Francesco [Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15 and U. Autónoma de Madrid, E-28049 Madrid (Spain); Ivanov, Dmitry Yu. [Sobolev Institute of Mathematics and Novosibirsk State University, 630090 Novosibirsk (Russian Federation); Murdaca, Beatrice; Papa, Alessandro [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo collegato di Cosenza, Arcavacata di Rende, I-87036 Cosenza (Italy)
2015-04-10
We apply the BLM scale setting procedure directly to amplitudes (cross sections) of several semihard processes. It is shown that, due to the presence of β{sub 0}-terms in the NLA results for the impact factors, the obtained optimal renormalization scale is not universal, but depends both on the energy and on the process in question. We illustrate this general conclusion considering the following semihard processes: (i) inclusive production of two forward high-p{sub T} jets separated by large interval in rapidity (Mueller-Navelet jets); (ii) high-energy behavior of the total cross section for highly virtual photons; (iii) forward amplitude of the production of two light vector mesons in the collision of two virtual photons.
Renormalization and the breakup of magnetic surfaces
International Nuclear Information System (INIS)
There has been very considerable progress in the last few years on problems that are equivalent to finding the global structure of magnetic field lines in toroidal systems. A general problem of this class has a solution that is so complicated that it is impossible to find equations for the location of a field line which are valid everywhere along an infinitely long line. However, recent results are making it possible to find the asymptotic behavior of such systems in the limit of long lengths. This is just the information that is desired in many situations, since it includes the determination of the existence, or nonexistence, of magnetic surfaces. The key to our present understanding is renormalization. The present state-of-the-art has been described in Robert MacKay's thesis, for which this is an advertisement
Manifestly diffeomorphism invariant classical Exact Renormalization Group
Morris, Tim R
2016-01-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renormalization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeomorphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
The Renormalization Group in Nuclear Physics
International Nuclear Information System (INIS)
Modern techniques of the renormalization group combined with effective field theory methods are revolutionizing nuclear many-body physics. In these lectures we will examine the motivation for RG in low-energy nuclear systems (which include astrophysical systems such as neutron stars) and the implementation of RG technology both formally and in practice. Of particular use will be flow equation approaches applied to Hamiltonians both in free space and in the medium, which are an accessible but powerful method to make nuclear physics more like quantum chemistry. We will see how interactions are evolved to increasingly universal form and become more amenable to perturbative methods. A key element in nuclear systems is the role of many-body forces and operators; dealing with their evolution is an important new challenge. The lectures will include practical details of RG calculations, which can be cast into basic matrix manipulations easily handled by MATLAB, Mathematica, or Python (as well as compiled languages). (author)
Fermionic functional integrals and the renormalization group
Feldman, Joel; Trubowitz, Eugene
2002-01-01
This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...
Spin connection and renormalization of teleparallel action
Energy Technology Data Exchange (ETDEWEB)
Krššák, Martin, E-mail: krssak@ift.unesp.br; Pereira, J. G., E-mail: jpereira@ift.unesp.br [Instituto de Física Teórica, Universidade Estadual Paulista, R. Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP (Brazil)
2015-10-31
In general relativity, inertia and gravitation are both included in the Levi–Civita connection. As a consequence, the gravitational action, as well as the corresponding energy–momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.
Large neutrino mixing from renormalization group evolution
International Nuclear Information System (INIS)
The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of νμ - ντ, if the νμ and ντ are assumed to be quasi-degenerate at the seesaw scale without constraining the mixing angles at that scale. In particular, it allows them to be similar to the quark mixings as in generic grand unified theories. We discuss implementation of this program in the case of MSSM and find that the predicted mixing remains stable and close to its maximal value, for all energies below the O(TeV) SUSY scale. We also discuss how a particular realization of this idea can be tested in neutrinoless double beta decay experiments. (author)
Supersymmetry and the functional renormalization group
International Nuclear Information System (INIS)
Dynamical supersymmetry breaking is an important issue for applications of supersymmetry in particle physics. Many approaches to investigate this problem break supersymmetry explicitly and it is hard to distinguish between dynamical and explicit supersymmetry breaking. The functional renormalization group equations allow for a nonperturbative approach that leaves supersymmetry intact. Therefore they offer a promising tool to investigate the dynamical breaking of supersymmetry. In this talk we employ this method to investigate the N=1 Wess-Zumino model in three dimensions at finite temperature. We recover many aspects of finite temperature QFT such as dimensional reduction and the the Stefan-Boltzmann law. Also we discuss supersymmetry breaking through the thermal boundary conditions and the phase diagram for the breaking of the Z2-symmetry at finite temperatures.
Manifestly diffeomorphism invariant classical Exact Renormalization Group
Morris, Tim R.; Preston, Anthony W. H.
2016-06-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
Efficient implementation of the time renormalization group
Vollmer, Adrian; Amendola, Luca; Catena, Riccardo
2016-02-01
The time renormalization group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to precompute only 13 antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under control, we find that the computation time for nonlinear corrections to the matter power spectrum decreases by a factor of 50. This opens up the possibility to use TRG for mass production as in Markov chain Monte Carlo methods. A fortran code demonstrating this new algorithm is publicly available.
Efficient implementation of the Time Renormalization Group
Vollmer, Adrian; Catena, Riccardo
2014-01-01
The Time Renormalization Group (TRG) is an effective method for accurate calculations of the matter power spectrum at the scale of the first baryonic acoustic oscillations. By using a particular variable transformation in the TRG formalism, we can reduce the 2D integral in the source term of the equations of motion for the power spectrum into a series of 1D integrals. The shape of the integrand allows us to pre-compute only thirteen antiderivatives numerically, which can then be reused when evaluating the outer integral. While this introduces a few challenges to keep numerical noise under control, we find that the computation time for nonlinear corrections to the matter power spectrum decreases by a factor of 50. This opens up the possibility to use of TRG for mass production as in Markov Chain Monte Carlo methods. A Fortran code demonstrating this new algorithm has been made publicly available.
Non-perturbative renormalization on the lattice
International Nuclear Information System (INIS)
Strongly-interacting theories lie at the heart of elementary particle physics. Their distinct behaviour shapes our world sui generis. We are interested in lattice simulations of supersymmetric models, but every discretization of space-time inevitably breaks supersymmetry and allows renormalization of relevant susy-breaking operators. To understand the role of such operators, we study renormalization group trajectories of the nonlinear O(N) Sigma model (NLSM). Similar to quantum gravity, it is believed to adhere to the asymptotic safety scenario. By combining the demon method with blockspin transformations, we compute the global flow diagram. In two dimensions, we reproduce asymptotic freedom and in three dimensions, asymptotic safety is demonstrated. Essential for these results is the application of a novel optimization scheme to treat truncation errors. We proceed with a lattice simulation of the supersymmetric nonlinear O(3) Sigma model. Using an original discretization that requires to fine tune only a single operator, we argue that the continuum limit successfully leads to the correct continuum physics. Unfortunately, for large lattices, a sign problem challenges the applicability of Monte Carlo methods. Consequently, the last chapter of this thesis is spent on an assessment of the fermion-bag method. We find that sign fluctuations are thereby significantly reduced for the susy NLSM. The proposed discretization finally promises a direct confirmation of supersymmetry restoration in the continuum limit. For a complementary analysis, we study the one-flavor Gross-Neveu model which has a complex phase problem. However, phase fluctuations for Wilson fermions are very small and no conclusion can be drawn regarding the potency of the fermion-bag approach for this model.
Cremonini, Sera; Liu, James T.; Szepietowski, Phillip
2009-01-01
We carry out the holographic renormalization of Einstein-Maxwell theory with curvature-squared corrections. In particular, we demonstrate how to construct the generalized Gibbons-Hawking surface term needed to ensure a perturbatively well-defined variational principle. This treatment ensures the absence of ghost degrees of freedom at the linearized perturbative order in the higher-derivative corrections. We use the holographically renormalized action to study the thermodynamics of R-charged b...
Fixed point action and topological charge for SU(2) gauge theory
International Nuclear Information System (INIS)
We present a theoretically consistent definition of the topological charge operator based on renormalization group arguments. Results of the measurement of the topological susceptibility at zero and finite temperature for SU(2) gauge theory are presented. (orig.)
Non-perturbative Renormalization of Bilinear Operators on Fine Lattice
Jeong, Hwancheol; Lee, Weonjong; Pak, Jeonghwan; Park, Sungwoo
2015-01-01
We present results of the wave function renormalization factor $Z_q$ and mass renormalization factor $Z_m$ obtained using non-perturbative renormalization (NPR) method in the RI-MOM scheme with HYP improved staggered quarks. We use fine ensembles of MILC asqtad lattices ($N_f = 2+1$) with $28^3 \\times 96$ geometry, $a \\approx 0.09$\\,fm, and $am_\\ell/am_s = 0.0062/0.031 $. We also study on scalability of $Z_q$ and $Z_m$ by comparing the results on the coarse and fine ensembles.
Cohomology and renormalization of BFYM theory in three dimensions
Energy Technology Data Exchange (ETDEWEB)
Accardi, A.; Belli, A. [Milan Univ. (Italy). Dipt. di Fisica; Martellini, M. [INFN, Milan (Italy).]|[Landau Network at ``Centro Volta``, Como (Italy); Zeni, M. [INFN, Milan (Italy).
1997-11-10
The first-order formalism for the 3D Yang-Mills theory is considered and two different formulations are introduced, in which the gauge theory appears to be a deformation of the topological BF theory. We perform the quantization and the algebraic analysis of the renormalization of both the models, which are found to be anomaly free. We discuss also their stability against radiative corrections, giving the full structure of possible counterterms, requiring an involved matricial renormalization of fields and sources. Both models are then proved to be equivalent to the Yang-Mills theory at the renormalized level. (orig.). 26 refs.
Georgiev, M; Polyanski, I; Petrova, P T; Tsintsarska, S; Gochev, A
2001-01-01
We consider the dynamic interlayer charge transfer across apex oxygens between CuO sub 2 planes in single-layered high-T sub c superconductors. Phonon-coupled axial transfer rates are derived by means of the reaction-rate method. They lead straightforwardly to temperature dependences for the axial resistivity. Doping and temperature dependences are also derived for the renormalized frequencies of phonon modes coupled to the interlayer charge transfer. Our results are compared with experimentally observed dependences. (author)
Renormalization and power counting of chiral nuclear forces
Energy Technology Data Exchange (ETDEWEB)
Long, Bingwei [JLAB
2013-08-01
I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.
Renormalization group methods for the spectra of disordered chains
International Nuclear Information System (INIS)
A family of real space renormalization techniques for calculating the Green's functions of disordered chains is developed and explored. The techniques are based on a recently proposed renormalization method which is rederived here and shown to be equivalent to a virtual crystal approximation on a renormalized Hamiltonian. The derivation suggests how other conventional alloy methods can be coupled to the renormalization concept. Various examples are discussed. Short-range order in the occupation of alloy sites and very general disorder in the Hamiltonian; diagonal, off-diagonal and environmental, are readily incorporated. The techniques are exact in the limits of high and low concentration and of complete short-range order, and for the Lloyd model. All states are found to be localized in agreement with exact treatments. Results for the alloy density of states are presented for various cases and compared to numerical simulations on long chains (105 atoms). (Author)
Renormalization of the Polyakov loop with gradient flow
Petreczky, P
2015-01-01
We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2+1 flavor QCD with highly improved staggered quarks (HISQ) and lattices with temporal extents of $N_\\tau=6$, $8$, $10$ and $12$ we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from $T=116$ MeV up to $T=815$ MeV, with small errors not only for the Polyakov loop in fundamental representation, but also for the Polyakov loops in higher representations. We compare our results with standard renormalization schemes and discuss the Casimir scaling of the Polyakov loops.
Renormalization of the Polyakov loop with gradient flow
Petreczky, P.; Schadler, H.-P.
2015-11-01
We use the gradient flow for the renormalization of the Polyakov loop in various representations. Using 2 +1 flavor QCD with highly improved staggered quarks and lattices with temporal extents of Nτ=6 , 8, 10 and 12 we calculate the renormalized Polyakov loop in many representations including fundamental, sextet, adjoint, decuplet, 15-plet, 24-plet and 27-plet. This approach allows for the calculations of the renormalized Polyakov loops over a large temperature range from T =116 MeV up to T =815 MeV , with small errors not only for the Polyakov loop in fundamental representation, but also for the Polyakov loops in higher representations. We compare our results with standard renormalization schemes and discuss the Casimir scaling of the Polyakov loops.
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Exact renormalization group as a scheme for calculations
International Nuclear Information System (INIS)
In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)
Renormalization of an effective model Hamiltonian by a counter term
Frewer, Michael; Frederico, Tobias; Pauli, Hans-Christian
2001-01-01
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
The Role of Renormalization Group in Fundamental Theoretical Physics
Shirkov, Dmitri V.
1997-01-01
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of fundamental physics.
Systematic Renormalization of the Effective Theory of Large Scale Structure
Abolhasani, Ali Akbar; Pajer, Enrico
2015-01-01
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to l...
Nonperturbative renormalization of scalar quantum electrodynamics in d=3
Energy Technology Data Exchange (ETDEWEB)
Dimock, J., E-mail: dimock@buffalo.edu [Department of Mathematics, SUNY at Buffalo, Buffalo, New York 14260 (United States)
2015-10-15
For scalar quantum electrodynamics on a three-dimensional toroidal lattice with a fine lattice spacing, we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to zero. We employ a renormalization group method which analyzes the flow of the mass and the vacuum energy as a problem in discrete dynamical systems. The main result is that counter terms can be chosen so that at the end of the iteration these quantities take preassigned values. No use is made of perturbation theory. The renormalization group transformations are defined with bounded fields, an approximation which can be justified in Balaban’s approach to the renormalization group.
Renormalization group approach to Einstein-Rosen waves
Harada, Tomohiro; Jhingan, Sanjay
2013-01-01
We present a renormalization group analysis to Einstein-Rosen waves or vacuum spacetimes with whole-cylinder symmetry. It is found that self-similar solutions appear as fixed points in the renormalization group transformation. These solutions correspond to the explosive gravitational waves and the collapsing gravitational waves at late times and early times, respectively. Based on the linear perturbation analysis of the self-similar solutions, we conclude that the self-similar evolution is st...
The Density Matrix Renormalization Group technique with periodic boundary conditions
Gendiar, Andrej; Surda, Anton
2000-01-01
The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D systems than the DMRG with open boundary conditions despite the latter describes much better strips of finite width. For calculation at criticality, phenomenological renormalization at finite strips is used together with a criterion for optimum strip width ...
Wilsonian renormalization group approach to N=2 supersymmetric sigma models
International Nuclear Information System (INIS)
We derive the Wilsonian renormalization group equation in two dimensional N=2 supersymmetric nonlinear sigma models. This equation reveals that these sigma models on compact Einstein Kaehler manifolds are asymptotically free. This result is general and does not depend on the specific forms of the Kaehler potentials. We also examine the renormalization group flow for a new model which connects two manifolds with different global symmetries. (author)
A nonperturbative parametrization and scenario for EFT renormalization
International Nuclear Information System (INIS)
We present a universal form of the T-matrices renormalized in nonperturbative regime and the ensuing notions and properties that fail conventional wisdoms. A universal scale is identified and shown to be renormalization group invariant. The effective range parameters are derived in a nonperturbative scenario with some new predictions within the realm of contact potentials. Some controversies are shown to be due to the failure of conventional wisdoms. (author)
Continuity of the renormalized volume under geometric limits
Pallete, Franco Vargas
2016-01-01
We extend the concept of renormalized volume for geometrically finite hyperbolic $3$-manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic structures over an acylindrical 3-manifold $M$ with geometrically finite limit. This allows us to show that the renormalized volume attains its minimum (in terms of the conformal class at $\\partial M = S$) at the geodesic class, the conformal class for which the boundary of the convex core is totally geodesic.
Investigation of renormalization effects in high temperature cuprate superconductors
International Nuclear Information System (INIS)
It has been found that the self-energy of high-TC cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi2Sr2CaCu2O8+δ and YBa2Cu3O7-δ were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above TC suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)
Quantum field theory and phase transitions: universality and renormalization group
International Nuclear Information System (INIS)
In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)
Technical fine-tuning problem in renormalized perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E.
1983-01-01
The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.
Investigation of renormalization effects in high temperature cuprate superconductors
Energy Technology Data Exchange (ETDEWEB)
Zabolotnyy, Volodymyr B.
2008-04-16
It has been found that the self-energy of high-T{sub C} cuprates indeed exhibits a well pronounced structure, which is currently attributed to coupling of the electrons either to lattice vibrations or to collective magnetic excitations in the system. To clarify this issue, the renormalization effects and the electronic structure of two cuprate families Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+{delta}} and YBa{sub 2}Cu{sub 3}O{sub 7-{delta}} were chosen as the main subject for this thesis. With a simple example of an electronic system coupled to a collective mode unusual renormalization features observed in the photoemission spectra are introduced. It is shown that impurity substitution in general leads to suppression of the unusual renormalization. Finally an alternative possibility to obtain a purely superconducting surface of Y-123 via partial substitution of Y atoms with Ca is introduced. It is shown that renormalization in the superconducting Y-123 has similar strong momentum dependence as in the Bi-2212 family. It is also shown that in analogy to Bi-2212 the renormalization appears to have strong dependence on the doping level (no kinks for the overdoped component) and practically vanishes above T{sub C} suggesting that coupling to magnetic excitations fits much better than competing scenarios, according to which the unusual renormalization in ARPES spectra is caused by the coupling to single or multiple phononic modes. (orig.)
Technical fine-tuning problem in renormalized perturbation theory
International Nuclear Information System (INIS)
The technical - as opposed to physical - fine tuning problem, i.e. the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a number of different models is studied. These include softly-broken supersymmetric models, and non-supersymmetric ones with a hierarchy of spontaneously-broken gauge symmetries. The models are renormalized using the BPHZ prescription, with momentum subtractions. Explicit calculations indicate that the tree-level hierarchy is not upset by the radiative corrections, and consequently no further fine-tuning is required to maintain it. Furthermore, this result is shown to run counter to that obtained via Dimensional Renormalization, (the only scheme used in previous literature on the subject). The discrepancy originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Within fully-renormalized perturbation theory the answer to the technical fine-tuning question (in the sense of whether the radiative corrections will ''readily'' respect the tree level gauge hierarchy or not) is contingent on the renormalization scheme used to define the model at the quantum level, rather than on the model itself. In other words, the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes
Renormalized Wick expansion for a modified PQCD
de Oca, Alejandro Cabo Montes
2007-01-01
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this mass less theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential, is evaluated in more detail in the case when only the quark condensate is retained. This lowest order...
Functional renormalization group methods in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Braun, J.
2006-12-18
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
Renormalization group approach to superfluid neutron matter
International Nuclear Information System (INIS)
In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)
Functional renormalization group methods in quantum chromodynamics
International Nuclear Information System (INIS)
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
Renormalized Wick expansion for a modified PQCD
International Nuclear Information System (INIS)
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and two masses mq and mg associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters mq and mq is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum. (author)
Quark lepton complementarity and renormalization group effects
International Nuclear Information System (INIS)
We consider a scenario for the quark-lepton complementarity relations between mixing angles in which the bimaximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle θ12 is ∼1σ (1.5 degree sign -2 degree sign ) above the best fit point coinciding practically with the tribimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to θ12 as well as to θ13 in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in a large part of the parameter space corrections Δθ12 are small or negligible. In the MSSM version of the scenario, the correction Δθ12 is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of ν1 and ν2 when leading contributions to θ12 running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of ν1 and ν2: φ>π/2
Wieczerkowski, C
1996-01-01
The renormalized trajectory of massless $\\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the dependence on the running $\\phi^4$-coupling. It is solved by means of perturbation theory. The expansion is proved to be finite to all orders. The proof includes a large momentum bound on amputated connected momentum space Green's functions.
Randomly charged polymers in porous environment
Directory of Open Access Journals (Sweden)
V. Blavatska
2013-01-01
Full Text Available We study the conformational properties of charged polymers in a solvent in the presence of structural obstacles correlated according to a power law ~x-a. We work within the continuous representation of a model of linear chain considered as a random sequence of charges qi=±q0. Such a model captures the properties of polyampholytes~-- heteropolymers comprising both positively and negatively charged monomers. We apply the direct polymer renormalization scheme and analyze the scaling behavior of charged polymers up to the first order of an ε=6-d, δ=4-a-expansion.
The applications of the renormalization group
International Nuclear Information System (INIS)
Three applications of the exact renormalization group (RG) to field theory and string theory are developed. (1) First, β-functions are related to the flow of the relevant couplings in the exact RG. The specific case of a cutoff λφ4 theory in four dimensions is discussed in detail. The underlying idea of convergence of the flow of effective lagrangians is developed to identify the β-functions. A perturbative calculations of the β-functions using the exact flow equations is then sketched. (2) Next, the operator product expansion (OPE) is motivated and developed within the context of effective lagrangians. The exact RG may be used to establish the asymptotic properties of the expansion. Again, the example field theory focused upon is a cutoff λφ4 in four dimensions. A detailed proof of the asymptotics for the special case of the expansion of φ(χ)φ(0) is given. The ideas of the proof are sufficient to prove the general case of any two local operators. Although both of the above applications are developed for a cutoff λφ4, the analysis may be extended to any theory with a physical cutoff. (3) Finally, some consequences of the proposal by Banks and Martinec that the classical string field equation can be written as as exact RG equation are examined. Cutoff conformal field theories on the sphere are identified as possible string field configurations. The Wilson fixed-point equation is generalized to conformal invariance and then taken to be the equation of motion for the string field. The equation's solutions for a restricted set of configurations are examined - namely, closed bosonic strings in 26 dimensions. Tree-level Virasoro-Shapiro (VS) S-matrix elements emerge in what is interpreted as a weak component-field expansion of the solution
Non-perturbative renormalization of three-quark operators
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High luminosity accelerators have greatly increased the interest in semi-exclusive and exclusive reactions involving nucleons. The relevant theoretical information is contained in the nucleon wave function and can be parametrized by moments of the nucleon distribution amplitudes, which in turn are linked to matrix elements of local three-quark operators. These can be calculated from first principles in lattice QCD. Defining an RI-MOM renormalization scheme, we renormalize three-quark operators corresponding to low moments non-perturbatively and take special care of the operator mixing. After performing a scheme matching and a conversion of the renormalization scale we quote our final results in the MS-bar scheme at μ=2 GeV
One-loop renormalization of a gravity-scalar system
Park, I Y
2016-01-01
Extending the renormalizability proposal of 4D Einstein gravity, we have recently proposed renormalizability of gravity-matter systems. The main goal of the present work is to conduct systematic one-loop renormalization of a gravity-matter system by applying our foliation-based quantization scheme. In this work we explicitly carry out renormalization of a gravity-scalar system with a Higgs-type potential. With the fluctuation part of the scalar field gauged away, the system becomes renormalizable through a metric field redefinition. We use dimensional regularization throughout. One of the salient aspects of our analysis is how the graviton propagator acquires the"mass" term. One-loop calculations lead to renormalization of the cosmological and Newton's constants. We discuss other implications of our results as well: time-varying vacuum energy density and masses of the elementary particles as well as the potential relevance of Neumann boundary condition for black hole information.
Renormalization of two-dimensional R2-gravity
International Nuclear Information System (INIS)
Two Dimensional Gravity with R2-term is quantized around the R2-Liouville solution in the semiclassical way. Renormalization, regularization (infra-red, ultra-violet) and a topological term (∂(arphi∂arphi) ) are carefully treated. All (1-loop) divergences are renormalized by the cosmological constant (μ) and the R2-coupling-constant (β) for the case β>0. The quantum meaning of the topological term is clarified. The renormalization group beta-functions of the couplings β and μ are obtained. It is found that the theory is conformal (i.e. the beta-functions=0) for w=(β/A).(16π.48π/(26-cm))≥1 (where A is a fixed area) exactly when the coupling constant ξ of the topological term takes the value of 1. As for 0m<26 and μ is asymptotically non-free. (orig.)
Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
Valderrama, Manuel Pavon
2016-01-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental ---perhaps unknown or unsolvable--- high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding ...
Transparent expression of the A2 condensate's renormalization
International Nuclear Information System (INIS)
We give a more transparent understanding of the vacuum expectation value of the renormalized local operator A2 by relating it to the gluon propagator integrated over the momentum. The quadratically divergent perturbative contribution is subtracted and the remainder, dominantly due to the O(1/p2) correction to the perturbative propagator at large p2 is logarithmically divergent. This provides a transparent derivation of the fact that this O(1/p2) term is related to the vacuum expectation value of the local A2 operator and confirms a previous claim based on the operator product expansion (OPE) of the gluon propagator. At leading logarithms the agreement is quantitative, with a standard running factor, between the local A2 condensate renormalized as described above and the one renormalized in the OPE context. This result supports the claim that the BRST invariant Landau-gauge A2 condensate might play an important role in describing the QCD vacuum
Renormalization Group in different fields of theoretical physics
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A very simple and general approach to the symmetry that is widely known as a Renormalization Group symmetry is presented. It essentially uses a functional formulation of group transformations that can be considered as a generalization of self-similarity transformations well known in mathematical physics since last century. This generalized Functional Self-Similarity symmetry and corresponding group transformations are discussed first for a number of simple physical problems taken from diverse fields of classical physics as well as for QED. Then we formulate the Renorm-Group Method as a regular procedure that essentially improves the approximate solutions near the singularity. After that we discuss relations between different formulations of Renormalization Group as they appear in various parts of a modern theoretical physics. Finally we present several topics of RGM application in modern QFT. (author)
Renormalization of massless Feynman amplitudes in configuration space
Nikolov, Nikolay M.; Stora, Raymond; Todorov, Ivan
2014-05-01
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration spaces. For a massless quantum field theory (QFT), we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincaré covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences — i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal — we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary — not necessarily primitively divergent — Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Renormalization of Massless Feynman Amplitudes in Configuration Space
Nikolov, Nikolay M; Todorov, Ivan
2014-01-01
A systematic study of recursive renormalization of Feynman amplitudes is carried out both in Euclidean and in Minkowski configuration space. For a massless quantum field theory (QFT) we use the technique of extending associate homogeneous distributions to complete the renormalization recursion. A homogeneous (Poincare covariant) amplitude is said to be convergent if it admits a (unique covariant) extension as a homogeneous distribution. For any amplitude without subdivergences - i.e. for a Feynman distribution that is homogeneous off the full (small) diagonal - we define a renormalization invariant residue. Its vanishing is a necessary and sufficient condition for the convergence of such an amplitude. It extends to arbitrary - not necessarily primitively divergent - Feynman amplitudes. This notion of convergence is finer than the usual power counting criterion and includes cancellation of divergences.
Renormalization group analysis of the gluon mass equation
Aguilar, A C; Papavassiliou, J
2014-01-01
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, whose deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various p...
Renormalization and periods in perturbative Algebraic Quantum Field Theory
Rejzner, Kasia
2016-01-01
In this paper I give an overview of mathematical structures appearing in perturbative algebraic quantum field theory (pAQFT) and I show how these relate to certain periods. pAQFT is a mathematically rigorous framework that allows to build models of physically relevant quantum field theories on a large class of Lorentzian manifolds. The basic objects in this framework are functionals on the space of field configurations and renormalization method used is the Epstein-Glaser (EG) renormalization. The main idea in the EG approach is to reformulate the renormalization problem, using functional analytic tools, as a problem of extending almost homogeneously scaling distributions that are well defined outside some partial diagonals in $\\mathbb{R}^n$. Such an extension is not unique, but it gives rise to a unique "residue", understood as an obstruction for the extended distribution to scale almost homogeneously. Physically, such scaling violations are interpreted as contributions to the $\\beta$ function.
Emergent geometry from field theory: Wilson's renormalization group revisited
Kim, Ki-Seok
2016-01-01
We find a geometrical description from a field theoretical setup based on Wilson's renormalization group in real space. We show that renormalization group equations of coupling parameters encode the metric structure of an emergent curved space, regarded to be an Einstein equation for the emergent gravity. Self-consistent equations of local order-parameter fields with an emergent metric turn out to describe low energy dynamics of a strongly coupled field theory, analogous to the Maxwell equation of the Einstein-Maxwell theory in the AdS$_{d+2}$/CFT$_{d+1}$ duality conjecture. We claim that the AdS$_{3}$/CFT$_{2}$ duality may be interpreted as Landau-Ginzburg theory combined with Wilson's renormalization group, which introduces vertex corrections into the Landau-Ginzburg theory in the large$-N_{s}$ limit, where $N_{s}$ is the number of fermion flavors.
On the BLM optimal renormalization scale setting for semihard processes
Caporale, Francesco; Murdaca, Beatrice; Papa, Alessandro
2015-01-01
The BFKL approach for the investigation of semihard processes is plagued by large next-to-leading corrections, both in the kernel of the universal BFKL Green's function and in the process-dependent impact factors, as well as by large uncertainties in the renormalization scale setting. All that calls for some optimization procedure of the perturbative series. In this respect, one of the most common methods is the Brodsky-Lepage-Mackenzie (BLM) one, that eliminates the renormalization scale ambiguity by absorbing the non-conformal $\\beta_0$-terms into the running coupling. In this paper, we apply BLM scale setting procedure directly to the amplitudes (cross sections) of several semihard processes. We show that, due to the presence of $\\beta_0$-terms in the next-to-leading expressions for the impact factors, the optimal renormalization scale is not universal, but depends both on the energy and on the type of process in question.
Identifying universality classes of absorbing phase transitions by block renormalization
International Nuclear Information System (INIS)
We propose a renormalization scheme that can be used as a reliable method to identify universality classes of absorbing phase transitions. Following the spirit of Wilson's block-spin renormalization group, the lattice is divided into blocks, assigning to them an effective state by a suitable Boolean function of the interior degrees of freedom. The effective states of adjacent blocks form certain patterns which are shown to occur with universal probability ratios if the underlying process is critical. Measuring these probability ratios in the limit of large block sizes, one obtains a set of universal numbers as an individual fingerprint for each universality class
Justification of the zeta function renormalization in rigid string model
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A consistent procedure for regularization of divergences and for subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov endash Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein endash Hurwitz zeta functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy. copyright 1997 American Institute of Physics
Fine-grained entanglement loss along renormalization-group flows
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We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian
Renormalization group approach to matrix models via noncommutative space
Energy Technology Data Exchange (ETDEWEB)
Kuroki, T. [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Furo-cho, Chikusa-ku, Nagoya Aichi 464-8602 (Japan); Kawamoto, S. [National Center for Theoretical Sciences, Hsinchu 30013 (China); Tomino, D. [Department of Physics, Tunghai University, Taichung 40704 (China)
2014-09-11
We develop a new method for analyzing the large-N limit of matrix models. We assign the concept of energy to each matrix element and integrate the most highest energy to get a new matrix model which has reduced rank. By regarding this procedure as a renormalization group, we deduce the critical exponents in the large-N limit by elaborating fixed points of renormalization group transformation. For consistency of our method, we compare our result to that obtained by another method and find nice agreement. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Symmetry of the Gap Deduced from the Phonon Renormalization
International Nuclear Information System (INIS)
The influence of the gap anisotropy on the superconductivity induced renormalization of q = 0 phonons is studied. An analytical expression for the shift and the broadening of the phonon lines is derived in second order of the electron-lattice coupling. The full k-dependency of the gap function is taken into account. The renormalization is calculated numerically for different anisotropies of the gap (s-wave, d-wave...) And compared to Raman experiments. The value of the hole-lattice coupling in the high-Tc materials can be estimated
Renormalization constants and asymptotic behaviour in quantum electrodynamics
International Nuclear Information System (INIS)
Using dimensional regularization a field theory contains at least one parameter less than the dimension of a mass. The Callan-Symanzik equations for the renormalization constants then become soluble entirely in terms of the coefficient functions. Explicit expressions are obtained for all the renormalization constants in Quantum Electrodynamics. At nonexceptional momenta the infrared behaviour and the three leading terms in the asymptotic expansion of any Greens function are controlled by the Callan-Symanzik equations. For the propagators the three leading terms are computed explicitly in terms of functions of α only. The gauge dependence of the electron propagator in momentum space is solved explicitly in all orders of perturbation theory. (Auth.)
Peripheral NN scattering from subtractive renormalization of chiral interactions
Batista, Edilson Ferreira; Timoteo, Varese Salvador
2013-01-01
We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between $0.1~ \\rm{fm}^{-1}$ and $1 ~ \\rm{fm}^{-1}$. In this range, the results are scale invariant and provide an overall goof agreement with the Nijmegen partial wave analysis up to at least $E_{\\rm{lab}} = 150 ~ \\rm{MeV}$, with a cutoff at $\\Lambda = 30~\\rm{fm}^{-1}$.
MOM renormalization group functions in the maximal abelian gauge
Bell, J M
2013-01-01
The one loop 3-point vertex functions of QCD in the maximal abelian gauge (MAG) are evaluated at the fully symmetric point at one loop. As a consequence the theory is renormalized in the various momentum (MOM) schemes which are defined by the trivalent vertices, as well as in the MSbar scheme. From these the two loop renormalization group functions in the MOM schemes are derived using the one loop conversion functions. In parallel we repeat the analysis for the Curci-Ferrari gauge which corresponds to the MAG in a specific limit. The relation between the Lambda parameters in different schemes is also provided.
T-Duality and Two-Loop Renormalization Flows
Haagensen, P E; Haagensen, Peter E.; Olsen, Kasper
1997-01-01
Manifest T-duality covariance of the one-loop renormalization group flows is shown for a generic bosonic sigma model with an abelian isometry, by referring a set of previously derived consistency conditions to the tangent space of the target. For a restricted background, T-duality transformations are then studied at the next order, and the ensuing consistency conditions are found to be satisfied by the two-loop Weyl anomaly coefficients of the model. This represents an extremely non-trivial test of the covariance of renormalization group flows under T-duality, and a stronger condition than T-duality invariance of the string background effective action.
Peripheral NN scattering from subtractive renormalization of chiral interactions
Energy Technology Data Exchange (ETDEWEB)
Batista, E. F. [Departamento de Ciências Exatas e Naturais, Universidade Estadual do Sudoeste da Bahia, 45700-000 Itapetinga - BA (Brazil); Szpigel, S. [Centro de Rádio-Astronomia e Astrofísica Mackenzie, Escola de Engenharia, Universidade Presbiteriana Mackenzie, 01302-907 São Paulo - SP (Brazil); Timóteo, V. S. [Grupo de Óptica e Modelagem NumérIca - GOMNI, Faculdade de Tecnologia - FT, Universidade Estadual de Campinas - UNICAMP, 13484-332 Limeira - SP (Brazil)
2014-11-11
We apply five subtractions in the Lippman-Schwinger (LS) equation in order to perform a non-perturbative renormalization of chiral N3LO nucleon-nucleon interactions. Here we compute the phase shifts for the uncoupled peripheral waves at renormalization scales between 0.1 fm{sup −1} and 1 fm{sup −1}. In this range, the results are scale invariant and provide an overall good agreement with the Nijmegen partial wave analysis up to at least E{sub lab} = 150 MeV, with a cutoff at Λ = 30 fm{sup −1}.
Systematic renormalization at all orders in the DiffRen and improved Epstein-Glaser schemes
Gracia-Bondía, José M
2015-01-01
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
Renormalization group analysis of electrons near a Van Hove singularity.
Gonzalez, J.(National Centre for Particle and High Energy Physics, Minsk, Belarus); Guinea, F.; Vozmediano, M.A.H.
1995-01-01
A model of interacting two dimensional electrons near a Van Hove singularity is studied, using renormalization group techniques. In hole doped systems, the chemical potential is found to be pinned near the singularity, when the electron-electron interactions are repulsive. The RG treatment of the leading divergences appearing in perturbation theory give rise to marginal behavior and anisotropic superconductivity.
Renorms and topological linear contractions on Hilbert spaces
Institute of Scientific and Technical Information of China (English)
施茂祥; 谭炳均; 陈国强
1999-01-01
Properties of and the relationships between (topological) proper contractions, (topological) strict contractions and (topological) contractions are investigated, Explicit renorms are constructed so that all operators in a (finite or countable) family or a semigroup simultaneously become proper contractions or strict contractions. Some results are obtained for operator weighted shifts or operator weighted continuous shifts to be topological strict contractions.
Renormalization group decimation technique for disordered binary harmonic chains
International Nuclear Information System (INIS)
The density of states of disordered binary harmonic chains is calculated using the Renormalization Group Decimation technique on the displacements of the masses from their equilibrium positions. The results are compared with numerical simulation data and with those obtained with the current method of Goncalves da Silva and Koiller. The advantage of our procedure over other methods is discussed. (author)
Simple perturbative renormalization scheme for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-06-30
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.
Renormalized Polyakov loop in the Fixed Scale Approach
Gavai, Rajiv V.
2010-01-01
I compute the deconfinement order parameter for the SU(2) lattice gauge theory, the Polyakov loop, using the fixed scale approach for two different scales and show how one can obtain a physical, renormalized, order parameter. The generalization to other gauge theories, including quenched or full QCD, is straightforward.
Transfer-matrix approach to percolation and phenomenological renormalization
Derrida, B.; Vannimenus, J.
1980-01-01
A transfer-matrix method is used to calculate the correlation length for strips of finite width in the bond and site percolation problem. From the knowledge of these correlation lengths we compute the thresholds and the critical exponent ν by the phenomenological renormalization method.
Holographic renormalization of 3D minimal massive gravity
Alishahiha, Mohsen; Qaemmaqami, Mohammad; Naseh, Ali; Shirzad, Ahmad
2016-01-01
We study holographic renormalization of 3D minimal massive gravity using the Chern-Simons-like formulation of the model. We explicitly present Gibbons- Hawking term as well as all counterterms needed to make the action finite in terms of dreibein and spin-connection. This can be used to find correlation functions of stress tensor of holographic dual field theory.
A Complete Renormalization Group Trajectory Between Two Fixed Points
Abdesselam, Abdelmalek
2006-01-01
We give a rigorous nonperturbative construction of a massless discrete trajectory for Wilson's exact renormalization group. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analog recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Directory of Open Access Journals (Sweden)
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
Renormalization and asymptotic states in Lorentz-violating QFT
Cambiaso, Mauro; Potting, Robertus
2014-01-01
Radiative corrections in quantum field theories with small departures from Lorentz symmetry alter structural aspects of the theory, in particular the definition of asymptotic single-particle states. Specifically, the mass-shell condition, the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism are affected.
Renormalization of NN Interaction with Relativistic Chiral Two Pion Exchange
Energy Technology Data Exchange (ETDEWEB)
Higa, R; Valderrama, M Pavon; Arriola, E Ruiz
2007-06-14
The renormalization of the NN interaction with the Chiral Two Pion Exchange Potential computed using relativistic baryon chiral perturbation theory is considered. The short distance singularity reduces the number of counter-terms to about a half as those in the heavy-baryon expansion. Phase shifts and deuteron properties are evaluated and a general overall agreement is observed.
Communication: Four-component density matrix renormalization group
International Nuclear Information System (INIS)
We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride
A simple perturbative renormalization scheme for supersymmetric gauge theories
International Nuclear Information System (INIS)
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of [(p+q)/δ]-delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, #betta# is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously. (orig.)
Rota-Baxter algebras and the Hopf algebra of renormalization
International Nuclear Information System (INIS)
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
The BFKL equation from the Wilson renormalization group
International Nuclear Information System (INIS)
We discuss the Wilson renormalization group approach to the effective action for low x physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov. (orig.)
The BFKL equation from the Wilson renormalization group
Energy Technology Data Exchange (ETDEWEB)
Jalilian-Marian, J.; Kovner, A. [Minnesota Univ., Minneapolis, MN (United States). Dept. of Physics; Leonidov, A. [Theoretical Physics Department, P.N. Lebedev Physics Institute, 117924 Leninsky pr. 53, Moscow (Russian Federation); Weigert, H. [University of Cambridge, Cavendish Laboratory, HEP, Madingley Road, Cambridge CB3 0HE (United Kingdom)
1997-10-27
We discuss the Wilson renormalization group approach to the effective action for low x physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov. (orig.). 13 refs.
The BFKL Equation from the Wilson Renormalization Group
Jalilian-Marian, J; Leonidov, A V; Weigert, H; Jalilian-Marian, Jamal; Kovner, Alex; Leonidov, Andrei; Weigert, Heribert
1997-01-01
We discuss the Wilson renormalization group approach to the effective action for low $x$ physics. It is shown that in the linearized, weak field regime the RG equation reduces to the BFKL equation for the evolution of the unintegrated gluon density. We discuss the relation of this approach with that of Lipatov.
Renormalization group trajectories from resonance factorized S-matrices
Martins, Marcio J.
1992-01-01
We propose and investigate a large class of models possessing resonance factorized S-matrices. The associated Casimir energy describes a rich pattern of renormalization group trajectories related to flows in the coset models based on the simply laced Lie Algebras. From a simplest resonance S-matrix, satisfying the ``$\\phi^3$-property'', we predict new flows in non-unitary minimal models.
Structure of Exact Renormalization Group Equations for field theory
Bervillier, C
2014-01-01
It is shown that exact renormalization group (RG) equations (including rescaling and field-renormalization) for respectively the scale-dependent full action $S[\\phi,t]$ and the scale-dependent full effective action $\\Gamma[\\Phi,t]$ --in which $t$ is the "RG-time" defined as the logarithm of a running momentum scale-- may be linked together by a Legendre transformation as simple as $\\Gamma[\\Phi,t] -S[\\phi,t] + \\phi \\cdot \\Phi=0$, with $\\Phi(x) =\\delta S[\\phi] /\\delta \\phi(x) $ (resp. $\\phi(x) =-\\delta \\Gamma [\\Phi]/\\delta \\Phi(x) $), where $\\phi$ and $\\Phi$ are dimensionless-renormalized quantities. This result, in which any explicit reference to a "cutoff procedure" is absent, makes sense in the framework of field theory. It may be compared to the dimensional regularization of the perturbative field theory, in which the running momentum scale is a pure scale of reference and not a momentum cutoff. It is built from the Wilson historic first exact RG equation in which the field-renormalization step is realized ...
Renormalization-scheme-independent perturbation theory by resumming logarithms
Dams, C.J.F.; Kleiss, R. H. P.
2005-01-01
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect to a scheme invariant quantity. Furthermore, we investigate whether the potentially large logarithms in such an expansion cause inaccuracy and how this can be improved.
Rota-Baxter algebras and the Hopf algebra of renormalization
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi-Fard, K.
2006-06-15
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)
Systematic renormalization of the effective theory of Large Scale Structure
Akbar Abolhasani, Ali; Mirbabayi, Mehrdad; Pajer, Enrico
2016-05-01
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and predictive. Here we introduce a systematic renormalization procedure, which neatly associates counterterms to the UV-sensitive diagrams order by order, as it is commonly done in quantum field theory. As a concrete example, we renormalize the one-loop power spectrum and bispectrum of both density and velocity. In addition, we present a series of results that are valid to all orders in perturbation theory. First, we show that while systematic renormalization requires temporally non-local counterterms, in practice one can use an equivalent basis made of local operators. We give an explicit prescription to generate all counterterms allowed by the symmetries. Second, we present a formal proof of the well-known general argument that the contribution of short distance perturbations to large scale density contrast δ and momentum density π(k) scale as k2 and k, respectively. Third, we demonstrate that the common practice of introducing counterterms only in the Euler equation when one is interested in correlators of δ is indeed valid to all orders.
Sine-Gordon model renormalization group solution and applications
International Nuclear Information System (INIS)
The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the g-ology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach. (author)
Directory of Open Access Journals (Sweden)
Adzhemyan L. Ts.
2016-01-01
Full Text Available The renormalization group theory is used to the study of the directed bond percolation (Gribov process near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ε-expansion where ε is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.
Adzhemyan, L. Ts.; Hnatič, M.; Kompaniets, M.; Lučivjanský, T.; Mižišin, L.
2016-02-01
The renormalization group theory is used to the study of the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ɛ-expansion where ɛ is the deviation from the upper critical dimension dc = 4. Within this procedure anomalous dimensions γ are expressed in terms of irreducible renormalized Feynman diagrams and thus the calculation of renormalization constants could be entirely skipped. The renormalization group is included by means of the R operation, and for computational purposes we choose the null momentum subtraction scheme.
Non-perturbative Renormalization of Bilinear Operators with Improved Staggered Quarks
Kim, Jangho; Lee, Weonjong; Yoon, Boram
2013-01-01
We present renormalization factors for the bilinear operators obtained using the non-perturbative renormalization method (NPR) in the RI-MOM scheme with improved staggered fermions on the MILC asqtad lattices ($N_f = 2+1$). We use the MILC coarse ensembles with $20^3 \\times 64$ geometry and $am_{\\ell}/am_s = 0.01/0.05$. We obtain the wave function renormalization factor $Z_q$ from the conserved vector current and the mass renormalization factor $Z_m$ from the scalar bilinear operator. We also present preliminary results of renormalization factors for other bilinear operators.
Carena, M S; Pilaftsis, Apostolos; Wagner, C E M
2000-01-01
We perform a systematic study of the one-loop renormalization-group-improved effective potential of the minimal supersymmetric extension of the Standard Model (MSSM), including CP violation induced radiatively by soft trilinear interactions related to squarks of the third generation. We calculate the charged and neutral Higgs-boson masses and couplings, including the two-loop logarithmic corrections that arise from QCD effects, as well as those associated with the top- and bottom-quark Yukawa couplings. We also include the potentially large two-loop non-logarithmic corrections induced by one-loop threshold effects on the top- and bottom-quark Yukawa couplings, due to the decoupling of the third-generation squarks. Within this minimal CP-violating framework, the charged and neutral Higgs sectors become intimately related to one another and therefore require a unified treatment. In the limit of a large charged Higgs-boson mass, $M_{H^{\\pm}} \\gg M_Z$, the lightest neutral Higgs boson resembles that in the Standa...
Volume Dependence of the Axial Charge of the Nucleon
Hall, N. L.; Thomas, A. W.; Young, R.D.(ARC Centre of Excellence for Particle Physics at the Terascale and CSSM, School of Chemistry and Physics, University of Adelaide, Adelaide, SA 5005, Australia); Zanotti, J. M.
2012-01-01
It is shown that the strong volume-dependence of the axial charge of the nucleon seen in lattice QCD calculations can be understood quantitatively in terms of the pion-induced interactions between neighbouring nucleons. The associated wave function renormalization leads to an increased suppression of the axial charge as the strength of the interaction increases, either because of a decrease in lattice size or in pion mass.
On the renormalization of non-commutative field theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N. [University of Vienna, Faculty of Physics, Vienna (Austria); Garschall, Thomas; Heindl, Franz; Schweda, Manfred [Vienna University of Technology, Institute for Theoretical Physics, Vienna (Austria); Gieres, Francois [Universite de Lyon, Universite Lyon 1 and CNRS/IN2P3, Institut de Physique Nucleaire, Bat. P. Dirac, Villeurbanne (France); Wohlgenannt, Michael [University of Vienna, Faculty of Physics, Vienna (Austria); Austro-Ukrainian Institute for Science and Technology, Vienna (Austria)
2013-01-15
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z {sup c} [j ] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization. (orig.)
On the renormalization of non-commutative field theories
International Nuclear Information System (INIS)
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [j ] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization. (orig.)
Anisotropic square lattice Potts ferromagnet: renormalization group treatment
International Nuclear Information System (INIS)
The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q -< 4). The b = 2 and b = 3 approximate correlation lenght critical exponent ν is calculated for all values of q and compared with den Nijs conjecture. The same calculation is performed, for all values of b, for the exponent ν(d=1) associated to the one-dimensional limit and the exact result ν (d=1) = 1 is recovered in the limit b → infinite. (Author)
On a renormalization group scheme for causal dynamical triangulations
Cooperman, Joshua H.
2016-03-01
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme—in concert with finite size scaling analysis—is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in a previous paper (Cooperman, arXiv:gr-qc/1410.0026). As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.
Renormalization and universality of blowup in hydrodynamic flows
Mailybaev, Alexei A
2012-01-01
We consider self-similar solutions describing intermittent bursts in shell models of turbulence, and study their relationship with blowup phenomena in continuous hydrodynamic models. First, we show that these solutions are very close to self-similar solution for the Fourier transformed inviscid Burgers equation corresponding to shock formation from smooth initial data. Then, the result is generalized to hyperbolic conservation laws in one space dimension describing compressible flows. It is shown that the renormalized wave profile tends to a universal function, which is independent both of initial conditions and of a specific form of the conservation law. This phenomenon can be viewed as a new manifestation of the renormalization group theory. Finally, we discuss possibilities for application of the developed theory for detecting and describing a blowup in incompressible flows.
E-cigarette Marketing and Older Smokers: Road to Renormalization
Cataldo, Janine K.; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas
2015-01-01
Objectives To describe older smokers’ perceptions of risks and use of e-cigarettes, and their responses to marketing and knowledge of, and opinions about, regulation of e-cigarettes. Methods Eight 90-minute focus groups with 8 to 9 participants met in urban and suburban California to discuss topics related to cigarettes and alternative tobacco products. Results Older adults are using e-cigarettes for cessation and as a way to circumvent no-smoking policies; they have false perceptions about the effectiveness and safety of e-cigarettes. They perceive e-cigarette marketing as a way to renormalize smoking. Conclusions To stem the current epidemic of nicotine addiction, the FDA must take immediate action because e-cigarette advertising promotes dual use and may contribute to the renormalization of smoking. PMID:25741681
Renormalization group approach to causal bulk viscous cosmological models
Energy Technology Data Exchange (ETDEWEB)
Belinchon, J A [Grupo Inter-Universitario de Analisis Dimensional, Dept. Fisica ETS Arquitectura UPM, Av. Juan de Herrera 4, Madrid (Spain); Harko, T [Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong (China); Mak, M K [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (China)
2002-06-07
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor.
Dynamical renormalization group approach to relaxation in quantum field theory
Boyanovsky, D
2003-01-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG).Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that...
Topologically twisted renormalization group flow and its holographic dual
Nakayama, Yu
2016-01-01
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a non-trivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS/CFT. We argue that the non-trivial fixed points require fine-tuning of the bulk theory in general, but remarkably we find that the $O(3)$ Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean AdS metric.
Renormalization group approach to causal bulk viscous cosmological models
International Nuclear Information System (INIS)
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor
Scaling algebras and renormalization group in algebraic quantum field theory
International Nuclear Information System (INIS)
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)
On the S-matrix renormalization in effective theories
Semenov-Tian-Shansky, K; Vereshagin, V
2005-01-01
This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal -- needed to fix the S-matrix, and non-minimal -- for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that in theories with the amplitudes which asymptotic behavior is governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixi...
Holographic entanglement entropy of N =2* renormalization group flow
Pang, Da-Wei
2015-10-01
The N =2* theory is obtained by deforming N =4 supersymmetric Yang-Mills theory with two relevant operators of dimensions 2 and 3. We study the holographic entanglement entropy of the N =2* theory along the whole renormalization group flow. We find that in the UV the holographic entanglement entropy for an arbitrary entangling region receives a universal logarithmic correction, which is related to the relevant operator of dimension 3. This universal behavior can be interpreted on the field theory side by perturbatively evaluating the entanglement entropy of a conformal field theory (CFT) under relevant deformations. In the IR regime, we obtain the large R behavior of the renormalized entanglement entropy for both a strip and a sphere entangling region, where R denotes the size of the entangling region. A term proportional to 1 /R is found for both cases, which can be attributed to the emergent CFT5 in the IR.
One Loop Mass Renormalization of Unstable Particles in Superstring Theory
Sen, Ashoke
2016-01-01
Most of the massive states in superstring theory are expected to undergo mass renormalization at one loop order. Typically these corrections should contain imaginary parts, indicating that the states are unstable against decay into lighter particles. However in such cases, direct computation of the renormalized mass using superstring perturbation theory yields divergent result. Previous approaches to this problem involve various analytic continuation techniques, or deforming the integral over the moduli space of the torus with two punctures into the complexified moduli space near the boundary. In this paper we use insights from string field theory to describe a different approach that gives manifestly finite result for the mass shift satisfying unitarity relations. The procedure is applicable to all states of (compactified) type II and heterotic string theories. We illustrate this by computing the one loop correction to the mass of the first massive state on the leading Regge trajectory in SO(32) heterotic st...
More on the renormalization group limit cycle in QCD
Energy Technology Data Exchange (ETDEWEB)
Evgeny Epelbaum; Hans-Werner Hammer; Ulf-G. Meissner; Andreas Nogga
2006-02-26
We present a detailed study of the recently conjectured infrared renormalization group limit cycle in QCD using chiral effective field theory. We show that small increases in the up and down quark masses, corresponding to a pion mass around 200 MeV, can move QCD to the critical renormalization group trajectory for an infrared limit cycle in the three-nucleon system. At the critical values of the quark masses, the binding energies of the deuteron and its spin-singlet partner are tuned to zero and the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. At next-to-leading order in the chiral counting, we find three parameter sets where this effect occurs. For one of them, we study the structure of the three-nucleon system using both chiral and contact effective field theories in detail. Furthermore, we calculate the influence of the limit cycle on scattering observables.
Signal inference with unknown response: calibration uncertainty renormalized estimator
Dorn, Sebastian; Greiner, Maksim; Selig, Marco; Böhm, Vanessa
2014-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of CURE is starting with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify CURE by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov Chain Monte Carlo sampling. We conclude that the...
Rapidity renormalized TMD soft and beam functions at two loops
Luebbert, Thomas; Stahlhofen, Maximilian
2016-01-01
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of pT-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Rapidity renormalized TMD soft and beam functions at two loops
Lübbert, Thomas; Oredsson, Joel; Stahlhofen, Maximilian
2016-03-01
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p ⊥-differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Rapidity renormalized TMD soft and beam functions at two loops
Energy Technology Data Exchange (ETDEWEB)
Luebbert, Thomas [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Oredsson, Joel [DESY, Hamburg (Germany). Theory Group; Lund Univ. (Sweden). Dept. of Astronomy and Theoretical Physics; Stahlhofen, Maximilian [DESY, Hamburg (Germany). Theory Group; Mainz Univ. (Germany). PRISMA Cluster of Excellence
2016-03-15
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p {sub perpendicular} {sub to} -differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Renormalized cluster expansion for multiple scattering in disordered systems
International Nuclear Information System (INIS)
We study wave propagation in a disordered system of scatterers and derive a renormalized cluster expansion for the optical potential or self-energy of the average wave. We show that in the problem of multiple scattering a repetitive structure of Ornstein-Zernike type may be detected. We derive exact expressions for two elementary constituents of the renormalized scattering series, called the reaction field operator and the short-range connector. These expressions involve sums of integrals of a product of a chain correlation function and a nodal connector. We expect that approximate calculation of the reaction field operator and the short-range connector allows one to find a good approximation to the self-energy, even for high density of scatterers. The theory applies to a wide variety of systems
Computing the Effective Action with the Functional Renormalization Group
Codello, Alessandro; Rachwal, Leslaw; Tonero, Alberto
2015-01-01
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action $\\Gamma_k$. The ordinary effective action $\\Gamma_0$ can be obtained by integrating the flow equation from an ultraviolet scale $k=\\Lambda$ down to $k=0$. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We use the results of Barvinsky, Vilkovisky and Avramidi on the non-local heat kernel coefficients to reproduce the four point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
Computing the effective action with the functional renormalization group
Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław; Tonero, Alberto
2016-04-01
The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action Γ _k. The ordinary effective action Γ _0 can be obtained by integrating the flow equation from an ultraviolet scale k=Λ down to k=0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.
A Rigorous Renormalization Group Method for Interfaces in Random Media
Bovier, Anton; Külske, Christof
1994-01-01
We prove the existence Gibbs states describing rigid interfaces in a disordered solid-on-solid (SOS) for low temperatures and for weak disorder in dimension D ≥ 4. This extends earlier results for hierarchical models to the more realistic models and proves a long-standing conjecture. The proof is based on the renormalization group method of Bricmont and Kupiainen originally developed for the analysis of low-temperature phases of the random field Ising model. In a broader context, we generaliz...
Quantum Hall Smectics, Sliding Symmetry and the Renormalization Group
Lawler, Michael J; Fradkin, Eduardo
2004-01-01
In this paper we discuss the implication of the existence of a sliding symmetry, equivalent to the absence of a shear modulus, on the low-energy theory of the quantum hall smectic (QHS) state. We show, through renormalization group calculations, that such a symmetry causes the naive continuum approximation in the direction perpendicular to the stripes to break down through infrared divergent contributions originating from naively irrelevant operators. In particular, we show that the correct f...
Renormalization-group flows and fixed points in Yukawa theories
DEFF Research Database (Denmark)
Mølgaard, Esben; Shrock, R.
2014-01-01
We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar...... regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared....
Nonthermal fixed points and the functional renormalization group
Berges, J.; Hoffmeister, G.
2008-01-01
Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium.
The density matrix renormalization group for ab initio quantum chemistry
Wouters, Sebastian
2015-01-01
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. It is used as a numerically exact solver for highly correlated regions in molecules. While the method works extremely well for one-dimensional systems, the correlated regions of interest are often far from one-dimensional. In this introductory talk, I will discuss the DMRG algorithm from a quantum information perspective, how quantum information theory h...
Lattice renormalization of the static quark derivative operator
Blossier, B; Morénas, V; Pène, O
2006-01-01
We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $\\tau_{1/2}(1)$ and $\\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
Renormalization analysis of catalytic Wright-Fisher diffusions
Czech Academy of Sciences Publication Activity Database
Swart, Jan M.; Fleischmann, K.
2006-01-01
Roč. 2006, č. 11 (2006), s. 585-654. ISSN 1083-6489 R&D Projects: GA ČR GA201/06/1323 Institutional research plan: CEZ:AV0Z10750506 Keywords : renormalization * catalytic Wright-Fisher diffusion * embedded particle system * extinction * unbounded growth * interacting diffusions * universality Subject RIV: BA - General Mathematics Impact factor: 0.676, year: 2006
Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model
Wang, Zhituo
2012-01-01
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
Renormalization Group Analysis of Weakly Rotating Turbulent Flows
Institute of Scientific and Technical Information of China (English)
王晓宏; 周全
2011-01-01
Dynamic renormalization group (RNG) analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence. For turbulent How subject to weak rotation, the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part. Then, with a low-order approximation, the coarsening procedure of RNG transformation is performed. After implementing the coarsening and rescaling procedures, the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k) ∝ k11/5 for weakly rotating turbulence. It is also shown that the Coriolis force will disturb the stability of the Kolmogorov -5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.%Dynamic renormalization group(RNG)analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence.For turbulent flow subject to weak rotation,the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part.Then,with a low-order approximation,the coarsening procedure of RNG transformation is performed.After implementing the coarsening and rescaling procedures,the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k)∝ k-11/5 for weakly rotating turbulence.It is also shown that the Coriolis force will disturb the stability of the Kolmogorov-5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.
Renormalization group analysis of the small-world network model
Newman, M. E. J.; Watts, D. J.
1999-01-01
We study the small-world network model, which mimics the transition between regular-lattice and random-lattice behavior in social networks of increasing size. We contend that the model displays a normal continuous phase transition with a divergent correlation length as the degree of randomness tends to zero. We propose a real-space renormalization group transformation for the model and demonstrate that the transformation is exact in the limit of large system size. We use this result to calcul...
Renormalization of coupling constants in the minimal SUSY models
Nevzorov, R. B.; Ter-Martirosyan, K. A.; Trusov, M.A.
2003-01-01
The considerable part of the parameter space in the MSSM corresponding to the infrared quasi fixed point scenario is excluded by LEP II bounds on the lightest Higgs boson mass. In the NMSSM the mass of the lightest Higgs boson reaches its maximum value in the strong Yukawa coupling limit when Yukawa couplings are essentially larger than gauge ones at the Grand Unification scale. In this case the renormalization group flow of Yukawa couplings and soft SUSY breaking terms is investigated. The q...
Renormalization group analysis of the gluon mass equation
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2014-04-01
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.
Subtractive Renormalization Group Invariance: Pionless EFT at NLO
International Nuclear Information System (INIS)
We show some results concerning the renormalization group (RG) invariance of the nucleon-nucleon (NN) interaction in pionless effective field theory at next-to-leading order (NLO), using a non-relativistic Callan-Symanzik equation (NRCS) for the driving term of the Lippmann-Schwinger (LS) equation with three recursive subtractions. The phase-shifts obtained for the RG evolved potential are same as those for the original potential, apart from relative differences of order 10-15.
Exact integral equation for the renormalized Fermi surface
Ledowski, Sascha; Kopietz, Peter
2002-01-01
The true Fermi surface of a fermionic many-body system can be viewed as a fixed point manifold of the renormalization group (RG). Within the framework of the exact functional RG we show that the fixed point condition implies an exact integral equation for the counterterm which is needed for a self-consistent calculation of the Fermi surface. In the simplest approximation, our integral equation reduces to the self-consistent Hartree-Fock equation for the counterterm.
Disordered systems and the functional renormalization group, a pedagogical introduction
International Nuclear Information System (INIS)
In this article, we review basic facts about disordered systems, especially the existence of many metastable states and and the resulting failure of dimensional reduction. Besides techniques based on the Gaussian variational method and replica-symmetry breaking (RSB), the functional renormalization group (FRG) is the only general method capable of attacking strongly disordered systems. We explain the basic ideas of the latter method and why it is difficult to implement. We finally review current progress for elastic manifolds in disorder (Author)
Operator Evolution via the Similarity Renormalization Group I: The Deuteron
Anderson, E. R.; Bogner, S. K.; Furnstahl, R. J.; Perry, R J
2010-01-01
Similarity Renormalization Group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less correlated wave functions...
Renormalization of the singular attractive $1/r^4$ potential
Alberg, Mary; Bawin, Michel; Brau, Fabian
2004-01-01
We study the radial Schr\\"odinger equation for a particle of mass $m$ in the field of a singular attractive $g^2/{r^4}$ potential with particular emphasis on the bound states problem. Using the regularization method of Beane \\textit{et al.}, we solve analytically the corresponding ``renormalization group flow" equation. We find in agreement with previous studies that its solution exhibits a limit cycle behavior and has infinitely many branches. We show that a continuous choice for the solutio...
Nonperturbative renormalization group approach to Lifshitz critical behaviour
Essafi, K.; Kownacki, J. -P.; Mouhanna, D.
2012-01-01
The behaviour of a d-dimensional vectorial N=3 model at a m-axial Lifshitz critical point is investigated by means of a nonperturbative renormalization group approach that is free of the huge technical difficulties that plague the perturbative approaches and limit their computations to the lowest orders. In particular being systematically improvable, our approach allows us to control the convergence of successive approximations and thus to get reliable physical quantities in d=3.
Matrix Representation of Renormalization in Perturbative Quantum Field Theory
Ebrahimi-Fard, K.; Guo, L.
2005-01-01
We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota-Baxter anti-homomorphism from general regularized functionals on the Feynman graph Hopf algebra to triangular matrices with entries in a Rota-Baxter algebra. For characters mapping to the group of unipotent triangular matrices we derive the algebraic Birkhoff decomposition for matrices using Spitzer's identity. This simpl...
Massive renormalization scheme and perturbation theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)
2015-02-04
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization
Kniehl, Bernd A
2009-01-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
A novel formulation of Cabibbo-Kobayashi-Maskawa matrix renormalization
Kniehl, Bernd A.; Sirlin, Alberto
2009-03-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization
Kniehl, Bernd A.; Sirlin, Alberto
2008-01-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical pro...
Renormalized theory of low-frequency hydrodynamic fluctuations in plasmas
International Nuclear Information System (INIS)
The basic statement of the renormalized statistical theory of low-frequency hydrogynamic fluctuations in magnetized plasmas are formulated. Stationary fluctuation spectra are calculated with account for the nonlinear interaction of fluctuations within the context of the theory developed for the general case of electromagnetic interaction. It is demonstrated that electromagnetic effects may influence essentially the spectral characteristics of the convective fluctuations and the relevant anomalous transport in plasmas. 82 refs
Power counting and Wilsonian renormalization in nuclear effective field theory
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Three dimensional nonlinear sigma models in the Wilsonian renormalization method
International Nuclear Information System (INIS)
The three dimensional nonlinear sigma model is nonrenormalizable within the perturbative method. Using the β function in the nonperturbative Wilsonian renormalization group method, we argue that some N = 2 supersymmetric nonlinear σ models are renormalizable in three dimensions. When the target space is an Einstein-Kaehler manifold with positive scalar curvature, such as CPN or QN, there are nontrivial ultraviolet (UV) fixed points, which can be used to define the nontrivial renormalized theory. If the target space has a negative scalar curvature, however, the theory has only an infrared Gaussian fixed point, and the meaningful continuum theory cannot be defined. We also construct a model that interpolates between the CPN and QN models with two coupling constants. This model has two non-trivial UV fixed points that can be used to define a nontrivial renormalized theory. Finally, we construct a class of conformal field theories with SU(N) symmetry, defined at the fixed point of the nonperturbative β function. These conformal field theories have a free parameter corresponding to the anomalous dimension of the scalar fields. If we choose a specific value of this parameter, we recover the conformal field theory defined at the UV fixed point of the CPN model, and the symmetry is enhanced to SU(N+1). (author)
Real-space renormalized dynamical mean field theory
Kubota, Dai; Sakai, Shiro; Imada, Masatoshi
2016-05-01
We propose real-space renormalized dynamical mean field theory (rr-DMFT) to deal with large clusters in the framework of a cluster extension of the DMFT. In the rr-DMFT, large clusters are decomposed into multiple smaller clusters through a real-space renormalization. In this work, the renormalization effect is taken into account only at the lowest order with respect to the intercluster coupling, which nonetheless reproduces exactly both the noninteracting and atomic limits. Our method allows us large cluster-size calculations which are intractable with the conventional cluster extensions of the DMFT with impurity solvers, such as the continuous-time quantum Monte Carlo and exact diagonalization methods. We benchmark the rr-DMFT for the two-dimensional Hubbard model on a square lattice at and away from half filling, where the spatial correlations play important roles. Our results on the spin structure factor indicate that the growth of the antiferromagnetic spin correlation is taken into account beyond the decomposed cluster size. We also show that the self-energy obtained from the large-cluster solver is reproduced by our method better than the solution obtained directly for the smaller cluster. When applied to the Mott metal-insulator transition, the rr-DMFT is able to reproduce the reduced critical value for the Coulomb interaction comparable to the large cluster result.
International Nuclear Information System (INIS)
Full text: The running of coupling constants is a well known phenomenon within Quantum Field Theory. It is also known that the renormalization group method can be extended to quantum field theory on curved space time. Nonetheless, although we know that the beta function of QED go to zero in the infrared limit fast enough to lead to constant charge at the classical level (in conformity with both the Appelquist-Carazzone theorem and experimental data), no analogous proof exists for General Relativity. Some authors have proposed that the infrared beta function of General Relativity is not trivial, and as such certain small running of the gravitational coupling might take place at astrophysical scales, leading in particular to changes on the role of dark matter in galaxies. We review and extend our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies, an approach we call RGGR. We extend our previous results by analyzing a larger sample of galaxies, now also including elliptical and dwarf spheroidal galaxies, besides disk galaxies (both LSB and HSB). We compare our RGGR results to both standard dark matter profiles (NFW, Isothermal, Burkert) and alternative models of gravity (MOND, MSTG), showing that the RGGR results are similar in quality to the best dark matter profiles (the cored ones, e.g., Isothermal and Burkert), while displaying a better fitting to the data than NFW, MOND or MSTG. To the latter, we evaluated both the shape of the rotation curve and the expected stellar mass-to-light ratios. Dwarf spheroidal (dSph) galaxies are small galaxies believed to be dominated by dark matter, with the highest fraction do dark matter per baryonic matter. These galaxies provide a strong test to any theory that mimics either all or part of the dark matter behavior. In particular, this is the only type of galaxy that MOND seems incapable of fitting the data. (author)
Classen, Laura; Herbut, Igor F.; Janssen, Lukas; Scherer, Michael M.
2016-03-01
We study the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the spin- and charge-density-wave phases meet. With the help of a functional renormalization group approach, we are able to reveal a complex structure of fixed points, the stability properties of which decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to the previous first-order ɛ expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2 ), no stable and physically admissible fixed point exists. Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic, and staggered density phases should consequently be governed by a triple point exhibiting first-order transitions.
Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets
Indian Academy of Sciences (India)
N Nimai Singh; S Biramani Singh
2000-02-01
Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefﬁcients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD–QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the uniﬁcation of top-- Yukawa couplings at the scale =0.59× 108GeV for a ﬁxed value of tan =58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of =0.59× 1011GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.
Energy Technology Data Exchange (ETDEWEB)
Song, Mi-Young; Yoon, Jung-Sik [Plasma Technology Research Center, National Fusion Research Institute, 814-2 Osikdo-Dong, Gunsan-City, Jeollabuk-Do 573-540 (Korea, Republic of); Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr [Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States); Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of)
2015-04-15
The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it is found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.
A Study of the forced Van der Pol generalized oscillator with renormalization group method
2013-01-01
In this paper the equation of forced Van der Pol generalized oscillator is examined with renormalization group method. A brief recall of the renormalization group technique is done. We have applied this method to the equation of forced Van der Pol generalized oscillator to search for its asymptotic solution and its renormalization group equation. The analysis of the numerical simulation graph is done; the method's efficiency is pointed out.
Space-time versus world-sheet renormalization group equation in string theory
International Nuclear Information System (INIS)
We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. (orig.)
A consistency question in the renormalization group analysis of deep inelastic scattering
International Nuclear Information System (INIS)
The application of renormalization group methods in perturbation theory results in a definite behavior for terms of higher orders under changes of renormalization prescription. Apparently, this fails to be true for the one-loop correction to the moments of the non-singlet structure functions, which is believed to be a renormalization group invariant. A possible explanation for this contradiction in the treatment of the terms taking into account non-pertubative effects is pointed. (Authors)
Perturbative renormalization factors of quark operators for domain-wall QCD
Aoki, Sinya; Izubuchi, Taku; Noaki, Junichi; Kuramashi, Yoshinobu; Taniguchi, Yusuke
1999-01-01
We calculate one-loop renormalization factors of several quark operators including bilinear, three- and four-quark operator for domain-wall fermion action. Since Green functions are constructed for external physical quark fields, our renormalization method is simple and can be easily applied to calculation of any quark operators. Our results show that these renormalized quark operators preserve several chiral properties of continuum massless QCD, which can be understood by the property of ext...
One-loop renormalization of fermionic currents with the overlap-Dirac operator
Alexandrou, C; Panagopoulos, H; Vicari, E
2000-01-01
We compute the one-loop lattice renormalization of the two-quark operators$\\bar{\\psi} \\Gamma \\psi$, where $\\Gamma$ denotes the generic Dirac matrix, forthe lattice formulation of QCD using the overlap-Dirac operator. We also study the renormalization of quark bilinears which are more extendedand have better chiral properties. Finally, we present improved estimates of these renormalization constants,coming from cactus resummation and from mean field perturbation theory.
Nonperturbative renormalization of the Delta-S=1 weak Hamiltonian including the G_1 operator
McGlynn, Greg
2016-01-01
Under renormalization, physical operators can mix with operators which vanish by the equations of motion. Such operators cannot contribute to matrix elements between physical states, but they contribute to operator mixing in renormalization schemes which are defined at an off-shell momentum point, such as the popular regularization-invariant schemes. For the first time, we renormalize the lattice $\\Delta S=1$ effective weak Hamiltonian taking into account the most important such operator, $G_1 \\propto \\overline s \\gamma_\
Renormalization of the iso-singlet scalar density in lattice QCD with Wilson quarks
International Nuclear Information System (INIS)
Due to the absence of an exact chiral symmetry in lattice QCD with Wilson fermions, the iso-singlet scalar density has to be renormalized both additively and multiplicatively. We propose to use chiral Ward identities between correlation functions derived from the Schroedinger functional to determine the relevant renormalization constants directly in the chiral limit. Although the method does not rely on perturbation theory, we here use it to determine the renormalization constants and to obtain an idea of the typical size of cutoff effects. Finally we comment on the prospects for a direct determination of the chiral condensate as expectation value of a renormalized scalar density
Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-04-28
We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.
Duetsch, Michael; Rejzner, Katarzyna
2013-01-01
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. For scalar fields the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stueckelberg and Petermann.
The fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models
International Nuclear Information System (INIS)
We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes. (orig.)
Renormalization of the new trajectory in the unitarized conventional dual model
International Nuclear Information System (INIS)
The contribution of one-loop planar diagrams to the two-reggeon two-particle amplitude is derived. Its regge limit splits into two separate contributions which must be interpreted as renormalization effects, to order g2, of the α and β trajectories. It is shown that the Neveu-Scherk renormalization prescription is able to render finite both contributions. The intercept of the β trajectory is shifted from its bare value by the renormalization procedure, whereas that of the α trajectrory is not renormalized as it was required by the gauge invariance of dual theories
Renormalization of the chromomagnetic operator on the lattice
Constantinou, M.; Costa, M.; Frezzotti, R.; Lubicz, V.; Martinelli, G.; Meloni, D.; Panagopoulos, H.; Simula, S.; ETM Collaboration
2015-08-01
We present our study of the renormalization of the chromomagnetic operator, OCM , which appears in the effective Hamiltonian describing Δ S =1 transitions in and beyond the Standard Model. We have computed, perturbatively to one loop, the relevant Green's functions with two (quark-quark) and three (quark-quark-gluon) external fields, at nonzero quark masses, using both the lattice and dimensional regularizations. The perturbative computation on the lattice is carried out using the maximally twisted-mass action for the fermions, while for the gluons we employed the Symanzik improved gauge action for different sets of values of the Symanzik coefficients. We have identified all the operators which can possibly mix with OCM , including lower-dimensional and nongauge invariant operators, and we have calculated those elements of the mixing matrix which are relevant for the renormalization of OCM. We have also performed numerical lattice calculations to determine nonperturbatively the mixings of the chromomagnetic operator with lower-dimensional operators, through proper renormalization conditions. For the first time, the 1 /a2-divergent mixing of the chromomagnetic operator with the scalar density has been determined nonperturbatively with high precision. Moreover, the 1 /a -divergent mixing with the pseudoscalar density, due to the breaking of parity within the twisted-mass regularization of QCD, has been calculated nonperturbatively and found to be smaller than its one-loop perturbative estimate. The QCD simulations have been carried out using the gauge configurations produced by the European Twisted Mass Collaboration with Nf=2 +1 +1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their physical values.
Renormalization group flow of scalar models in gravity
International Nuclear Information System (INIS)
In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.
A direct renormalization group approach for the excluded volume problem
International Nuclear Information System (INIS)
A direct renormalization group approach is proposed, to the excluded volume problem in a square lattice by considering percolating self-avoiding paths in a b x b cell, where b = 2,3. Two ways of counting these paths are presented. In the first one, we get the exponent ν = 0.715 for b = 2 and ν = 0.719 for b = 3, whereas in the second one ν = 0.771 for b = 2 and ν = 0.748 for b = 3. Comments are made on the extrapolation to b → infinite. (Author)
Anomalous Contagion and Renormalization in Dynamical Networks with Nodal Mobility
Manrique, Pedro D; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F
2015-01-01
The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on average, underlying nodal mobility can dramatically distort outbreak profiles. Highly nonlinear dynamical regimes emerge in which increasing mobility either amplifies or suppresses outbreak severity. Predicted profiles mimic recent outbreaks of real-space contagion (social unrest) and online contagion (pro-ISIS support). We show that this nodal mobility can be renormalized in a precise way for a particular class of dynamical networks.
Renormalized anisotropic exchange for representing heat assisted magnetic recording media
Energy Technology Data Exchange (ETDEWEB)
Jiao, Yipeng; Liu, Zengyuan; Victora, R. H., E-mail: victora@umn.edu [MINT Center, Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
2015-05-07
Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation.
Renormalized entanglement entropy flow in mass-deformed ABJM theory
Kim, Kyung Kiu; Kwon, O.-Kab; Park, Chanyong; Shin, Hyeonjoon
2014-08-01
We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in (2+1)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in (2+1)-dimensions are consistent with the Zamolodchikov c-function proposed in (1+1)-dimensional conformal field theory.
Non-renormalization theorems andN=2 supersymmetric backgrounds
International Nuclear Information System (INIS)
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed
Renormalization group analyses of an SU(2) lattice guage theory
International Nuclear Information System (INIS)
Using Migdal's recursion relation for renormalization group calculations, we describe an approximation for the average value of a Wilson loop and calculate ka2 vs 1/g2 for SU(2) actions of the form s/sub p/ = -2(β/sub f/ cos theta/2 + β/sub a/ cos theta). We use loops as large as 40 x 40 on a 4-dimensional lattice. We also find evidence for a phase transition in the region β/sub a/ approx. -2, β/sub f/ > 0.7 using Tan and Xu's modification of the recursion relation. 14 refs., 7 figs
Field theory entropy, the H theorem, and the renormalization group
International Nuclear Information System (INIS)
We consider entropy and relative entropy in field theory and establish relevant monotonicity properties with respect to the couplings. The relative entropy in a field theory with a hierarchy of renormalization-group fixed points ranks the fixed points, the lowest relative entropy being assigned to the highest multicritical point. We argue that as a consequence of a generalized H theorem Wilsonian RG flows induce an increase in entropy and propose the relative entropy as the natural quantity which increases from one fixed point to another in more than two dimensions. copyright 1996 The American Physical Society
Tensor renormalization group analysis of CP(N-1) model
Kawauchi, Hikaru
2016-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.
Information-geometric approach to the renormalization group
Bény, Cédric; Osborne, Tobias J.
2015-08-01
We propose a general formulation of the renormalization group (RG) as a family of quantum channels which connect the microscopic physical world to the observable world at some scale. By endowing the set of quantum states with an operationally motivated information geometry, we induce the space of Hamiltonians with a corresponding metric geometry. The resulting structure allows one to quantify information loss along RG flows in terms of the distinguishability of thermal states. In particular, we introduce a family of functions, expressible in terms of two-point correlation functions, which are nonincreasing along the flow. Among those, we study the speed of the flow and its generalization to infinite lattices.
Dynamical gap generation in graphene with frequency dependent renormalization effects
Carrington, M E; von Smekal, L; Thoma, M H
2016-01-01
We study the frequency dependencies in the renormalization of the fermion Greens function for the $\\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.
Autonomous Renormalization of Phi^4 in Finite Geometry
Ritschel, U
1993-01-01
The autonomous renormalization of the O(N)-symmetric scalar theory is based on an infinite re-scaling of constant fields, whereas finite-momentum modes remain finite. The natural framework for a detailed analysis of this method is a system of finite size, where all non-constant modes can be integrated out perturbatively and the constant mode is treated by a saddle-point approximation in the thermodynamic limit. The calculation provides a better understanding of the properties of of the effective action and corroborates earlier findings concerning a heavy Higgs particle at about 2 TeV.
Renormalized anisotropic exchange for representing heat assisted magnetic recording media
International Nuclear Information System (INIS)
Anisotropic exchange has been incorporated in a description of magnetic recording media near the Curie temperature, as would be found during heat assisted magnetic recording. The new parameters were found using a cost function that minimized the difference between atomistic properties and those of renormalized spin blocks. Interestingly, the anisotropic exchange description at 1.5 nm discretization yields very similar switching and magnetization behavior to that found at 1.2 nm (and below) discretization for the previous isotropic exchange. This suggests that the increased accuracy of anisotropic exchange may also reduce the computational cost during simulation
Non-perturbative renormalization constants using Ward identities
International Nuclear Information System (INIS)
We extend the application of vector and axial Ward identities to calculate bA, bP and bT, coefficients that give the mass dependence of the renormalization constants of the corresponding bilinear operators in the quenched theory. The extension relies on using operators with non-degenerate quark masses. It allows a complete determination of the O(a) improvement coefficients for bilinears in the quenched approximation using Ward Identities alone. Only the scale dependent normalization constants Z0P (or Z0S) and ZT are undetermined. We present results of a pilot numerical study using hadronic correlators
Renormalizing the kinetic energy operator in elementary quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Coutinho, F A B [Faculdade de Medicina, Universidade de Sao Paulo e LIM 01-HCFMUSP, 05405-000 Sao Paulo (Brazil); Amaku, M [Faculdade de Medicina Veterinaria e Zootecnia, Universidade de Sao Paulo, 05508-970 Sao Paulo (Brazil)], E-mail: coutinho@dim.fm.usp.br
2009-09-15
In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form {psi}(r) = u(r)/r, where u(0) {ne} 0. The expectation value of the kinetic energy operator for such wavefunctions diverges. We show that it is possible to introduce a potential energy with an expectation value that also diverges, exactly cancelling the kinetic energy divergence. This renormalization procedure produces a self-adjoint Hamiltonian. We solve some problems with this new Hamiltonian to illustrate its usefulness.
Current distribution in systems with anomalous diffusion: renormalization group approach
International Nuclear Information System (INIS)
We investigate the asymptotic properties of the large deviation function of the integrated particle current in systems, in or out of thermal equilibrium, whose dynamics exhibits anomalous diffusion. The physical systems covered by our study include mutually repelling particles with a drift, a driven lattice gas displaying a continuous nonequilibrium phase transition and particles diffusing in an anisotropic random advective field. It is exemplified how renormalization group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically the anomalous dimension of the noise correlators
Nuclear Symmetries of the similarity renormalization group for nuclear forces
Arriola, E. Ruiz; Timoteo, V. S.; Szpigel, S.(Centro de Rádio-Astronomia e Astrofísica Mackenzie, Escola de Engenharia, Universidade Presbiteriana Mackenzie, Brazil)
2013-01-01
We review the role played by long-distance symmetries within the context of the similarity renormalization group approach. This is based on phase-shift-preserving continuous unitary transformations that evolve Hamiltonians with a cutoff on energy differences. We find that there is a similarity cutoff of 3/fm for which almost perfect fulfillment of Wigner SU(4) symmetry is found at the two body level. This suggests to look for similar symmetry patterns for three- and four-body forces. We also ...
Renormalized two-pump modulational instability in plasmas
International Nuclear Information System (INIS)
It is shown that the two-pump modulational instability in a plasma is different from one-mode modulational instability. In the case when the frequency difference of two pumps δω = ωo - ω1 is much less than the frequency of each pump ω0.1, the virtual fields at frequencies ''+ -'' (ω0 + δω) need to be taken into account in the development of modulational instability. They lead to a ''renormalized'' concept of modulational instability which changes the prediction of the common approach. (Author)
Renormalization and applications of baryon distribution amplitudes in QCD
Energy Technology Data Exchange (ETDEWEB)
Rohrwild, Juergen Holger
2009-07-17
Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)
Renormalization and applications of baryon distribution amplitudes QCD
Energy Technology Data Exchange (ETDEWEB)
Rohrwild, Juergen Holger
2009-07-17
Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)
A nonequilibrium renormalization group approach to turbulent reheating
International Nuclear Information System (INIS)
We use nonequilibrium renormalization group (RG) techniques to analyse the thermalization process in quantum field theory, and, by extension, reheating after inflation. Even if at a high scale Λ the theory is described by a non-dissipative λψ4 theory, and the RG running induces nontrivial noise and dissipation. For long wavelength and slowly varying field configurations, the noise and dissipation are white and ohmic, respectively. The theory will then tend to thermalize to an effective temperature given by the fluctuation-dissipation theorem
Functional renormalization group study of nuclear and neutron matter
Energy Technology Data Exchange (ETDEWEB)
Drews, Matthias; Weise, Wolfram [Physik Department, Technische Universität München, D-85747 Garching (Germany); ECT*, Villa Tambosi, I-38123 Villazzano (Trento) (Italy)
2016-01-22
A chiral model based on nucleons interacting via boson exchange is investigated. Fluctuation effects are included consistently beyond the mean-field approximation in the framework of the functional renormalization group. The liquid-gas phase transition of symmetric nuclear matter is studied in detail. No sign of a chiral restoration transition is found up to temperatures of about 100 MeV and densities of at least three times the density of normal nuclear matter. Moreover, the model is extended to asymmetric nuclear matter and the constraints from neutron star observations are discussed.
Functional renormalization-group approach to decaying turbulence
International Nuclear Information System (INIS)
We reconsider the functional renormalization-group (FRG) approach to decaying Burgers turbulence, and extend it to decaying Navier–Stokes and surface quasi-geostrophic turbulence. The method is based on a renormalized small-time expansion, equivalent to a loop expansion, and naturally produces a dissipative anomaly and a cascade after a finite time. We explicitly calculate and analyze the one-loop FRG equations in the zero-viscosity limit as a function of the dimension. For Burgers turbulence they reproduce the FRG equation obtained in the context of random manifolds, extending previous results of one of us. Breakdown of energy conservation due to shocks and the appearance of a direct energy cascade corresponds to failure of dimensional reduction in the context of disordered systems. For Navier–Stokes turbulence in three dimensions, the velocity–velocity correlation function acquires a linear dependence on the distance, ζ2 = 1, in the inertial range, instead of Kolmogorov’s ζ2 = 2/3; however, the possibility remains for corrections at two- or higher-loop order. In two dimensions, we obtain a numerical solution which conserves energy and exhibits an inverse cascade, with explicit analytical results for both large and small distances, in agreement with the scaling proposed by Batchelor. In large dimensions, the one-loop FRG equation for Navier–Stokes turbulence converges to that of Burgers turbulence. (paper)
Dynamical renormalization group approach to relaxation in quantum field theory
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The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths
Measuring the aspect ratio renormalization of anisotropic-lattice gluons
International Nuclear Information System (INIS)
Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios χ0=4,6,10 and inverse lattice spacing in the range as-1=660--840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in the Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size L, while in the former, parameters showed only a weak dependence on L easily extrapolated to L=∞. The renormalized anisotropy χR was measured using both the torelon dispersion relation and the sideways potential method. There is general agreement between these approaches, but there are discrepancies which are evidence for the presence of lattice artifact contributions. For the torelon these are estimated to be O(αSas2/R2), where R is the flux-tube radius. We also present some new data that suggest that rotational invariance is established more accurately for the mean-link action than the plaquette action
Holographic renormalization group and cosmology in theories with quasilocalized gravity
International Nuclear Information System (INIS)
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations
Unitary Networks from the Exact Renormalization of Wave Functionals
Fliss, Jackson R; Parrikar, Onkar
2016-01-01
The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was established in the sense that at large $N$ the generating functional of correlation functions of single trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the $O(N)$ vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared rece...
Algebraic renormalization and Feynman integrals in configuration spaces
Ceyhan, Ozgur
2013-01-01
This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory. We consider a variant of the wonderful compactification of configuration spaces that works simultaneously for all graphs with a given number of vertices and that also accounts for the external structure of Feynman graph. As in our previous work, we consider two version of the Feynman amplitude in configuration space, which we refer to as the real and complex versions. In the real version, we show that we can extend to the massive case a method of evaluating Feynman integrals, based on expansion in Gegenbauer polynomials, that we investigated previously in the massless case. In the complex setting, we show that we can use algebro-geometric methods to renormalize the Feynman amplitudes, so that the renormalized values of the Feynman integrals are given by periods of a mixed ...
Monte Carlo renormalization: Test on the triangular Ising model
International Nuclear Information System (INIS)
We test the performance of the Monte Carlo renormalization method using the Ising model on the triangular lattice. We apply block-spin transformations which allow for adjustable parameters so that the transformation can be optimized. This optimization takes into account the relation between corrections to scaling and the location of the fixed point. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions, by means of transfer matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation lies far away from the nearest-neighbour critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because corrections to scaling are supposed to be absent at the fixed point. We define a modified block-spin transformation which shifts the fixed point back to the vicinity of the nearest-neighbour critical Hamiltonian. This modified transformation leads to results for the Ising critical exponents that converge faster, and are more accurate than those obtained with the majority rule. (author)
Holographic renormalization group and cosmology in theories with quasilocalized gravity
Energy Technology Data Exchange (ETDEWEB)
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-03-15
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations.
A Note on Holographic Renormalization of Probe D-Branes
Benincasa, Paolo
2009-01-01
A great deal of progress has been recently made in the study of holography for non-conformal branes. Considering the near-horizon limit of backgrounds generated by such branes, we discuss the holographic renormalization of probe D-branes in these geometries. More specifically, we discuss in some detail systems with a codimension-one defect. For this class of systems, the mode which describes the probe branes wrapping a maximal 2-sphere in the transverse space behaves like a free massive scalar propagating in a higher-dimensional (asymptotically) AdS_{q+1}-space. The counterterms needed are then the ones of a free massive scalar in asymptotically AdS_{q+1}. The original problem can be recovered by compactifying the AdS-space on a torus and finally performing the analytic continuation of q to the value of interest, which can be fractional. We compute the one-point correlator for the operator dual to the embedding function. We finally comment on holographic renormalization in the more general cases of codimensio...
A non-renormalization theorem for conformal anomalies
Petkou, Anastasios C; Petkou, Anastasios; Skenderis, Kostas
1999-01-01
We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the adS/CFT correspondence. Our results imply that 2- and 3-point functions of chiral primary operators in N=4 SU(N) SYM will not renormalize provided that a ``generalized Adler-Bardeen theorem'' holds. We further show that recent arguments connecting the non-renormalizability of the above mentioned correlation function to a bonus U(1)_Y symmetry are incomplete due to possible U(1)_Y violating contact terms. The tree level contribution to the contact terms may be set to zero by considering appropriately normalized operators. Non-renormalizability of the above mentioned correlation functions, however, will follow only if these c...
Collapse transition of randomly branched polymers: renormalized field theory.
Janssen, Hans-Karl; Stenull, Olaf
2011-05-01
We present a minimal dynamical model for randomly branched isotropic polymers, and we study this model in the framework of renormalized field theory. For the swollen phase, we show that our model provides a route to understand the well-established dimensional-reduction results from a different angle. For the collapse θ transition, we uncover a hidden Becchi-Rouet-Stora supersymmetry, signaling the sole relevance of tree configurations. We correct the long-standing one-loop results for the critical exponents, and we push these results on to two-loop order. For the collapse θ' transition, we find a runaway of the renormalization group flow, which lends credence to the possibility that this transition is a fluctuation-induced first-order transition. Our dynamical model allows us to calculate for the first time the fractal dimension of the shortest path on randomly branched polymers in the swollen phase as well as at the collapse transition and related fractal dimensions. PMID:21728509
Two-loop renormalization of Wilson loop for Drell-Yan production
Belitsky, A. V.
1998-01-01
We study the renormalization of the Wilson loop with a path corresponding to the Drell-Yan lepton pair production in two-loop approximation of perturbation theory. We establish the renormalization group equation in next-to-leading order and find a process specific anomalous dimension Gamma_DY in the corresponding approximation.
On the wave function renormalization for Wilson actions and their 1PI actions
Igarashi, Y; Sonoda, H
2016-01-01
We clarify the relation between the wave function renormalization for Wilson actions and that for the 1PI actions in the exact renormalization group formalism. Our study depends crucially on the use of two independent cutoff functions for the Wilson actions. We relate our results to those obtained previously by Bervillier, Rosten, and Osborn & Twigg.
Non-perturbative renormalization of the static quark theory in a large volume
Korcyl, Piotr; Ishikawa, Tomomi
2015-01-01
We report on progress to renormalize non-pertubatively the static heavy quark theory on the lattice. In particular, we present first results for position-space renormalization scheme for heavy-light bilinears. We test our approach on RBC's 16^3 x 32 lattice ensemble with m_pi = 420 MeV, Iwasaki gauge action and domain wall light fermions.
Remarks on the Renormalization Properties of Lorentz- and CPT-Violating Quantum Electrodynamics
Santos, Tiago R. S.; Sobreiro, Rodrigo F.
2016-08-01
In this work, we employ algebraic renormalization technique to show the renormalizability to all orders in perturbation theory of the Lorentz- and CPT-violating QED. Essentially, we control the breaking terms by using a suitable set of external sources. Thus, with the symmetries restored, a perturbative treatment can be consistently employed. After showing the renormalizability, the external sources attain certain physical values, which allow the recovering of the starting physical action. The main result is that the original QED action presents the three usual independent renormalization parameters. The Lorentz-violating sector can be renormalized by 19 independent parameters. Moreover, vacuum divergences appear with extra independent renormalization. Remarkably, the bosonic odd sector (Chern-Simons-like term) does not renormalize and is not radiatively generated. One-loop computations are also presented and compared with the existing literature.
A novel scheme for the wave function renormalization of the composite operators
International Nuclear Information System (INIS)
We propose a novel renormalization scheme for the hadronic operators. The renormalization factor of the operator in this scheme is normalized by the correlation function at tree level in coordinate space. If we focus on the pseudo scalar operator, then its renormalization factor is related to the mass renormalization factor of the fermion through the partially conserved axial-vector current relation. Using the renormalization factor for the pseudo scalar operator in our scheme, we obtain the mass anomalous dimension of the SU(3) gauge theory coupled to Nf=12 massless fundamental fermions, which has an infrared fixed point (IRFP). The mass anomalous dimension at the IRFP is estimated as γm∗=0.044−0.024+0.025(stat.)−0.032+0.057(syst.)
Shojaei-Fard, Ali
2010-01-01
In the first purpose, we concentrate on the theory of quantum integrable systems underlying the Connes-Kreimer approach. We introduce a new family of Hamiltonian systems depended on the perturbative renormalization process in renormalizable theories. It is observed that the renormalization group can determine an infinite dimensional integrable system such that this fact provides a link between this proposed class of motion integrals and renormalization flow. Moreover, with help of the integral renormalization theorems, we study motion integrals underlying Bogoliubv character and BCH series to obtain a new family of fixed point equations. In the second goal, we consider the combinatorics of Connes-Marcolli approach to provide a Hall rooted tree type reformulation from one particular object in this theory namely, universal Hopf algebra of renormalization $H_{\\mathbb{U}}$. As the consequences, interesting relations between this Hopf algebra and some well-known combinatorial Hopf algebras are obtained and also, o...
Two-loop renormalization in the standard model, part I. Prolegomena
International Nuclear Information System (INIS)
In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)
International Nuclear Information System (INIS)
The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A,B. A density matrix ρ is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of ρ are neglected. It is conjectured that the decreasing behaviour of the eigenvalues is gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH)N up to N = 34. A Hilbert space of dimension 5. x 1018 is explored. The ground state energy is 10-3eV within the full Cl value in the case N = 18. The DMRG method compares favourably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a comparison is made with the DMRG energy values. Finally, the spin-spin and density-density correlation functions are computed; the results suggest that the antiferromagnetic order of the exact solution does not extend up to large distances but exists locally. No charge density waves are present. (author)
Ghaffarnejad, Hossein
2014-01-01
We use two dimensional analogue of Einstein-Hilbert gravity minimally coupled with a mass-less, charge-less quantum scalar matter field. The matter field propagates on spherically symmetric four dimensional curved space time which in two dimensional analogue its 2-sphere part is described by a dilaton scalar field. We seek renormaized expectation value of stress tensor operator of the spherical quantum scalar field. Hadamard renormalization prescription is applied in this article leading to non-free trace anomaly of covariantly conserved nonsingular stress tensor. Its covariantly conservation condition demands to input a variable cosmological parameter. With this variable cosmological parameter the derived trace anomaly will be correspond with results of the works presented in Refs. [5, 6, 7, 8, 14, 15, 16] where the zeta function regularization method is used and trace anomaly is obtained in terms of Ricci scalar of corresponding two dimensional metric and derivatives of the dilaton field. Also we obtain dif...
International Nuclear Information System (INIS)
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O8+δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model
de Carvalho, Vanuildo S.; Freire, Hermann
2013-10-01
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi2Sr2CaCu2O8 + δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.
Conserved quantities and renormalization group flows in two-dimensional field theory
Gerganov, Bogomil Enchev
2000-12-01
Several problems in two-dimensional field theory are investigated. The concepts of classical and quantum integrability in two space-time dimensions are presented in the Introduction and a number of algebraic structures associated with integrable systems are described. Some results of conformal field theory (CFT) and perturbed conformal field theory are reviewed. In Chapter 2, the problem of interaction of two-level atoms in fibrillar geometry with electro-magnetic radiation is studied in perturbation theory. A new formalism is developed, representing the atomic spin operators with elementary fermions, and a resemblance between the structures of this model and quantum electrodynamics is established. Although the system studied is not itself integrable, it can be shown that the integrable quantum sine-Gordon model has some validity as an approximate theory. The following two chapters study the properties of several multi-field generalizations of the sine-Gordon model. The Bukhvostov-Lipatov model is studied in Chapter 3. The classical integrability of the fermionic version of the model is established, both in the bulk and on the half line, by explicitly building a conserved charge of Lorentz spin 3. The quantum integrability of the more general double-cosine model is investigated using perturbed CFT. The analysis showed in particular that the conservation law is spoiled at the quantum level on the Bukhvostov-Lipatov submanifold of the parameter space. In Chapter 4 an N-field model is considered-its interaction term being a product of N cosines. For N >= 2 a conservation law of Lorentz spin 3 is found to first order in perturbed CFT on a manifold where the interaction becomes marginal. The integrability of the model on this manifold is further studied using renormalization techniques and for N = 2, 3, and 4, integrable points are found at which the model is equivalent to the bosonized Gross-Neveu model. Finally, the renormalization properties of a class of integrable
Charged Rotating Black Branes in Various Dimensions
Khodam-Mohammadi, A
2007-01-01
In this thesis, two different aspects of asymptotically charged rotating black branes in various dimensions are studied. In the first part, the thermodynamics of these spacetimes is investigated, while in the second part the no hair theorem for these spacetimes in four dimensions is considered. In part I, first, the Euclidean actions of a d-dimensional charged rotating black brane are computed through the use of the counterterms renormalization method both in the canonical and the grand-canonical ensemble, and it is shown that the logarithmic divergencies associated to the Weyl anomalies and matter field vanish. Second, a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the electric charge is obtained, which shows that these quantities satisfy the first law of thermodynamics. Third, by using the conserved quantities and the Euclidean actions, the thermodynamics potentials of the system in terms of the temperature, the angular velocities and the electric potential are obtai...
Renormalized field theory of collapsing directed randomly branched polymers.
Janssen, Hans-Karl; Wevelsiep, Frank; Stenull, Olaf
2009-10-01
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation. PMID:19905335
Renormalization group and critical behaviour in gravitational collapse
Hara, T; Adachi, S; Hara, Takashi; Koike, Tatsuhiko; Adachi, Satoshi
1996-01-01
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various types of universality and scaling observed in numerical studies. In particular, universality in initial data space and universality for different models are understood in a unified way. (2) It enables us to perform a detailed analysis of time evolution beyond linear perturbation, by providing rigorous controls on nonlinear terms. Under physically reasonable assumptions we prove: (1) Uniqueness of the relevant mode around a fixed point implies universality in initial data space. (2) The critical exponent \\beta_{\\rm BH} and the unique positive eigenvalue \\kappa of the relevant mode is exactly related by \\beta_{\\rm BH} = \\beta /\\kappa, where \\beta is a scaling exponent. (3) The above (1) and (2) hold also for discretely self-similar case (replacing ``fixed point'' with ``limi...
Scaling and Renormalization in two dimensional Quantum Gravity
Codello, Alessandro
2014-01-01
We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal dimension of the theory and the scaling of the reparametrization-invariant two point function. Then we compute the scaling exponents entering in this relations by means of the functional RG. We show that a key ingredient to obtain the correct results already known from Liouville theory is the use of the exponential parametrization for metric fluctuations. We also show that with this parametrization we can recover the correct finite part of the effective action as the $\\epsilon \\to 0$ continuation of gravity in $d=2+\\epsilon$ dimensions.
Renormalization Group Optimized Perturbation Theory at Finite Temperatures
Kneur, J -L
2015-01-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar $ \\lambda\\phi^4$ field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-$N$ results of the $O(N)$ model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard therm...
Momentum-subtraction renormalization techniques in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Foda, O.
1987-10-01
Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should.
Local Scale Transformations on the Lattice with Tensor Network Renormalization.
Evenbly, G; Vidal, G
2016-01-29
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients. PMID:26871313
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal
2016-01-01
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Higher spin Fronsdal equations from the exact renormalization group
Jin, Kewang; Leigh, Robert G.; Parrikar, Onkar
2015-06-01
We show that truncating the exact renormalization group equations of free U( N) vector models in the single-trace sector to the linearized level reproduces the Fronsdal equations on AdS d+1 for all higher spin fields, with the correct boundary conditions. More precisely, we establish canonical equivalence between the linearized RG equations and the familiar local, second order differential equations on AdS d+1, namely the higher spin Fronsdal equations. This result is natural because the second-order bulk equations of motion on AdS simply report the value of the quadratic Casimir of the corresponding conformal modules in the CFT. We thus see that the bulk Hamiltonian dynamics given by the boundary exact RG is in a different but equivalent canonical frame than that which is most natural from the bulk point of view.
Non-perturbative improvement and renormalization of lattice operators
International Nuclear Information System (INIS)
The Alpha Collaboration has proposed an optimal value for cSW in the Sheikholeslami-Wohlert action, chosen to remove O(a) effects. To measure hadronic matrix elements to the same accuracy we need a method of finding O(a) improved operators, and their renormalization constants. We determine the Z factors by a non-perturbative method, measuring the matrix elements for single quark states propagating through gauge fields in the Landau gauge. The data show large effects coming from chiral symmetry breaking. This allows us to find the improvement coefficients too, by requiring that the amount of chiral symmetry breaking agrees with that predicted by the chiral Ward identities. (orig.)
Stability of renormalization group trajectories and the fermion flavor problem
Goldfain, Ervin
2007-04-01
An outstanding puzzle of the current standard model for particle physics (SM) is that both leptons and quarks arise in replicated patterns. Our work suggests that the number of fermion flavors occurring in the SM may be directly derived from the dynamics of renormalization group equations. The starting point is the system describing the coupling flow in the gauge sector [ dgidt.= βi(gi)=bi(N,nf)gi^3 +O(gi^5 ) ] where i=(1,2,3) labels the gauge group of dimension N, nf is the number of fermion flavors and t the sliding scale. With the help of the Routh-Hurwitz criterion, we find that the SM solution nf=6 follows from demanding stability of the linearized flow about its fixed points.
The renormalized theory of beam-beam interaction
International Nuclear Information System (INIS)
A new approach to calculate analytically the particle distribution in the presence of beam-beam interaction and synchrotron radiation effects for an electron-positron colliding beam storage ring is presented. The method is based on correct calculation of the Green's function which includes the full effect of the beam-beam force on the distortion of particle orbits, borrowing the renormalization technique of quantum field therory. By this way, the theory is applicable to any level of beam-beam interaction, no matter whether chaos ensues in phase space or not. This paper is devoted mostly to verificaiton of the theory by comparison with the results of computer simulations. Fairly good agreements are obtained. 5 refs., 3 figs
Resummation and renormalization in effective theories of particle physics
Jakovac, Antal
2015-01-01
Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...
The Polarizable Embedding Density Matrix Renormalization Group Method
Hedegård, Erik D
2016-01-01
The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures ...
The density matrix renormalization group for ab initio quantum chemistry
Wouters, Sebastian
2014-01-01
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational co...
Renormalization and asymptotic safety in truncated quantum Einstein gravity
International Nuclear Information System (INIS)
A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be achieved in a space of lagrangians differing only by a field dependent conformal factor. In particular the Noether currents and the quantum constraints can be defined as finite composite operators. The form of the field-dependence in the conformal factor changes with the renormalization scale and a closed formula is obtained for the beta functional governing its flow. The flow possesses a unique fixed point at which the trace anomaly is shown to vanish. The approach to the fixed point adheres to Weinberg's 'asymptotic safety' scenario, both in the gravitational wave/cosmological sector and in the stationary sector. (author)
Momentum-subtraction renormalization techniques in curved space-time
International Nuclear Information System (INIS)
Momentum-subtraction techniques, specifically BPHZ and Zimmermann's Normal Product algorithm, are introduced as useful tools in the study of quantum field theories in the presence of background fields. In a model of a self-interacting massive scalar field, conformally coupled to a general asymptotically-flat curved space-time with a trivial topology, momentum-subtractions are shown to respect invariance under general coordinate transformations. As an illustration, general expressions for the trace anomalies are derived, and checked by explicit evaluation of the purely gravitational contributions in the free field theory limit. Furthermore, the trace of the renormalized energy-momentum tensor is shown to vanish at the Gell-Mann Low eigenvalue as it should
Renormalization group evolution of the universal theories EFT
Wells, James D
2015-01-01
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theori...
Renormalized turbulence theory of ion pressure gradient driven drift modes
International Nuclear Information System (INIS)
From the nonlinear gyrokinetic equation we formulate the renormalized turbulence equation for the eta/sub i/-mode drift wave instability. The study shows that the dominant nonlinear damping mechanism is from the E x B convection of the pressure fluctuation and that the kinetic modifications to the fluid E x B mode coupling, studied earlier, shift the spectrum toward the shorter wavelengths. Balancing the linear growth rate with the nonlinear dampling rate at the linearly most unstable region, we calculate the anomalous ion thermal conductivity which exceeds the neoclassical plateau formula and gives a value of the same order as that previously computed by Horton, Choi and Tank, but with a kinetic enhancement factor. Also, the thermal conductivity formula remains finite for vanishing density gradient. 23 refs
Emergent Space-Time via a Geometric Renormalization Method
Rastgoo, Saeed
2016-01-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...
Fully Lagrangian Renormalized Approximation theory of fluid turbulence: Progress report
International Nuclear Information System (INIS)
The purpose of this paper is to discuss our refinement and extension of the work of Y. Kaneda on a Lagrangian Renormalized Approximation (LRA) for homogeneous hydrodynamic turbulence. Kaneda's results are important to the development of a consistent theory of turbulence because the LRA theory successfully overcomes the failure of other turbulence theories (namely the Direct Interaction Approximation) to predict the Kolmogorov wavenumber spectrum. It is thought that this success is due to the use of a Lagrangian rather than Eulerian description of the fluid so that convection of the small eddies by the large ones is properly treated. However, some aspects of these results are puzzling and are considered here. For example, the form of the correlation function and the value of the Kolmogorov constant, K, depend on the choice of the form of the correlation function
Chiral symmetry restoration and axial vector renormalization for Wilson fermions
Reisz, T
2000-01-01
Lattice gauge theories with Wilson fermions break chiral symmetry. In theU(1) axial vector current this manifests itself in the anomaly. On the otherhand it is generally expected that the axial vector flavour mixing current isnon-anomalous. We give a short, but strict proof of this to all orders ofperturbation theory, and show that chiral symmetry restauration implies aunique multiplicative renormalization constant for the current. This constantis determined entirely from an irrelevant operator in the Ward identity. Thebasic ingredients going into the proof are the lattice Ward identity, chargeconjugation symmetry and the power counting theorem. We compute therenormalization constant to one loop order. It is largely independent of theparticular lattice realization of the current.
Heavy fermion mass predictions and renormalization group equations
International Nuclear Information System (INIS)
It has recently become popular to predict the low energy fermion mass spectrum based on a high scale, Mx ∼ 1016 GeV/c2, ansatz for the Yukawa couplings. The evolution to low energy being achieved using renormalization group equations, with supersymmetry extant above a breaking scale Ms ∼ 103 GeV/c2. In this paper it is shown how the heavy fermion and Higgs masses are determined by fixed points and thus will obtain in many specific models. This gives Mt ∼ 184 GeV/c2, Mh ∼ 122 GeV/c2 and imposing a hierarchy of scalar vacuum expectation values Mb ∼ 4.1, Mr ∼ 1.78 GeV/c2. The dependence on αs, (Mzdegree) and Ms is elucidated
(Non)renormalization of Anomalous Conductivities and Holography
Gursoy, Umut
2014-01-01
The chiral magnetic and the chiral vortical effects are recently discovered phenomena arising from chiral gauge and gravitational anomalies that lead to generation of electric currents in presence of magnetic field or vorticity. The magnitude of these effects is determined by the anomalous conductivities. These conductivities can be calculated by the linear response theory, and in the strong coupling limit this calculation can be carried out by the holographic techniques. Earlier calculations in case of conformal field theories indicate non-renormalization of these conductivities where the holographic calculation agrees with the free field limit. We extend this holographic study to non-conformal theories exhibiting mass-gap and confinement-deconfinement type transitions in a holographic model based on the analytic black hole solution of Gao and Zhang. We show that radiative corrections are also absent in these non-conformal theories confirming indirect arguments of Jensen et al in a direct and non-trivial fas...
Higgs boson, renormalization group, and naturalness in cosmology
International Nuclear Information System (INIS)
We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems. (orig.)
Reaction-diffusion processes and non-perturbative renormalization group
International Nuclear Information System (INIS)
This paper is devoted to investigating non-equilibrium phase transitions to an absorbing state, which are generically encountered in reaction-diffusion processes. It is a review, based on Canet, Delamotte, Deloubriere and Wschebor (2004 Phys. Rev. Lett. 92 195703); Canet, Chate and Delamotte (2004 Phys. Rev. Lett. 92 255703) and Canet et al (2005 Phys. Rev. Lett. 95 100601), of recent progress in this field that has been allowed by a non-perturbative renormalization group approach. We mainly focus on branching and annihilating random walks and show that their critical properties strongly rely on non-perturbative features and that hence the use of a non-perturbative method turns out to be crucial to get a correct picture of the physics of these models
Advanced density matrix renormalization group method for nuclear structure calculations
Legeza, Ö; Poves, A; Dukelsky, J
2015-01-01
We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous $400$ KeV discrepancy in the ground state energy of $^{56}$Ni. We then report the first DMRG results in the $pf+g9/2$ shell model space for the ground $0^+$ and first $2^+$ states of $^{64}$Ge which are benchmarked with reference data obtained from Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of the two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.
Renormalized stress tensor in one-bubble spacetimes
Montes, X
1999-01-01
We compute the two-point function and the renormalized expectation value of the stress tensor of a quantum field interacting with a nucleating bubble. Two simple models are considered. One is the massless field in the Vilenkin-Ipser-Sikivie spacetime describing the gravitational field of a reflection symmetric domain wall. The other is vacuum decay in flat spacetime where the quantum field only interacts with the tunneling field on the bubble wall. In both cases the stress tensor is of the perfect fluid form. The assymptotic form of the equation of state are given for each model. In the VIS case, we find that $p=-(1/3)\\rho$, where the energy density $\\rho$ is dominated by the gradients of supercurvature modes.
Lambda^{QCD}_{MS} from Renormalization Group Optimized Perturbation
Kneur, J -L
2011-01-01
A recent extension of a variationally optimized perturbation, combined with renormalization group properties in a straightforward way, can provide approximations to nonperturbative quantities such as the chiral symmetry breaking order parameters typically. We apply this to evaluate, up to third order in this modified perturbation, the ratio Fpi/Lambda, where Fpi is the pion decay constant and Lambda the basic QCD scale in the modified MS scheme. Using experimental Fpi input value we obtain Lambda(nf=2) ~ 255_{-15}^{+40} MeV, where quoted errors are estimates of theoretical uncertainties of the method. This compares reasonably well with some recent lattice simulation results. We briefly discuss prospects (and obstacles) for extrapolation to alpha_S(mu) at perturbative mu values.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
International Nuclear Information System (INIS)
Results of a renormalization group study for the 2-dimensional Hubbard model close to half-filling at finite temperature are presented. Bosonic degrees of freedom corresponding to antiferromagnetic and d-wave superconducting order are introduced, and flow equations for the corresponding coupling constants are deduced from an exact flow equation for the effective average action. The influence of bosonic fluctuations on the onset of local antiferromagnetic order is discussed. At low enough temperatures and close to half-filling the discrete symmetry of the lattice is broken and incommensurate antiferromagnetic fluctuations dominate. The phase diagram is shown for the parameter regime close to half-filling in the presence of vanishing as well as non-vanishing next-to-nearest-neighbor hopping t'. Finally, the potential emergence of d-wave superconducting order at larger distances from half-filling is discussed.
Background field method and the cohomology of renormalization
Anselmi, Damiano
2016-03-01
Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian gauge symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions of the theorem are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved arguments that are available in the literature.
Background field method and the cohomology of renormalization
Anselmi, Damiano
2015-01-01
Using the background field method and the Batalin-Vilkovisky formalism, we prove a key theorem on the cohomology of perturbatively local functionals of arbitrary ghost numbers, in renormalizable and nonrenormalizable quantum field theories whose gauge symmetries are general covariance, local Lorentz symmetry, non-Abelian Yang-Mills symmetries and Abelian symmetries. Interpolating between the background field approach and the usual, nonbackground approach by means of a canonical transformation, we take advantage of the properties of both approaches and prove that a closed functional is the sum of an exact functional plus a functional that depends only on the physical fields and possibly the ghosts. The assumptions are the mathematical versions of general properties that characterize the counterterms and the local contributions to the potential anomalies. This makes the outcome a theorem on the cohomology of renormalization, rather than the whole local cohomology. The result supersedes numerous involved argumen...
Renormalization Group Running of Newton's G: The Static Isotropic Case
Hamber, H W; Hamber, Herbert W.; Williams, Ruth M.
2007-01-01
Corrections are computed to the classical static isotropic solution of general relativity, arising from non-perturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely non-perturbative scale, closely connected with the gravitational vacuum condensate, and thereby, it is argued, related to the observed effective cosmological constant. Several analogies between the proposed vacuum condensate picture of quantum gravitation, and non-perturbative aspects of vacuum condensation in strongly coupled non-abelian gauge theories are developed. In contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The expected running of Newton's constant $G$ is compared to known vacuum polarization induced effects in QED and QCD. The general analysis is then extended to a set of covariant non-local effective field equati...
Local Scale Transformations on the Lattice with Tensor Network Renormalization
Evenbly, G.; Vidal, G.
2016-01-01
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
A renormalization in group study of supersymmetric field theories
International Nuclear Information System (INIS)
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
A renormalization in group study of supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Heilmann, Marianne
2015-05-13
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
International Nuclear Information System (INIS)
20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)
Indian Academy of Sciences (India)
Mosumi Das; S Ramasesha
2006-01-01
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the $1^{1} B_{u}^{-}$ exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.
Active space decomposition with multiple sites: Density matrix renormalization group algorithm
Parker, Shane M
2014-01-01
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few {\\mu}Eh or less) with M = 128 in both cases, which is in contrast to conventional ab initio density matrix renormalization group.
Renormalization and Hopf algebraic structure of the five-dimensional quartic tensor field theory
International Nuclear Information System (INIS)
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes–Kreimer-like Hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail, at one- and two-loop levels, the Hochschild cohomology allowing to write the combinatorial Dyson–Schwinger equations. Feynman tensor graph Hopf subalgebras are also exhibited. (paper)
Energy Technology Data Exchange (ETDEWEB)
Parker, Shane M.; Shiozaki, Toru [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States)
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Kopitzki, K; Timmer, J
1998-01-01
Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatio-temporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.
Kullback-Leibler and Renormalized Entropy Applications to EEGs of Epilepsy Patients
Quiroga, R Q; Lehnertz, K; Grassberger, Peter
1999-01-01
Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.
Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
Avohou, Remi Cocou; Tanasa, Adrian
2015-01-01
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes-Kreimer-like Hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail, at one- and two-loop levels, the Hochschild cohomology allowing to write the combinatorial Dyson-Schwinger equations. Feynman tensor graph Hopf subalgebras are also exhibited.
Revisiting on-shell renormalization conditions in theories with flavour mixing
Grimus, W
2016-01-01
In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are non-singular in $\\varepsilon = p^2 - m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.
The Weil-Petersson metric and the renormalized volume of hyperbolic 3-manifolds
Krasnov, Kirill
2009-01-01
We survey the renormalized volume of hyperbolic 3-manifolds, as a tool for Teichmuller theory, using simple differential geometry arguments to recover results sometimes first achieved by other means. One such application is McMullen's quasifuchsian (or more generally Kleinian) reciprocity, for which different arguments are proposed. Another is the fact that the renormalized volume of quasifuchsian (or more generally geometrically finite) hyperbolic 3-manifolds provides a Kahler potential for the Weil-Petersson metric on Teichmuller space. Yet another is the fact that the grafting map is symplectic, which is proved using a variant of the renormalized volume defined for hyperbolic ends.
International Nuclear Information System (INIS)
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μEh or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation
One-loop amplitudes on orbifolds and the renormalization of coupling constants
International Nuclear Information System (INIS)
We consider three-point one-loop amplitudes for strings propagating on orbifolds that preserve a supersymmetry. For three external gauge bosons, we compute the explicit wave-function renormalization of the external legs and show that it leads to the correct value for the Yang-Mills β-function. For two gauge bosons and a graviton, we show that there is no renormalization of the coupling, but if the graviton is replaced with an antisymmetric tensor, then the coupling is renormalized. (orig.)
Renormalization procedure for random tensor networks and the canonical tensor model
International Nuclear Information System (INIS)
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is a generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem that relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks
Non-perturbative renormalization of overlap quark bilinears on domain wall fermion configurations
Liu, Zhaofeng; Yang, Yi-Bo; Dong, Shao-Jing; Glatzmaier, Michael; Gong, Ming; Liu, Keh-Fei; Li, Anyi; Zhang, Jian-Bo
2013-01-01
We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations. Both overlap and domain wall fermions have chiral symmetry on the lattice. The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity. The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme. Results in the MS-bar scheme are obtained by using perturbative conversion ratios. The analysis uses in total six ensembles with lattice sizes 24^3x64 and 32^3x64.
Gabadadze, Gregory
2008-01-01
We consider Bose-Einstein condensation of massive electrically charged scalars in a uniform background of charged fermions. We focus on the case when the scalar condensate screens the background charge, while the net charge of the system resides on its boundary surface. A distinctive signature of this substance is that the photon acquires a Lorentz-violating mass in the bulk of the condensate. Due to this mass, the transverse and longitudinal gauge modes propagate with different group velocities. We give qualitative arguments that at high enough densities and low temperatures a charged system of electrons and helium-4 nuclei, if held together by laboratory devices or by force of gravity, can form such a substance. We briefly discuss possible manifestations of the charged condensate in compact astrophysical objects.
The so-called renormalization group method applied to the specific prime number logarithmic decrease
Peterman, A.
2000-01-01
A so-called Renormalization Group (RG) analysis is performed in order to shed some light on why the density of prime numbers in $\\Bbb N^*$ decreases like the single power of the inverse neperian logarithm.
A Geometrical Formulation of the Renormalization Group Method for Global Analysis
Kunihiro, Teiji
1995-01-01
On the basis of the classical theory of envelopes, we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
Introduction to the renormalization group study in relativistic quantum field theory
International Nuclear Information System (INIS)
An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.)
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
International Nuclear Information System (INIS)
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of ΔB=2 parity-odd four-fermion operators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by nonperturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schroedinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered. (orig.)
Renormalization of lattice-regularized quantum gravity models I. General considerations
Cooperman, Joshua H
2014-01-01
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A crucial complement to lattice regularization is the process of renormalization through which a continuous description of the quantum theory arises. I provide a comprehensive conceptual discussion of the renormalization of lattice-regularized quantum gravity models. I begin with a presentation of the renormalization group from the Wilsonian perspective. I then consider the application of the renormalization group in four contexts: quantum field theory on a continuous nondynamical spacetime, quantum field theory on a lattice-regularized nondynamical spacetime, quantum field theory of continuous dynamical spacetime, and quantum field theory of lattice-regularized dynamical spacetime. The first three contexts serve to identify successively the particular issues that arise in the...
Energy Technology Data Exchange (ETDEWEB)
Kim, Sung Soo [Department of Applied Mathematics, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Jung, Young-Dae [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590 (United States)
2013-12-15
The renormalization plasma screening effects on the electron-ion collision are investigated in dense partially ionized hydrogen plasmas. The Hamilton-Jacobi and eikonal methods with the effective interaction potential are employed to obtain the eikonal scattering phase shift and eikonal cross section for the electron-ion collision. It is found that the influence of renormalization screening strongly suppresses the eikonal scattering phase shift as well as the eikonal cross section, especially, for small impact parameter regions. In addition, the renormalization screening effect reduces the total eikonal cross section in all energy domains. The variation of the renormalization effects on the electron-ion collision in dense partially ionized hydrogen plasmas is also discussed.
A geometrical formulation of the renormalization group method for global analysis
Kunihiro, T
1995-01-01
On the basis of the classical theory of envelope,we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
MS and RI-MOM renormalization of three-quark operators
International Nuclear Information System (INIS)
The most widely used renormalization condition in continuum QCD is the modified minimal subtraction (MS) scheme, which requires the use of dimensional regularization. Because dimensional regularization is not possible on a 4-dimensional lattice, regularization invariant (RI) renormalization conditions such as the RI-MOM schemes are used instead. Since such a scheme is also viable in the continuum we aim to employ perturbative QCD calculations to provide conversion between RI-MOM and MS renormalization factors for three-quark operators. These conversion factors can then be applied to renormalized lattice results for e.g. nucleon distribution amplitudes or coupling constants in order to facilitate better comparability to values obtained from continuum methods such as QCD sum rules.
MS and RI-MOM renormalization of three-quark operators
Energy Technology Data Exchange (ETDEWEB)
Gruber, Michael [Institut fuer Theoretische Physik, Universitaet Regensburg (Germany)
2013-07-01
The most widely used renormalization condition in continuum QCD is the modified minimal subtraction (MS) scheme, which requires the use of dimensional regularization. Because dimensional regularization is not possible on a 4-dimensional lattice, regularization invariant (RI) renormalization conditions such as the RI-MOM schemes are used instead. Since such a scheme is also viable in the continuum we aim to employ perturbative QCD calculations to provide conversion between RI-MOM and MS renormalization factors for three-quark operators. These conversion factors can then be applied to renormalized lattice results for e.g. nucleon distribution amplitudes or coupling constants in order to facilitate better comparability to values obtained from continuum methods such as QCD sum rules.
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction-Diffusion Systems
Fischer, J.
2015-10-01
In the present work we introduce the notion of a renormalized solution for reaction-diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction-diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.
Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma
International Nuclear Information System (INIS)
A renormalization procedure for the perturbation expansion of the Vlasov-Poisson equation is presented to describe stationary homogeneous turbulence. By using the diagramatic scheme the theory is shown to be renormalizable to any order. The expressions for the renormalized propagator, the renormalized dielectric function, and the intrinsically incoherent source are given. The renormalization leads to a complete separation of the fluctuating distribution function f/sub k/ into two parts, the coherent part, which is proved to represent the dielectric effect of the medium, and the intrinsically incoherent part, which represents the effect of nonlinear source. The turbulent collisional operator in the transport equation is proved equal to GAMMA0, the frequency broadening when k = 0
International Nuclear Information System (INIS)
A so-called renormalization group (RG) analysis is performed in order to shed some light on why the density of prime numbers in N* decreases like the single power of the inverse neperian logarithm. (orig.)
An apparent inconsistency between the Dyson and renormalization group equations in QCD
International Nuclear Information System (INIS)
We show that there is an apparent inconsistency between the renormalization group and Dyson equations for the fermion propagator in QCD except in the special QED-like gauge. This has some bearing on the electromagnetic mass shift problem. (author)
Two-and three-dimension Potts magnetism in the renormalization group approximation
International Nuclear Information System (INIS)
Through a real space Renormalization Group (RG) technique we discuss the criticality of various physical systems, calculate order parameters for geometrical problems and analyse convergence aspects of the RG theory. (author)