In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
Holographic Renormalization in Dense Medium
International Nuclear Information System (INIS)
Park, Chanyong
2014-01-01
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
Ab initio excited states from the in-medium similarity renormalization group
Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.
2017-04-01
We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
Energy Technology Data Exchange (ETDEWEB)
Hergert, H., E-mail: hergert@nscl.msu.edu [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics, The Ohio State University, Columbus, OH 43210 (United States); Bogner, S.K., E-mail: bogner@nscl.msu.edu [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Morris, T.D., E-mail: morrist@nscl.msu.edu [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Schwenk, A., E-mail: schwenk@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Tsukiyama, K., E-mail: tsuki.kr@gmail.com [Center for Nuclear Study, Graduate School of Science, University of Tokyo, Hongo, Tokyo, 113-0033 (Japan)
2016-03-21
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
International Nuclear Information System (INIS)
Hergert, H.; Bogner, S.K.; Morris, T.D.; Schwenk, A.; Tsukiyama, K.
2016-01-01
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
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.
Block generators for the similarity renormalization group
Energy Technology Data Exchange (ETDEWEB)
Huether, Thomas; Roth, Robert [TU Darmstadt (Germany)
2016-07-01
The Similarity Renormalization Group (SRG) is a powerful tool to improve convergence behavior of many-body calculations using NN and 3N interactions from chiral effective field theory. The SRG method decouples high and low-energy physics, through a continuous unitary transformation implemented via a flow equation approach. The flow is determined by a generator of choice. This generator governs the decoupling pattern and, thus, the improvement of convergence, but it also induces many-body interactions. Through the design of the generator we can optimize the balance between convergence and induced forces. We explore a new class of block generators that restrict the decoupling to the high-energy sector and leave the diagonalization in the low-energy sector to the many-body method. In this way one expects a suppression of induced forces. We analyze the induced many-body forces and the convergence behavior in light and medium-mass nuclei in No-Core Shell Model and In-Medium SRG calculations.
Driven similarity renormalization group: Third-order multireference perturbation theory.
Li, Chenyang; Evangelista, Francesco A
2017-03-28
A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.
Renormalization group in modern physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1988-01-01
Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view the authors present a simple derivation of the renorm-group (RG) in QFT liberated from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare different RG's
Renormalization theory of stationary homogeneous strong turbulence in a collisionless plasma
International Nuclear Information System (INIS)
Zhang, Y.Z.
1984-01-01
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 GAMMA 0 , the frequency broadening when k = 0
Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades
Saveliev, V. L.; Gorokhovski, M. A.
2012-12-01
Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.
Renormalization Group in different fields of theoretical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1992-02-01
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)
G-Boson renormalizations and mixed symmetry states
International Nuclear Information System (INIS)
Scholten, O.
1986-01-01
In the IBA model the low-lying collective states are described in terms of a system of interacting s- and d-bosons. A boson can be interpreted as corresponding to collective J=0 or J=2 fermion pair states. As such the IBA model space can be seen as only a small subsector of the full shell model space. For medium heavy nuclei such a truncation of the model space is necessary to make calculations feasible. As is well known truncations of a model space make it necessary to renormalize the model parameters. In this work some renormalizations of the Hamiltonian and the E2 transition operator will be discussed. Special attention will be given to the implication of these renormalizations for the properties of mixed symmetry states. The effects of renormalization are obtained by considering the influence of fermion pair states that have been omitted from the model basis. Here the authors focus attention on the effect of the low-lying two particle J=4 state, referred to as g-boson or G-pair state. Renormalizations of the d-boson energy, the E2 effective charges, and symmetry force are discussed
Point transformations and renormalization in the unitary gauge. III. Renormalization effects
International Nuclear Information System (INIS)
Sherry, T.N.
1976-06-01
An analysis of two simple gauge theory models is continued using point transformations rather than gauge transformations. The renormalization constants are examined directly in two gauges, the renormalization (Landau) and unitary gauges. The result is that the individual coupling constant renormalizations are identical when calculated in each of the above two gauges, although the wave-function and proper vertex renormalizations differ
Dimensional renormalization and comparison of renormalization schemes in quantum electrodynamics
International Nuclear Information System (INIS)
Coquereaux, R.
1979-02-01
The method of dimensional renormalization as applied to quantum electrodynamics is discussed. A general method is given which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes
Investigation of renormalization effects in high temperature cuprate superconductors
International Nuclear Information System (INIS)
Zabolotnyy, Volodymyr B.
2008-01-01
It has been found that the self-energy of high-T 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 2 Sr 2 CaCu 2 O 8+δ and YBa 2 Cu 3 O 7-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 T 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.)
Renormalization group theory of phase transitions in square Ising systems
International Nuclear Information System (INIS)
Nienhuis, B.
1978-01-01
Some renormalization group calculations are presented on a number of phase transitions in a square Ising model, both second and first order. Of these transitions critical exponents are calculated, the amplitudes of the power law divergences and the locus of the transition. In some cases attention is paid to the thermodynamic functions also far from the critical point. Universality and scaling are discussed and the renormalization group theory is reviewed. It is shown how a renormalization transformation, which relates two similar systems with different macroscopic dimensions, can be constructed, and how some critical properties of the system follow from this transformation. Several numerical and analytical applications are presented. (Auth.)
Renormalization transformation of periodic and aperiodic lattices
International Nuclear Information System (INIS)
Macia, Enrique; Rodriguez-Oliveros, Rogelio
2006-01-01
In this work we introduce a similarity transformation acting on transfer matrices describing the propagation of elementary excitations through either periodic or Fibonacci lattices. The proposed transformation can act at two different scale lengths. At the atomic scale the transformation allows one to express the systems' global transfer matrix in terms of an equivalent on-site model one. Correlation effects among different hopping terms are described by a series of local phase factors in that case. When acting on larger scale lengths, corresponding to short segments of the original lattice, the similarity transformation can be properly regarded as describing an effective renormalization of the chain. The nature of the resulting renormalized lattice significantly depends on the kind of order (i.e., periodic or quasiperiodic) of the original lattice, expressing a delicate balance between chemical complexity and topological order as a consequence of the renormalization process
Holographic renormalization and supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Genolini, Pietro Benetti [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom); Cassani, Davide [LPTHE, Sorbonne Universités UPMC Paris 6 and CNRS, UMR 7589,F-75005, Paris (France); Martelli, Dario [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom)
2017-02-27
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N=2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.
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.)
On the nucleon renormalization in many nucleon problems due to pionic degrees of freedom
International Nuclear Information System (INIS)
Sauer, P.U.; Sawicki, M.; Furui, Sadataka.
1985-01-01
Conceptual problems of unified two-nucleon force models are discussed. The force models are based on the pion-nucleon vertex and attempt a description of the nucleon-nucleon interaction below and above pion threshold. The conceptual problems arise from the nucleon renormalization due to pionic degrees of freedom. Keeping channels with a single pion only no renormalization procedure can be given which is consistent in the one-nucleon and in the many-nucleon systems. The medium dependence of the one-pion exchange potential is illustrated. (author)
Bogolyubov renormalization group and symmetry of solution in mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.; Kovalev, V.F.
2000-01-01
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium
Multiscale unfolding of real networks by geometric renormalization
García-Pérez, Guillermo; Boguñá, Marián; Serrano, M. Ángeles
2018-06-01
Symmetries in physical theories denote invariance under some transformation, such as self-similarity under a change of scale. The renormalization group provides a powerful framework to study these symmetries, leading to a better understanding of the universal properties of phase transitions. However, the small-world property of complex networks complicates application of the renormalization group by introducing correlations between coexisting scales. Here, we provide a framework for the investigation of complex networks at different resolutions. The approach is based on geometric representations, which have been shown to sustain network navigability and to reveal the mechanisms that govern network structure and evolution. We define a geometric renormalization group for networks by embedding them into an underlying hidden metric space. We find that real scale-free networks show geometric scaling under this renormalization group transformation. We unfold the networks in a self-similar multilayer shell that distinguishes the coexisting scales and their interactions. This in turn offers a basis for exploring critical phenomena and universality in complex networks. It also affords us immediate practical applications, including high-fidelity smaller-scale replicas of large networks and a multiscale navigation protocol in hyperbolic space, which betters those on single layers.
Renormalization in few body nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Tomio, L.; Biswas, R. [Instituto de Fisica Teorica, UNESP, 01405-900 Sao Paulo (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminenese, Niteroi (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, CTA 12228-900 Sao Jose dos Campos (Brazil)
2001-09-01
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 {sup 3}S{sub l} -{sup 3} D{sub 1} 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
Renormalization in few body nuclear physics
International Nuclear Information System (INIS)
Tomio, L.; Biswas, R.; Delfino, A.; Frederico, T.
2001-01-01
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 3 S l - 3 D 1 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
Unambiguity of renormalization group calculations in QCD
International Nuclear Information System (INIS)
Vladimirov, A.A.
1979-01-01
A detailed analysis of the reduction of ambiguities determined by an arbitrary renormalization scheme is presented for the renormalization group calculations of physical quantities in quantum chromodynamics (QCD). Some basic formulas concerning the renormalization-scheme dependence of Green's and renormalization group functions are given. A massless asymptotically free theory with one coupling constant g is considered. In conclusion, several rules for renormalization group calculations in QCD are formulated
Perturbation theory for the effective diffusion constant in a medium of random scatterers
International Nuclear Information System (INIS)
Dean, D S; Drummond, I T; Horgan, R R; Lefevre, A
2004-01-01
We develop perturbation theory and physically motivated resummations of the perturbation theory for the problem of a tracer particle diffusing in a random medium. The random medium contains point scatterers of density ρ uniformly distributed throughout the material. The tracer is a Langevin particle subjected to the quenched random force generated by the scatterers. Via our perturbative analysis, we determine when the random potential can be approximated by a Gaussian random potential. We also develop a self-similar renormalization group approach based on thinning out the scatterers; this scheme is similar to that used with success for diffusion in Gaussian random potentials and agrees with known exact results. To assess the accuracy of this approximation scheme, its predictions are confronted with results obtained by numerical simulation
Energy Technology Data Exchange (ETDEWEB)
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)
2006-12-15
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.)
International Nuclear Information System (INIS)
Lenaghan, J.T.; Rischke, D.H.
2000-01-01
The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest. (author)
Compositeness condition in the renormalization group equation
International Nuclear Information System (INIS)
Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko
1990-01-01
The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)
Cylinder renormalization for Siegel disks and a constructive Measurable Riemann Mapping Theorem
Gaydashev, D G
2006-01-01
The boundary of the Siegel disk of a quadratic polynomial with an irrationally indifferent fixed point with the golden mean rotation number has been observed to be self-similar. The geometry of this self-similarity is universal for a large class of holomorphic maps. A renormalization explanation of this universality has been proposed in the literature. However, one of the ingredients of this explanation, the hyperbolicity of renormalization, has not been proved yet. The present work considers a cylinder renormalization - a novel type of renormalization for holomorphic maps with a Siegel disk which is better suited for a hyperbolicity proof. A key element of a cylinder renormalization of a holomorphic map is a conformal isomorphism of a dynamical quotient of a subset of $\\field{C}$ to a bi-infinite cylinder $\\field{C} / \\field{Z}$. A construction of this conformal isomorphism is an implicit procedure which can be performed using the Measurable Riemann Mapping Theorem. We present a constructive proof of the Mea...
The evolution of Bogolyubov's renormalization group
International Nuclear Information System (INIS)
Shirkov, D.V.
2000-01-01
We review the evolution of the concept of Renormalization Group (RG). This notion, as was first introduced in quantum field theory (QFT) in the mid-fifties in N.N.Bogolyubov's formulation, is based upon a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of a boundary condition) specifying some particular solution. To illustrate this approach's effectiveness, we end with its application to the analysis of the laser beam self-focusing in a non-linear medium
Renormalized action improvements
International Nuclear Information System (INIS)
Zachos, C.
1984-01-01
Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references
Algebraic renormalization. Perturbative renormalization, symmetries and anomalies
International Nuclear Information System (INIS)
Piguet, O.
1995-01-01
This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)
A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order
International Nuclear Information System (INIS)
Haagensen, P.E.; Latorre, J.I.
1993-01-01
We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems
International Nuclear Information System (INIS)
Lopatnikova, A.; Berker, A.N.
1997-01-01
Superfluidity and phase separation in 3 He- 4 He mixtures immersed in aerogel are studied by renormalization-group theory. The quenched disorder imposed by aerogel, both at the atomic level and at the geometric level, is included. The calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of the quenched probability distributions of random interactions. Random-bond effects on the onset of superfluidity and random-field effects on superfluid-superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general predictions and experiments. The effects of the atomic and geometric randomness of aerogel are investigated separately and jointly. copyright 1997 The American Physical Society
Renormalization of fermion mixing
International Nuclear Information System (INIS)
Schiopu, R.
2007-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)
2006-12-15
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.)
International Nuclear Information System (INIS)
Actis, S.; Passarino, G.
2006-12-01
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.)
Can renormalization group flow end in a Big Mess?
International Nuclear Information System (INIS)
Morozov, Alexei; Niemi, Antti J.
2003-01-01
The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed
Introduction to the nonequilibrium functional renormalization group
International Nuclear Information System (INIS)
Berges, J.; Mesterházy, D.
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 from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.
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
The Renormalization Group in Nuclear Physics
International Nuclear Information System (INIS)
Furnstahl, R.J.
2012-01-01
Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.
Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.
2017-08-01
We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.
Renormalization and effective lagrangians
International Nuclear Information System (INIS)
Polchinski, J.
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)
Renormalization methods in solid state physics
Energy Technology Data Exchange (ETDEWEB)
Nozieres, P [Institut Max von Laue - Paul Langevin, 38 - Grenoble (France)
1976-01-01
Renormalization methods in various solid state problems (e.g., the Kondo effect) are analyzed from a qualitative vantage point. Our goal is to show how the renormalization procedure works, and to uncover a few simple general ideas (universality, phenomenological descriptions, etc...).
Aspects of renormalization in finite-density field theory
Energy Technology Data Exchange (ETDEWEB)
Fitzpatrick, A. Liam; Torroba, Gonzalo; Wang, Huajia
2015-05-26
We study the renormalization of the Fermi surface coupled to a massless boson near three spatial dimensions. For this, we set up a Wilsonian RG with independent decimation procedures for bosons and fermions, where the four-fermion interaction “Landau parameters” run already at tree level. Our explicit one-loop analysis resolves previously found obstacles in the renormalization of finite-density field theory, including logarithmic divergences in nonlocal interactions and the appearance of multilogarithms. The key aspects of the RG are the above tree-level running, and a UV-IR mixing between virtual bosons and fermions at the quantum level, which is responsible for the renormalization of the Fermi velocity. We apply this approach to the renormalization of 2 k F singularities, and to Fermi surface instabilities in a companion paper, showing how multilogarithms are properly renormalized. We end with some comments on the renormalization of finite-density field theory with the inclusion of Landau damping of the boson.
Introduction to the functional renormalization group
International Nuclear Information System (INIS)
Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian
2010-01-01
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.)
Renormalization group and asymptotic freedom
International Nuclear Information System (INIS)
Morris, J.R.
1978-01-01
Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions
Equation-free dynamic renormalization in a glassy compaction model
International Nuclear Information System (INIS)
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-01-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena
Equation-free dynamic renormalization in a glassy compaction model
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-07-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.
Enter, Aernout C.D. van; Fernández, Roberto
For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the
Constructive renormalization theory
International Nuclear Information System (INIS)
Rivasseau, Vincent
2000-01-01
These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga. I emphasize here the rigorous non-perturbative or constructive aspects of the theory. The usual formalism for the renormalization group in field theory or statistical mechanics is reviewed, together with its limits. The constructive formalism is introduced step by step. Taylor forest formulas allow to perform easily the cluster and Mayer expansions which are needed for a single step of the renormalization group in the case of Bosonic theories. The iteration of this single step leads to further difficulties whose solution is briefly sketched. The second part of the course is devoted to Fermionic models. These models are easier to treat on the constructive level so they are very well suited to beginners in constructive theory. It is shown how the Taylor forest formulas allow to reorganize perturbation theory nicely in order to construct the Gross-Neveu 2 model without any need for cluster or Mayer expansions. Finally applications of this technique to condensed matter and renormalization group around Fermi surface are briefly reviewed. (author)
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
Hadamard and minimal renormalizations
International Nuclear Information System (INIS)
Castagnino, M.A.; Gunzig, E.; Nardone, P.; Paz, J.P.
1986-01-01
A common language is introduced to study two, well-known, different methods for the renormalization of the energy-momentum tensor of a scalar neutral quantum field in curved space-time. Different features of the two renormalizations are established and compared
Higher derivatives and renormalization in quantum cosmology
International Nuclear Information System (INIS)
Mazzitelli, F.D.
1991-10-01
In the framework of the canonical quantization of general relativity, quantum field theory on a fixed background formally arises in an expansion in powers of the Planck length. In order to renormalize the theory, quadratic terms in the curvature must be included in the gravitational action from the beginning. These terms contain higher derivatives which change the Hamiltonian structure of the theory completely, making the relation between the renormalized-theory and the original one not clear. We show that it is possible to avoid this problem. We replace the higher derivative theory by a second order one. The classical solutions of the latter are also solutions of the former. We quantize the theory, renormalize the infinities and show that there is a smooth limit between the classical and the renormalized theories. We work in a Robertson Walker minisuperspace with a quantum scalar field. (author). 32 refs
Renormalization: infinity in today microscopic physics
International Nuclear Information System (INIS)
Zinn-Justin, J.
2000-01-01
The expectations put in quantum electrodynamics were deceived when first calculations showed that divergencies, due to the pinpoint aspect of the electron, continued to exist. Later, as a consequence of new experimental data and theoretical progress, an empirical method called renormalization was proposed to allow the evaluation of expressions involving infinite terms. The development of this method opened the way to the theory of re-normalizing fields and gave so successful results that it was applied to all fundamental interactions except gravity. This theory allowed the standard model in weak, electromagnetic and strong interactions to be confronted successfully with experimental data during more than 25 years. This article presents the progressive evolution of ideas in the concept of renormalization. (A.C.)
Renormalization in charged colloids: non-monotonic behaviour with the surface charge
International Nuclear Information System (INIS)
Haro-Perez, C; Quesada-Perez, M; Callejas-Fernandez, J; Schurtenberger, P; Hidalgo-Alvarez, R
2006-01-01
The static structure factor S(q) is measured for a set of deionized latex dispersions with different numbers of ionizable surface groups per particle and similar diameters. For a given volume fraction, the height of the main peak of S(q), which is a direct measure of the spatial ordering of latex particles, does not increase monotonically with the number of ionizable groups. This behaviour cannot be described using the classical renormalization scheme based on the cell model. We analyse our experimental data using a renormalization model based on the jellium approximation, which predicts the weakening of the spatial order for moderate and large particle charges. (letter to the editor)
International Nuclear Information System (INIS)
Stephens, C. R.
2006-01-01
In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime
Technical fine-tuning problem in renormalized perturbation theory
International Nuclear Information System (INIS)
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
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.
Renormalization group in statistical physics - momentum and real spaces
International Nuclear Information System (INIS)
Yukalov, V.I.
1988-01-01
Two variants of the renormalization group approach in statistical physics are considered, the renormalization group in the momentum and the renormalization group in the real spaces. Common properties of these methods and their differences are cleared up. A simple model for investigating the crossover between different universality classes is suggested. 27 refs
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).
Renormalization of the δ expansion in curved space-time
International Nuclear Information System (INIS)
Cho, H.T.
1991-01-01
Renormalization of a recently proposed δ expansion for a self-interacting scalar field theory in curved space-time is examined. The explicit calculation is carried out up to order δ 2 , which indicates that the expansion is renormalizable, but reduces to essentially the λφ 4 theory when the cutoff is removed. A similar conclusion has been reached in a previous paper where the case of flat space-time is considered
Renormalization in general theories with inter-generation mixing
International Nuclear Information System (INIS)
Kniehl, Bernd A.; Sirlin, Alberto
2011-11-01
We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties. (orig.)
Finite cluster renormalization and new two step renormalization group for Ising model
International Nuclear Information System (INIS)
Benyoussef, A.; El Kenz, A.
1989-09-01
New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs
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 and critical phenomena
International Nuclear Information System (INIS)
Ji Qing
2004-01-01
The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced. It is pointed out that this method really reflects the most important physical features of critical phenomena, i.e. self-similarity, and set up a practical solving method from it. This way of setting up a theory according to the features of the physical system is really a good lesson for today's physicists. (author)
A note on similarity in single-phase and porous-medium natural convection
International Nuclear Information System (INIS)
Lyall, H.G.
1981-03-01
The similarity laws for single-phase and porous-medium natural convection are developed. For single-phase flow Nu = Nu(Ra) implies that inertial effects are negligible, while Nu = Nu(Ra.Pr) implies that viscous effects are. The first correlation is adequate for Pr>10, while the second applies for Pr<0.01. For intermediate values of Pr, a more general correlation, Nu = Nu(Ra,Pr) is necessary. For a porous-medium, if inertial effects and dispersion are negligible, Nu* = Nu*(Ra*). However dispersion will only be negligible if the ratio of grain size d to the width of the region L is very small (d/L<< l). If this condition does not hold it is necessary to model d/L. If inertial effects are significant, i.e. the Reynolds number is too large for Darcy's law to apply, a group containing the effective Prandtl number, Pr*, also needs to be modelled for similarity. (author)
Renormalized modes in cuprate superconductors
Gupta, Anushri; Kumari, Anita; Verma, Sanjeev K.; Indu, B. D.
2018-04-01
The renormalized mode frequencies are obtained with the help of quantum dynamical approach of many body phonon Green's function technique via a general Hamiltonian (excluding BCS Hamiltonian) including the effects of phonons and electrons, anharmonicities and electron-phonon interactions. The numerical estimates have been carried out to study the renormalized mode frequency of high temperature cuprate superconductor (HTS) YBa2Cu3O7-δ using modified Born-Mayer-Huggins interaction potential (MBMHP) best applicable to study the dynamical properties of all HTS.
Two-loop renormalization in the standard model, part I. Prolegomena
Energy Technology Data Exchange (ETDEWEB)
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)
2006-12-15
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.)
Renormalization group approach in the turbulence theory
International Nuclear Information System (INIS)
Adzhemyan, L.Ts.; Vasil'ev, A.N.; Pis'mak, Yu.M.
1983-01-01
In the framework of the renormalization groUp approach in the turbulence theory sUggested in another paper, the problem of renormalization and evaluation of critical dimensions of composite operators is discussed. Renormalization of a system of operators of canonical dimension equal to 4, including the operator F=phiΔphi (where phi is the velocity field), is considered. It is shown that the critical dimension Δsub(F)=0. The appendice includes the brief proofs of two theorems: 1) the theorem on the equivalence between the arbitrary stochastic problem and quantum field theory; 2) the theorem which determines the reduction of Green functions of the stochastic problem to the hypersurface of coinciding times
On renormalization of axial anomaly
International Nuclear Information System (INIS)
Efremov, A.V.; Teryaev, O.V.
1989-01-01
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
The renormalization scale-setting problem in QCD
Energy Technology Data Exchange (ETDEWEB)
Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)
2013-09-01
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 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 the 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 scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending
NLO renormalization in the Hamiltonian truncation
Elias-Miró, Joan; Rychkov, Slava; Vitale, Lorenzo G.
2017-09-01
Hamiltonian truncation (also known as "truncated spectrum approach") is a numerical technique for solving strongly coupled quantum field theories, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is limited only by the available computational resources. The renormalization program improves the accuracy by carefully integrating out the high-energy states, instead of truncating them away. In this paper, we develop the most accurate ever variant of Hamiltonian Truncation, which implements renormalization at the cubic order in the interaction strength. The novel idea is to interpret the renormalization procedure as a result of integrating out exactly a certain class of high-energy "tail states." We demonstrate the power of the method with high-accuracy computations in the strongly coupled two-dimensional quartic scalar theory and benchmark it against other existing approaches. Our work will also be useful for the future goal of extending Hamiltonian truncation to higher spacetime dimensions.
Renormalization group and fixed points in quantum field theory
International Nuclear Information System (INIS)
Hollowood, Timothy J.
2013-01-01
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.
Field renormalization in photonic crystal waveguides
DEFF Research Database (Denmark)
Colman, Pierre
2015-01-01
A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... orders of magnitude larger than in bulk material. We show that it takes into account in a simple and efficient way the specificity of the nonlinearity in nanostructures that is determined by geometrical parameters like the effective mode area and the group index. The renormalization of the nonlinear...
Optimization of renormalization group transformations in lattice gauge theory
International Nuclear Information System (INIS)
Lang, C.B.; Salmhofer, M.
1988-01-01
We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)
Renormalization in p-adic quantum field theory
International Nuclear Information System (INIS)
Smirnov, V.A.
1990-01-01
A version of p-adic perturbative Euclidean quantum field theory is presented. It is based on the new type of propagator which happens to be rather natural for p-adic space-time. Low-order Feynamn diagrams are explicity calculated and typical renormalization schemes are introduced: analytic, dimensional and BPHZ renormalizations. The calculations show that in p-adic Feynman integrals only logarithmic divergences appear. 14 refs.; 1 fig
Renormalization in the complete Mellin representation of Feynman amplitudes
International Nuclear Information System (INIS)
Calan, C. de; David, F.; Rivasseau, V.
1981-01-01
The Feynmann amplitudes are renormalized in the formalism of the CM representation. This Mellin-Barnes type integral representation, previously introduced for the study of asymptotic behaviours, is shown to have the following interesting property: in contrast with the usual subtraction procedures, the renormalization leaves the CM intergrand unchanged, and only results into translations of the integration path. The explicit CM representation of the renormalized amplitudes is given. In addition, the dimensional regularization and the extension to spinor amplitudes are sketched. (orig.)
Unique determination of the effective potential in terms of renormalization group functions
International Nuclear Information System (INIS)
Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.
2008-01-01
The perturbative effective potential V in the massless λφ 4 model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d 4 V/dφ 4 )| φ=μ =λ is used, where μ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.
Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension
International Nuclear Information System (INIS)
Levermore, C.D.; Nadler, W.; Stein, D.L.
1995-01-01
We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice
Pairing renormalization and regularization within the local density approximation
International Nuclear Information System (INIS)
Borycki, P.J.; Dobaczewski, J.; Nazarewicz, W.; Stoitsov, M.V.
2006-01-01
We discuss methods used in mean-field theories to treat pairing correlations within the local density approximation. Pairing renormalization and regularization procedures are compared in spherical and deformed nuclei. Both prescriptions give fairly similar results, although the theoretical motivation, simplicity, and stability of the regularization procedure make it a method of choice for future applications
In-medium no-core shell model for ab initio nuclear structure calculations
International Nuclear Information System (INIS)
Gebrerufael, Eskendr
2017-01-01
In this work, we merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multi-reference in-medium similarity renormalization group (IM-SRG), to define a novel many-body approach for the comprehensive description of ground and excited states of closed- and open-shell medium-mass nuclei. Building on the key advantages of the two methods - the decoupling of excitations at the many-body level in the IM-SRG, and the exact diagonalization in the NCSM applicable up to medium-light nuclei - their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. The efficiency and rapid model-space convergence of the new approach make it ideally suited for ab initio studies of ground and low-lying excited states of nuclei up to the medium-mass regime. Interactions constructed within the framework of chiral effective field theory provide an excellent opportunity to describe properties of nuclei from first principles, i.e., rooted in quantum chromodynamics, they overcome the lack of predictive power of phenomenological potentials. The hard core of these interactions causes strong short-range correlations, which we soften by using the similarity-renormalization-group transformation that accelerates the model-space convergence of many-body calculations. Three-nucleon effects, which are mandatory for the correct description of bulk properties of nuclei, are included in our calculations by using the normal-ordered two-body approximation, which has been shown to be sufficient to capture the main effects of the three-nucleon interaction. Using these interactions, we analyze energies of ground and excited states in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. Furthermore, we study the Hoyle state in 12 C - a three-alpha cluster state that cannot be converged in standard NCSM
The renormalization of the electroweak standard model
International Nuclear Information System (INIS)
Boehm, M.; Spiesberger, H.; Hollik, W.
1984-03-01
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.)
Renormalization of the inflationary perturbations revisited
Markkanen, Tommi
2018-05-01
In this work we clarify aspects of renormalization on curved backgrounds focussing on the potential ramifications on the amplitude of inflationary perturbations. We provide an alternate view of the often used adiabatic prescription by deriving a correspondence between the adiabatic subtraction terms and traditional renormalization. Specifically, we show how adiabatic subtraction can be expressed as a set of counter terms that are introduced by redefining the bare parameters of the action. Our representation of adiabatic subtraction then allows us to easily find other renormalization prescriptions differing only in the finite parts of the counter terms. As our main result, we present for quadratic inflation how one may consistently express the renormalization of the spectrum of perturbations from inflation as a redefinition of the bare cosmological constant and Planck mass such that the observable predictions coincide with the unrenormalized result.
Renormalization group coupling flow of SU(3) gauge theory
QCDTARO Collaboration
1998-01-01
We present our new results on the renormalization group coupling flow obtained i n 3 dimensional coupling space $(\\beta_{11},\\beta_{12},\\beta_{twist})$. The value of $\\beta_{twist}$ turns out to be small and the coupling flow projected on $(\\beta_{11},\\beta_{12})$ plane is very similar with the previous result obtained in the 2 dimensional coupling space.
Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
Guagnelli, M; Peña, C; Sint, S; Vladikas, A
2006-01-01
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
Critical phenomena and renormalization group transformations
International Nuclear Information System (INIS)
Castellani, C.; Castro, C. di
1980-01-01
Our main goal is to guide the reader to find out the common rational behind the various renormalization procedures which have been proposed in the last ten years. In the first part of these lectures old arguments on universality and scaling will be briefly recalled. To our opinion these introductory remarks allow one to stress the physical origin of the two majore renormalization procedures, which have been used in the theory of critical phenomena: the Wilson and the field theoretic approach. All the general properties of a ''good'' renormalization transformation will also come out quite naturally. (author)
Perturbative and constructive renormalization
International Nuclear Information System (INIS)
Veiga, P.A. Faria da
2000-01-01
These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)
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.
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Hypercuboidal renormalization in spin foam quantum gravity
Bahr, Benjamin; Steinhaus, Sebastian
2017-06-01
In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.
Transformation of renormalization groups in 2N-component fermion hierarchical model
International Nuclear Information System (INIS)
Stepanov, R.G.
2006-01-01
The 2N-component fermion model on the hierarchical lattice is studied. The explicit formulae for renormalization groups transformation in the space of coefficients setting the Grassmannian-significant density of the free measure are presented. The inverse transformation of the renormalization group is calculated. The definition of immovable points of renormalization groups is reduced to solving the set of algebraic equations. The interesting connection between renormalization group transformations in boson and fermion hierarchical models is found out. It is shown that one transformation is obtained from other one by the substitution of N on -N [ru
Setting the renormalization scale in QCD: The principle of maximum conformality
DEFF Research Database (Denmark)
Brodsky, S. J.; Di Giustino, L.
2012-01-01
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when the renormali......A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale mu of the running coupling alpha(s)(mu(2)). The purpose of the running coupling in any gauge theory is to sum all terms involving the beta function; in fact, when...... the renormalization scale is set properly, all nonconformal beta not equal 0 terms in a perturbative expansion arising from renormalization are summed into the running coupling. The remaining terms in the perturbative series are then identical to that of a conformal theory; i.e., the corresponding theory with beta...... = 0. The resulting scale-fixed predictions using the principle of maximum conformality (PMC) are independent of the choice of renormalization scheme-a key requirement of renormalization group invariance. The results avoid renormalon resummation and agree with QED scale setting in the Abelian limit...
Cohomology and renormalization of BFYM theory in three dimensions
International Nuclear Information System (INIS)
Accardi, A.; Belli, A.; Zeni, M.
1997-01-01
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.)
A key heterogeneous structure of fractal networks based on inverse renormalization scheme
Bai, Yanan; Huang, Ning; Sun, Lina
2018-06-01
Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.
The Background-Field Method and Noninvariant Renormalization
International Nuclear Information System (INIS)
Avdeev, L.V.; Kazakov, D.I.; Kalmykov, M.Yu.
1994-01-01
We investigate the consistency of the background-field formalism when applying various regularizations and renormalization schemes. By an example of a two-dimensional σ model it is demonstrated that the background-field method gives incorrect results when the regularization (and/or renormalization) is noninvariant. In particular, it is found that the cut-off regularization and the differential renormalization belong to this class and are incompatible with the background-field method in theories with nonlinear symmetries. 17 refs
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.
Renormalization in self-consistent approximation schemes at finite temperature I: theory
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-07-01
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)
Renormalization of supersymmetric theories
International Nuclear Information System (INIS)
Pierce, D.M.
1998-06-01
The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses
Golden mean Siegel disk universality and renormalization
Gaidashev, Denis; Yampolsky, Michael
2016-01-01
We provide a computer-assisted proof of one of the central open questions in one-dimensional renormalization theory -- universality of the golden-mean Siegel disks. We further show that for every function in the stable manifold of the golden-mean renormalization fixed point the boundary of the Siegel disk is a quasicircle which coincides with the closure of the critical orbit, and that the dynamics on the boundary of the Siegel disk is rigid. Furthermore, we extend the renormalization from on...
Off-shell renormalization in Higgs effective field theories
Binosi, Daniele; Quadri, Andrea
2018-04-01
The off-shell one-loop renormalization of a Higgs effective field theory possessing a scalar potential ˜ {({Φ}^{\\dagger}Φ -υ^2/2)}^N with N arbitrary is presented. This is achieved by renormalizing the theory once reformulated in terms of two auxiliary fields X 1,2, which, due to the invariance under an extended Becchi-Rouet-Stora-Tyutin symmetry, are tightly constrained by functional identities. The latter allow in turn the explicit derivation of the mapping onto the original theory, through which the (divergent) multi-Higgs amplitude are generated in a purely algebraic fashion. We show that, contrary to naive expectations based on the loss of power counting renormalizability, the Higgs field undergoes a linear Standard Model like redefinition, and evaluate the renormalization of the complete set of Higgs self-coupling in the N → ∞ case.
The renormalization group and lattice QCD
International Nuclear Information System (INIS)
Gupta, R.
1989-01-01
This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory
Some applications of renormalized RPA in bosonic field theories
International Nuclear Information System (INIS)
Hansen, H.; Chanfray, G.
2003-01-01
We present some applications of the renormalized RPA in bosonic field theories. We first present some developments for the explicit calculation of the total energy in Φ 4 theory and discuss its phase structure in 1 + 1 dimensions. We also demonstrate that the Goldstone theorem is satisfied in the O(N) model within the renormalized RPA. (authors)
Renormalization of the new trajectory in the unitarized conventional dual model
International Nuclear Information System (INIS)
Quiros, M.
1978-08-01
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 g 2 , 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 method and singularities in the theory of Langmuir turbulence
International Nuclear Information System (INIS)
Pelletier, G.
1977-01-01
The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. This improved renormalization is emphasized. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion. (author)
Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics
International Nuclear Information System (INIS)
Heckathorn, D.
1979-01-01
Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)
Renormalization and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Krommes, J.A.
1980-02-01
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.
Renormalization and plasma physics
International Nuclear Information System (INIS)
Krommes, J.A.
1980-02-01
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
Sigma models and renormalization of string loops
International Nuclear Information System (INIS)
Tseytlin, A.A.
1989-05-01
An extension of the ''σ-model β-functions - string equations of motion'' correspondence to the string loop level is discussed. Special emphasis is made on how the renormalization group acts in string loops and, in particular, on the renormalizability property of the generating functional Z-circumflex for string amplitudes (related to the σ model partition function integrated over moduli). Renormalization of Z-circumflex at one and two loop order is analyzed in some detail. We also discuss an approach to renormalization based on operators of insertion of topological fixtures. (author). 70 refs
Differential renormalization of gauge theories
International Nuclear Information System (INIS)
Aguila, F. del; Perez-Victoria, M.
1998-01-01
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)
Effective AdS/renormalized CFT
Fan, JiJi
2011-01-01
For an effective AdS theory, we present a simple prescription to compute the renormalization of its dual boundary field theory. In particular, we define anomalous dimension holographically as the dependence of the wave-function renormalization factor on the radial cutoff in the Poincare patch of AdS. With this definition, the anomalous dimensions of both single- and double- trace operators are calculated. Three different dualities are considered with the field theory being CFT, CFT with a dou...
The two-loop renormalization of general quantum field theories
International Nuclear Information System (INIS)
Damme, R.M.J. van.
1984-01-01
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.)
The fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models
International Nuclear Information System (INIS)
Foda, O.E.
1983-01-01
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.)
Trace and axial anomalies in dimensional renormalization through Zimmermann-like identities
International Nuclear Information System (INIS)
Bonneau, G.
1980-01-01
The problem of anomalies is solved in dimensional renormalization in two steps. Firstly one shows that trace and γ 5 anomalies can be expressed as the anomalous normal product N[gsub(μ rho)Osub(μ rho lambda)...(x)] where gsub(μ rho) is the metric tensor in D-4 dimensions (D being the space-time dimension) and Osub(μ rho lambda)...(x) a monomial in the fields and their derivatives. Then, with techniques similar to those used in a previous work to study N[(4-D)Osub(μ rho lambda)(x)], we prove a Zimmermann-like identity that gives the decomposition of such anomalous normal product on 'usual' normal products, the coefficients being explicitly given as residues of the simple pole in v = 4-D of definite proper Green functions where the overall subtraction has not been done. We apply the above formalism to obtain the renormalization group as a consequence of trace anomalies in the dilatation current and to derive the Adler-Bardeen theorem for massive QED. (orig.)
Space-time versus world-sheet renormalization group equation in string theory
International Nuclear Information System (INIS)
Brustein, R.; Roland, K.
1991-05-01
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.)
Renormalization-group theory for the eddy viscosity in subgrid modeling
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
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
Nonperturbative Renormalization of Composite Operators with Overlap Fermions
Energy Technology Data Exchange (ETDEWEB)
J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams
2005-12-01
We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.
A complete non-perturbative renormalization prescription for quasi-PDFs
Energy Technology Data Exchange (ETDEWEB)
Alexandrou, Constantia [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; The Cyprus Institute, Nicosia (Cyprus); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Constantinou, Martha [Temple Univ., Philadelphia, PA (United States). Dept. of Physics; Hadjiyiannakou, Kyriakos [The Cyprus Institute, Nicosia (Cyprus); Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Panagopoulos, Haralambos [Cyprus Univ., Nicosia (Cyprus). Dept. of Physics; Collaboration: European Twisted Mass Collaboration
2017-06-15
In this work we present, for the first time, the non-perturbative renormalization for the unpolarized, helicity and transversity quasi-PDFs, in an RI{sup '} scheme. The proposed prescription addresses simultaneously all aspects of renormalization: logarithmic divergences, finite renormalization as well as the linear divergence which is present in the matrix elements of fermion operators with Wilson lines. Furthermore, for the case of the unpolarized quasi-PDF, we describe how to eliminate the unwanted mixing with the twist-3 scalar operator. We utilize perturbation theory for the one-loop conversion factor that brings the renormalization functions to the MS-scheme at a scale of 2 GeV. We also explain how to improve the estimates on the renormalization functions by eliminating lattice artifacts. The latter can be computed in one-loop perturbation theory and to all orders in the lattice spacing. We apply the methodology for the renormalization to an ensemble of twisted mass fermions with N{sub f}=2+1+1 dynamical quarks, and a pion mass of around 375 MeV.
Minamisono, K; Sumikama, T; Nagatomo, T; Matsuta, K; Minamisono, T; Fukuda, M; Koshigiri, K; Morita, M
2000-01-01
The beta-ray angular distributions from purely spin aligned sup 1 sup 2 B and sup 1 sup 2 N were precisely measured to determine a new limit of the G-parity irregular induced tensor form factor in weak nucleon axial vector currents and to study the in-medium mass renormalization of nucleons through the axial charge. Since the major systematic error in the previous result which originated from the intensity fluctuation of the incident beam used for the production of the nuclei was removed in the present measurement, the more reliable result was obtained: 0.01 <= 2M f sub T /f sub A <= 0.34 (90 % CL). The result is consistent with the theoretical prediction in the framework of which induced tensor form factor is proportional to the mass difference between the up and down quarks. We also determined the axial charge of the weak nucleon current to be y = 4.66 +- 0.12, which may disclose an in-medium mass reduction of the decaying nucleon of 11 +- 4 %.
Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review
Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-12-01
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on
On the renormalization group equations of quantum electrodynamics
International Nuclear Information System (INIS)
Hirayama, Minoru
1980-01-01
The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)
The ab-initio density matrix renormalization group in practice
Energy Technology Data Exchange (ETDEWEB)
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
The ab-initio density matrix renormalization group in practice.
Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Renormalization group analysis of a simple hierarchical fermion model
International Nuclear Information System (INIS)
Dorlas, T.C.
1991-01-01
A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of a global critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using information about the asymptotic renormalization behaviour. It turns out that the 'trivial' fixed point gives rise to a two-parameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the appliclation of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved. (orig.)
Renormalization group theory of critical phenomena
International Nuclear Information System (INIS)
Menon, S.V.G.
1995-01-01
Renormalization group theory is a framework for describing those phenomena that involve a multitude of scales of variations of microscopic quantities. Systems in the vicinity of continuous phase transitions have spatial correlations at all length scales. The renormalization group theory and the pertinent background material are introduced and applied to some important problems in this monograph. The monograph begins with a historical survey of thermal phase transitions. The background material leading to the renormalization group theory is covered in the first three chapters. Then, the basic techniques of the theory are introduced and applied to magnetic critical phenomena in the next four chapters. The momentum space approach as well as the real space techniques are, thus, discussed in detail. Finally, brief outlines of applications of the theory to some of the related areas are presented in the last chapter. (author)
Correlated random-phase approximation from densities and in-medium matrix elements
Energy Technology Data Exchange (ETDEWEB)
Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)
2016-07-01
The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.
Class renormalization: islands around islands
International Nuclear Information System (INIS)
Meiss, J.D.
1986-01-01
An orbit of 'class' is one that rotates about a periodic orbit of one lower class with definite frequency. This contrasts to the 'level' of a periodic orbit which is the number of elements in its continued fraction expansion. Level renormalization is conventionally used to study the structure of quasi-periodic orbits. The scaling structure of periodic orbits encircling other periodic orbits in area preserving maps is discussed here. Fixed points corresponding to the accumulation of p/q bifurcations are found and scaling exponents determined. Fixed points for q > 2 correspond to self-similar islands around islands. Frequencies of the island boundary circles at the fixed points are obtained. Importance of this scaling for the motion of particles in stochastic regions is emphasized. (author)
Strong renormalization scheme dependence in τ-lepton decay: Fact or fiction?
International Nuclear Information System (INIS)
Chyla, J.
1995-01-01
The question of the renormalization scheme dependence of the τ semileptonic decay rate is examined in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this dependence and the actual selection of a subset of ''acceptable'' renormalization schemes. It is pointed out that this criticism is valid only within a particular definition of the ''strength'' of the renormalization scheme dependence and should not discourage further attempts to use the semileptonic τ decay rate for quantitative tests of perturbative QCD
Non-perturbative renormalization of three-quark operators
Energy Technology Data Exchange (ETDEWEB)
Goeckeler, Meinulf [Regensburg Univ. (Germany). Inst. fuer Theoretische Physik; Horsley, Roger [Edinburgh Univ. (United Kingdom). School of Physics and Astronomy; Kaltenbrunner, Thomas [Regensburg Univ. (DE). Inst. fuer Theoretische Physik] (and others)
2008-10-15
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 wavefunction 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 scheme at {mu}=2 GeV. (orig.)
Recent developments in chiral dynamics of hadrons and hadrons in a nuclear medium
International Nuclear Information System (INIS)
Oset, E.; Sarkar, S.; Vicente Vacas, M.J.; Kaskulov, M.; Roca, L.; Magas, V.K.; Ramos, A.; Toki, H.
2007-01-01
In this talk I present recent developments in chiral dynamics of hadrons and hadrons in a medium addressing the following points: interaction of the octet of pseudoscalar mesons with the octet of baryons of the nucleon, showing recent experimental evidence on the existence of two Λ(1405) states, the interaction of the octet of pseudoscalar mesons with the decuplet of baryons of the Δ, with particular emphasis on the Λ(1520) resonance, dynamically generated by this interaction. Then I review the interaction of kaons in a nuclear medium and briefly discuss the situation around the claims of deeply bound states in nuclei. The large renormalization of the Λ(1520) in the nuclear medium is shown as another example of successful application of the chiral unitary techniques
Effects of renormalizing the chiral SU(2) quark-meson model
Zacchi, Andreas; Schaffner-Bielich, Jürgen
2018-04-01
We investigate the restoration of chiral symmetry at finite temperature in the SU(2) quark-meson model, where the mean field approximation is compared to the renormalized version for quarks and mesons. In a combined approach at finite temperature, all the renormalized versions show a crossover transition. The inclusion of different renormalization scales leave the order parameter and the mass spectra nearly untouched but strongly influence the thermodynamics at low temperatures and around the phase transition. We find unphysical results for the renormalized version of mesons and the combined one.
International Nuclear Information System (INIS)
Mestel, B D; Osbaldestin, A H
2004-01-01
Generalizing from the case of golden mean frequency to a wider class of quadratic irrationals, we extend our renormalization analysis of the self-similarity of correlation functions in a quasiperiodically forced two-level system. We give a description of all piecewise-constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case. We establish a criterion for periodic orbits to be globally bounded, and also calculate the asymptotic height of the main peaks in the correlation function
Two pion mediated scalar isoscalar NN interaction in the nuclear medium
International Nuclear Information System (INIS)
Kaskulov, Murat M.; Oset, E.; Vacas, M.J. Vicente
2006-01-01
We study the modification of the nucleon-nucleon interaction in a nuclear medium in the scalar isoscalar channel, mediated by the exchange of two correlated (σ channel) or uncorrelated pions. For this purpose we use a standard approach for the renormalization of pions in nuclei. The corrections obtained for the NN interaction in the medium in this channel are of the order of 20% of the free one in average, and the consideration of short-range correlations plays an important role in providing these moderate changes. Yet, the corrections are sizable enough to suggest further studies of the stability and properties of nuclear matter
Zeta Functions, Renormalization Group Equations, and the Effective Action
International Nuclear Information System (INIS)
Hochberg, D.; Perez-Mercader, J.; Molina-Paris, C.; Visser, M.
1998-01-01
We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley-DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action and use this to derive the leading logarithms in the one-loop effective action for arbitrary quantum field theories. copyright 1998 The American Physical Society
Renormalization in the stochastic quantization of field theories
International Nuclear Information System (INIS)
Brunelli, J.C.
1991-01-01
In the stochastic quantization scheme of Parisi and Wu the renormalization of the stochastic theory of some models in field theory is studied. Following the path integral approach for stochastic process the 1/N expansion of the non linear sigma model is performed and, using a Ward identity obtained, from a BRS symmetry of the effective action of this formulation. It is shown the renormalizability of the model. Using the Langevin approach for stochastic process the renormalizability of the massive Thirring model is studied showing perturbatively the vanishing of the renormalization group's beta functions at finite fictitious time. (author)
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 an abelian gauge theory in stochastic quantization
International Nuclear Information System (INIS)
Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.
1987-01-01
The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)
Mass renormalization in sine-Gordon model
International Nuclear Information System (INIS)
Xu Bowei; Zhang Yumei
1991-09-01
With a general gaussian wave functional, we investigate the mass renormalization in the sine-Gordon model. At the phase transition point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. (author). 8 refs, 1 fig
Excited state TBA and renormalized TCSA in the scaling Potts model
Lencsés, M.; Takács, G.
2014-09-01
We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin chain.
DeWitt-Schwinger renormalization and vacuum polarization in d dimensions
International Nuclear Information System (INIS)
Thompson, R. T.; Lemos, Jose P. S.
2009-01-01
Calculation of the vacuum polarization, 2 (x)>, and expectation value of the stress tensor, μν (x)>, has seen a recent resurgence, notably for black hole spacetimes. To date, most calculations of this type have been done only in four dimensions. Extending these calculations to d dimensions includes d-dimensional renormalization. Typically, the renormalizing terms are found from Christensen's covariant point splitting method for the DeWitt-Schwinger expansion. However, some manipulation is required to put the correct terms into a form that is compatible with problems of the vacuum polarization type. Here, after a review of the current state of affairs for 2 (x)> and μν (x)> calculations and a thorough introduction to the method of calculating 2 (x)>, a compact expression for the DeWitt-Schwinger renormalization terms suitable for use in even-dimensional spacetimes is derived. This formula should be useful for calculations of 2 (x)> and μν (x)> in even dimensions, and the renormalization terms are shown explicitly for four and six dimensions. Furthermore, use of the finite terms of the DeWitt-Schwinger expansion as an approximation to 2 (x)> for certain spacetimes is discussed, with application to four and five dimensions.
Renormalization constants for 2-twist operators in twisted mass QCD
International Nuclear Information System (INIS)
Alexandrou, C.; Constantinou, M.; Panagopoulos, H.; Stylianou, F.; Korzec, T.
2011-01-01
Perturbative and nonperturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the nonperturbative evaluation of the one-derivative twist-2 vector and axial-vector operators. Nonperturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing a corresponding to β=3.9, 4.05, 4.20. Subtraction of O(a 2 ) terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to O(a 2 ). The renormalization conditions are defined in the RI ' -MOM scheme, for both perturbative and nonperturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to MS at 2 GeV using 3-loop perturbative results for the conversion factors.
Energy Technology Data Exchange (ETDEWEB)
Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2017-01-30
We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.
Phases of renormalized lattice gauge theories with fermions
International Nuclear Information System (INIS)
Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)
1979-01-01
Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory
Tadpole renormalization and relativistic corrections in lattice NRQCD
Shakespeare, Norman H.; Trottier, Howard D.
1998-08-01
We make a detailed comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. We renormalize improved gauge-field and NRQCD actions using the mean-link u0,L in the Landau gauge, and using the fourth root of the average plaquette u0,P. Simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed both at leading [O(MQv4)] and at next-to-leading [O(MQv6)] order in the relativistic expansion, where MQ is the renormalized quark mass, and v2 is the mean-squared velocity. Results are obtained at a large number of lattice spacings, in the range of about 0.14-0.38 fm. A number of features emerge, all of which favor tadpole renormalization using u0,L. This includes a much better scaling behavior of the hyperfine splittings in the three quarkonium systems when u0,L is used. We also find that relativistic corrections to the spin splittings are smaller when u0,L is used, particularly for the cc¯ and bc¯ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below about 1 in lattice units. Simulations with u0,L also appear to be better behaved in this context: the bare quark masses turn out to be larger when u0,L is used, compared to when u0,P is used on lattices with comparable spacings. These results also demonstrate the need to go beyond tree-level tadpole improvement for precision simulations.
Renormalization of QED with planar binary trees
International Nuclear Information System (INIS)
Brouder, C.
2001-01-01
The Dyson relations between renormalized and bare photon and electron propagators Z 3 anti D(q)=D(q) and Z 2 anti S(q)=S(q) are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. (orig.)
Quantum field theory and phase transitions: universality and renormalization group
International Nuclear Information System (INIS)
Zinn-Justin, J.
2003-08-01
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.)
Renormalization and effective actions for general relativity
International Nuclear Information System (INIS)
Neugebohrn, F.
2007-05-01
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 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
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.)
Wetting transitions: A functional renormalization-group approach
International Nuclear Information System (INIS)
Fisher, D.S.; Huse, D.A.
1985-01-01
A linear functional renormalization group is introduced as a framework in which to treat various wetting transitions of films on substrates. A unified treatment of the wetting transition in three dimensions with short-range interactions is given. The results of Brezin, Halperin, and Leibler in their three different regimes are reproduced along with new results on the multicritical behavior connecting the various regimes. In addition, the critical behavior as the coexistence curve is approached at complete wetting is analyzed. Wetting in the presence of long-range substrate-film interactions that fall off as power laws is also studied. The possible effects of the nonlinear terms in the renormalization group are examined briefly and it appears that they do not alter the critical behavior found using the truncated linear renormalization group
Renormalization group in quantum mechanics
International Nuclear Information System (INIS)
Polony, J.
1996-01-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc
Renormalization of the γ-ray strength functions of light nuclei
International Nuclear Information System (INIS)
Canbula, B.; Ersan, S.; Babacan, H.
2015-01-01
γ-ray strength function is the key input for the photonuclear reactions, which have a special astrophysical importance, and should be renormalized by using the nuclear level density for calculating the theoretical average radiative capture width, but performing such renormalization is challenging for light nuclei. With this motivation, recently introduced level density parameter formula including collective effects is used to calculate the average radiative capture width of light nuclei, and therefore to renormalize their γ-ray strength functions. Obtained normalization factors are tested in (n, γ) reactions for the necessity of renormalization for light nuclei. (author)
Method of renormalization potential for one model of Hartree-Fock-Slater type
Zasorin, Y V
2002-01-01
A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential
Radiative muon capture and renormalization of the induced pseudoscalar coupling constant in nuclei
International Nuclear Information System (INIS)
Hasinoff, M.D.; Armstrong, D.S.; Azuelos, G.
1992-08-01
Radiative Muon Capture (RMC), μ - Z → ν μ (Z - 1)γ, is a weak semi-leptonic process which is particularly sensitive to the induced pseudoscalar coupling constant, g p , of the weak hadronic current. After a brief introduction and review of the general theoretical background relevant to RMC, the most recent data from TRIUMF and PSI are presented and compared to the latest theoretical calculations. The extracted g p values are compared to the PCAC prediction for RMC on a free proton to determine whether or not there is any significant renormalization of g p inside the nuclear medium. A progress report on the TRIUMF RMC experiment on hydrogen is also presented. refs., 12 figs., 3 tabs
Renormalization in Large Momentum Effective Theory of Parton Physics.
Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Yong
2018-03-16
In the large-momentum effective field theory approach to parton physics, the matrix elements of nonlocal operators of quark and gluon fields, linked by straight Wilson lines in a spatial direction, are calculated in lattice quantum chromodynamics as a function of hadron momentum. Using the heavy-quark effective theory formalism, we show a multiplicative renormalization of these operators at all orders in perturbation theory, both in dimensional and lattice regularizations. The result provides a theoretical basis for extracting parton properties through properly renormalized observables in Monte Carlo simulations.
Renormalization of g-boson effects under weak coupling condition
International Nuclear Information System (INIS)
Zhang Zhanjun; Yang Jie; Liu Yong; Sang Jianping
1998-01-01
An approach based on perturbation theory is proposed to renormalized g-boson effects for sdgIBM system, which modifies that presented earlier by Druce et al. The weak coupling condition as the usage premise of the two approaches is proved to be satisfied. Two renormalization spectra are calculated for comparison and analyses. Results show that the g-boson effects are renormalized more completely by the approach proposed
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.
Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Palombi, F. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Papinutto, M.; Pena, C. [CERN, Geneva (Switzerland). Physics Dept., Theory Div.; Wittig, H. [Mainz Univ. (Germany). Inst. fuer Kernphysik
2007-06-15
We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of {delta}B=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.)
Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach
Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene
2018-03-01
When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.
Renormalization Methods - A Guide For Beginners
International Nuclear Information System (INIS)
Cardy, J
2004-01-01
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 φ 4 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
Renormalization using the background-field method
International Nuclear Information System (INIS)
Ichinose, S.; Omote, M.
1982-01-01
Renormalization using the background-field method is examined in detail. The subtraction mechanism of subdivergences is described with reference to multi-loop diagrams and one- and two-loop counter-term formulae are explicitly given. The original one-loop counter-term formula of 't Hooft is thereby improved. The present method of renormalization is far easier to manage than the usual one owing to the fact only gauge-invariant quantities are to be considered when worked in an appropriate gauge. Gravity and Yang-Mills theories are studied as examples. (orig.)
Renormalization and Interaction in Quantum Field Theory
International Nuclear Information System (INIS)
RATSIMBARISON, H.M.
2008-01-01
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. [fr
g-Boson renormalization effects in the interacting Boson model for nondegenerate orbits
Duval, P. D.; Pittel, S.; Barrett, B. R.; Druce, C. H.
1983-09-01
A nonperturbative model-space truncation procedure is utilized to include the effects of a single g boson on the parameters of the neutron-proton Interacting Boson Model in the realistic case of nondegenerate single-particle orbits. Particular emphasis is given to the single-boson energies ɛdϱ (ϱ = v, π), with numerical results presented for the even isotopes of Hg. Only part of the observed renormalization is obtained. Possible sources of further renormalizations to ɛdϱ are discussed. Results are also presented for the renormalizations of the boson quadrupole parameters κ and χϱ.
Grzywacz, Piotr; Qin, Jian; Morse, David C
2007-12-01
Attempts to use coarse-grained molecular theories to calculate corrections to the random-phase approximation (RPA) for correlations in polymer mixtures have been plagued by an unwanted sensitivity to the value of an arbitrary cutoff length, i.e., by an ultraviolet (UV) divergence. We analyze the UV divergence of the inverse structure factor S(-1)(k) predicted by a "one-loop" approximation similar to that used in several previous studies. We consider both miscible homopolymer blends and disordered diblock copolymer melts. We show, in both cases, that all UV divergent contributions can be absorbed into a renormalization of the values of the phenomenological parameters of a generalized self-consistent field theory (SCFT). This observation allows the construction of an UV convergent theory of corrections to SCFT phenomenology. The UV-divergent one-loop contribution to S(-1)(k) is shown to be the sum of (i) a k -independent contribution that arises from a renormalization of the effective chi parameter, (ii) a k-dependent contribution that arises from a renormalization of monomer statistical segment lengths, (iii) a contribution proportional to k(2) that arises from a square-gradient contribution to the one-loop fluctuation free energy, and (iv) a k-dependent contribution that is inversely proportional to the degree of polymerization, which arises from local perturbations in fluid structure near chain ends and near junctions between blocks in block copolymers.
On renormalization-invariant masses
International Nuclear Information System (INIS)
Fleming, H.; Furuya, K.
1978-02-01
It is shown that spontaneous generation of renormalization invariant mass is possible in infra-red stable theories with more than one coupling constant. If relations among the coupling constants are permitted the effect can be made compatible with pertubation theory
Non-perturbative renormalization of HQET and QCD
International Nuclear Information System (INIS)
Sommer, Rainer
2003-01-01
We discuss the necessity of non-perturbative renormalization in QCD and HQET and explain the general strategy for solving this problem. A few selected topics are discussed in some detail, namely the importance of off shell improvement in the MOM-scheme on the lattice, recent progress in the implementation of finite volume schemes and then particular emphasis is put on the recent idea to carry out a non-perturbative renormalization of the Heavy Quark Effective Theory (HQET)
Products of composite operators in the exact renormalization group formalism
Pagani, C.; Sonoda, H.
2018-02-01
We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.
All-order renormalization of propagator matrix for fermionic system with flavor mixing
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A. [California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
2013-08-15
We consider a mixed system of Dirac fermions in a general parity-nonconserving theory and renormalize the propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic all-order expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions. We identify residual degrees of freedom in the WFR matrices and propose an additional renormalization condition to exhaust them. We then explain how our results may be generalized to the case of unstable fermions, in which we encounter the phenomenon of WFR bifurcation. In the special case of a solitary unstable fermion, the all-order-renormalized propagator is presented in a particularly compact form.
Communication: Random phase approximation renormalized many-body perturbation theory
International Nuclear Information System (INIS)
Bates, Jefferson E.; Furche, Filipp
2013-01-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations
The Implementation of the Renormalized Complex MSSM in FeynArts and FormCalc
Fritzsche, T; Heinemeyer, S; Rzehak, H; Schappacher, C
2014-01-01
We describe the implementation of the renormalized complex MSSM (cMSSM) in the diagram generator FeynArts and the calculational tool FormCalc. This extension allows to perform UV-finite one-loop calculations of cMSSM processes almost fully automatically. The Feynman rules for the cMSSM with counterterms are available as a new model file for FeynArts. Also included are default definitions of the renormalization constants; this fixes the renormalization scheme. Beyond that all model parameters are generic, e.g. we do not impose any relations to restrict the number of input parameters. The model file has been tested extensively for several non-trivial decays and scattering reactions. Our renormalization scheme has been shown to give stable results over large parts of the cMSSM parameter space.
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Renormalization Group scale-setting in astrophysical systems
Domazet, Silvije; Štefančić, Hrvoje
2011-09-01
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.
Renormalization Group scale-setting in astrophysical systems
International Nuclear Information System (INIS)
Domazet, Silvije; Stefancic, Hrvoje
2011-01-01
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.
Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System
Kim, Chungku
2018-06-01
We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.
Vacuum polarization and renormalized charge in ν-dimensions
International Nuclear Information System (INIS)
Marinho Junior, R.M.; Lucinda, J.
1984-01-01
The expression for the vacuum polarization is obtained for any momentum transfer in ν dimensions. Using the Wilson loop for QED, the renormalized electric charge in ν dimensions is calculated. (Author) [pt
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 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...
Renormalized semiclassical quantization for rescalable Hamiltonians
International Nuclear Information System (INIS)
Takahashi, Satoshi; Takatsuka, Kazuo
2004-01-01
A renormalized semiclassical quantization method for rescalable Hamiltonians is proposed. A classical Hamilton system having a potential function that consists of homogeneous polynomials like the Coulombic potential can have a scale invariance in its extended phase space (phase space plus time). Consequently, infinitely many copies of a single trajectory constitute a one-parameter family that is characterized in terms of a scaling factor. This scaling invariance in classical dynamics is lost in quantum mechanics due to the presence of the Planck constant. It is shown that in a system whose classical motions have a self-similarity in the above sense, classical trajectories adopted in the semiclassical scheme interact with infinitely many copies of their own that are reproduced by the relevant scaling procedure, thereby undergoing quantum interference among themselves to produce a quantized spectrum
Gauge-independent renormalization of the N2HDM
Krause, Marcel; López-Val, David; Mühlleitner, Margarete; Santos, Rui
2017-12-01
The Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) is an interesting benchmark model for a Higgs sector consisting of two complex doublet and one real singlet fields. Like the Next-to-Minimal Supersymmetric extension (NMSSM) it features light Higgs bosons that could have escaped discovery due to their singlet admixture. Thereby, the model allows for various different Higgs-to-Higgs decay modes. Contrary to the NMSSM, however, the model is not subject to supersymmetric relations restraining its allowed parameter space and its phenomenology. For the correct determination of the allowed parameter space, the correct interpretation of the LHC Higgs data and the possible distinction of beyond-the-Standard Model Higgs sectors higher order corrections to the Higgs boson observables are crucial. This requires not only their computation but also the development of a suitable renormalization scheme. In this paper we have worked out the renormalization of the complete N2HDM and provide a scheme for the gauge-independent renormalization of the mixing angles. We discuss the renormalization of the Z_2 soft breaking parameter m 12 2 and the singlet vacuum expectation value v S . Both enter the Higgs self-couplings relevant for Higgs-to-Higgs decays. We apply our renormalization scheme to different sample processes such as Higgs decays into Z bosons and decays into a lighter Higgs pair. Our results show that the corrections may be sizable and have to be taken into account for reliable predictions.
Renormalization of Supersymmetric QCD on the Lattice
Costa, Marios; Panagopoulos, Haralambos
2018-03-01
We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.
Renormalization-scheme-invariant QCD and QED: The method of effective charges
International Nuclear Information System (INIS)
Grunberg, G.
1984-01-01
We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter Λ, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales
A simple method for one-loop renormalization in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Markkanen, Tommi [Helsinki Institute of Physics and Department of Physics, P.O. Box 64, FI-00014, University of Helsinki (Finland); Tranberg, Anders, E-mail: tommi.markkanen@helsinki.fi, E-mail: anders.tranberg@uis.no [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)
2013-08-01
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.
Justification of the zeta-function renormalization in rigid string model
International Nuclear Information System (INIS)
Nesterenko, V.V.; Pirozhenko, I.G.
1997-01-01
A consistent procedure for regularization of divergences and for the subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov-Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein-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
Hopf-algebraic renormalization of QED in the linear covariant gauge
Energy Technology Data Exchange (ETDEWEB)
Kißler, Henry, E-mail: kissler@physik.hu-berlin.de
2016-09-15
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.
Renormalization of Fermi Velocity in a Composite Two Dimensional Electron Gas
Weger, M.; Burlachkov, L.
We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a0, where a0 = ħ2ɛ1/me2 is the Bohr radius, separated by layers with a dielectric constant ɛ2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters kFa0 and kFc ɛ2/ɛ1. We find that when ɛ2/ɛ1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near kF, and v(kF) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δk/kF is a few percent) and becomes sharper as ɛ2/ɛ1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T2. Preliminary measurements suggest an increase in vk in YBCO very close to kF.
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 trajectory for non-linear sigma model and improved scaling behaviour
International Nuclear Information System (INIS)
Guha, A.; Okawa, M.; Zuber, J.B.
1984-01-01
We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(infinite) in two dimensions. Four finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models. (orig.)
The Physical Renormalization of Quantum Field Theories
International Nuclear Information System (INIS)
Binger, Michael William.; Stanford U., Phys. Dept.; SLAC
2007-01-01
The profound revolutions in particle physics likely to emerge from current and future experiments motivates an improved understanding of the precise predictions of the Standard Model and new physics models. Higher order predictions in quantum field theories inevitably requires the renormalization procedure, which makes sensible predictions out of the naively divergent results of perturbation theory. Thus, a robust understanding of renormalization is crucial for identifying and interpreting the possible discovery of new physics. The results of this thesis represent a broad set of investigations in to the nature of renormalization. The author begins by motivating a more physical approach to renormalization based on gauge-invariant Green's functions. The resulting effective charges are first applied to gauge coupling unification. This approach provides an elegant formalism for understanding all threshold corrections, and the gauge couplings unify in a more physical manner compared to the usual methods. Next, the gauge-invariant three-gluon vertex is studied in detail, revealing an interesting and rich structure. The effective coupling for the three-gluon vertex, α(k 1 2 , k 2 2 , k 3 2 ), depends on three momentum scales and gives rise to an effective scale Q eff 2 (k 1 2 , k 2 2 , k 3 2 ) which governs the (sometimes surprising) behavior of the vertex. The effects of nonzero internal masses are important and have a complicated threshold and pseudo-threshold structure. The pinch-technique effective charge is also calculated to two-loops and several applications are discussed. The Higgs boson mass in Split Supersymmetry is calculated to two-loops, including all one-loop threshold effects, leading to a downward shift in the Higgs mass of a few GeV. Finally, the author discusses some ideas regarding the overall structure of perturbation theory. This thesis lays the foundation for a comprehensive multi-scale analytic renormalization scheme based on gauge-invariant Green
Renormalization of non-abelian gauge theories in curved space-time
International Nuclear Information System (INIS)
Freeman, M.D.
1984-01-01
We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe
Quantum renormalization group approach to geometric phases in spin chains
International Nuclear Information System (INIS)
Jafari, R.
2013-01-01
A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size
Anisotropic square lattice Potts ferromagnet: renormalization group treatment
International Nuclear Information System (INIS)
Oliveira, P.M.C. de; Tsallis, C.
1981-01-01
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 - [pt
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-07-01
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
A renormalization group theory of cultural evolution
Fáth, Gábor; Sarvary, Miklos
2005-03-01
We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision-making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter. As the importance of social interactions increases or agents become more intelligent, we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society. A similar phase transition may explain the so-called “cultural explosion’’ in human evolution some 50,000 years ago.
Renormalization of the QEMD of a dyon field
International Nuclear Information System (INIS)
Panagiotakopoulos, C.
1983-01-01
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. (orig.)
Renormalization of the QEMD of a dyon field
International Nuclear Information System (INIS)
Panagiotakopoulos, C.
1982-05-01
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)
Non-perturbative versus perturbative renormalization of lattice operators
International Nuclear Information System (INIS)
Goeckeler, M.; Technische Hochschule Aachen; Horsley, R.; Ilgenfritz, E.M.; Oelrich, H.; Forschungszentrum Juelich GmbH; Schierholz, G.; Forschungszentrum Juelich GmbH; Perlt, H.; Schiller, A.; Rakow, P.
1995-09-01
Our objective is to compute the moments of the deep-inelastic structure functions of the nucleon on the lattice. A major source of uncertainty is the renormalization of the lattice operators that enter the calculation. In this talk we compare the renormalization constants of the most relevant twist-two bilinear quark operators which we have computed non-perturbatively and perturbatively to one loop order. Furthermore, we discuss the use of tadpole improved perturbation theory. (orig.)
Extended BPH renormalization of cutoff scalar field theories
International Nuclear Information System (INIS)
Chalmers, G.
1996-01-01
We show through the use of diagrammatic techniques and a newly adapted BPH renormalization method that general momentum cutoff scalar field theories in four dimensions are perturbatively renormalizable. Weinberg close-quote s convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. The naive use of the convergence theorem together with the BPH method is not appropriate for understanding the local divergences and renormalizability of these theories. We also show that the renormalized Green close-quote s functions are the same as in ordinary Φ 4 theory up to corrections suppressed by inverse powers of the cutoff. These conclusions are consistent with those of existing proofs based on the renormalization group. copyright 1996 The American Physical Society
Non-perturbative renormalization on the lattice
International Nuclear Information System (INIS)
Koerner, Daniel
2014-01-01
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.
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
Energy Technology Data Exchange (ETDEWEB)
Groh, Kai
2012-10-15
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
International Nuclear Information System (INIS)
Groh, Kai
2012-10-01
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of
Renormalization Scale-Fixing for Complex Scattering Amplitudes
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; Llanes-Estrada, Felipe J.; /Madrid U.
2005-12-21
We show how to fix the renormalization scale for hard-scattering exclusive processes such as deeply virtual meson electroproduction by applying the BLM prescription to the imaginary part of the scattering amplitude and employing a fixed-t dispersion relation to obtain the scale-fixed real part. In this way we resolve the ambiguity in BLM renormalization scale-setting for complex scattering amplitudes. We illustrate this by computing the H generalized parton distribution at leading twist in an analytic quark-diquark model for the parton-proton scattering amplitude which can incorporate Regge exchange contributions characteristic of the deep inelastic structure functions.
Renormalization of gauge theories without cohomology
International Nuclear Information System (INIS)
Anselmi, Damiano
2013-01-01
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. (orig.)
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
International Nuclear Information System (INIS)
Tzenov, Stephan I.
2002-01-01
Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail
Renormalization and asymptotic freedom in quantum gravity
International Nuclear Information System (INIS)
Tomboulis, E.T.
1984-01-01
The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)
Renormalization of a distorted gauge: invariant theory
International Nuclear Information System (INIS)
Hsu, J.P.; Underwood, J.A.
1976-02-01
A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities
A renormalization group scaling analysis for compressible two-phase flow
International Nuclear Information System (INIS)
Chen, Y.; Deng, Y.; Glimm, J.; Li, G.; Zhang, Q.; Sharp, D.H.
1993-01-01
Computational solutions to the Rayleigh--Taylor fluid mixing problem, as modeled by the two-fluid two-dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone suggests fixed-point behavior. The profile of statistical quantities within the mixing zone exhibit self-similarity under fixed-point scaling to a limited degree. The effect of compressibility is also examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predicted from a renormalization group fixed-point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
Application of 't Hooft's renormalization scheme to two-loop calculations 230
International Nuclear Information System (INIS)
Vladimirov, A.A.
1975-01-01
The advantages of the Hooft scheme for asymptotic calculations in the renormalization group have been demonstrated. Two-loop calculations have been carried out in three renormalized models: in scalar electrodynamics, in a pseudoscalar Yukawa theory and in the Weiss-Zumino supersymmetrical model [ru
Renormalization of the g-boson effects for Os isotopes
International Nuclear Information System (INIS)
Zhang Zhanjun; Liu Yong; Sang Jianping
1996-01-01
A modified renormalization approach based on that proposed by Druce et al. is presented. The overall agreement between the spectra calculated here and the accurate spectra is significantly improved. We also use Druce's approach to generate the renormalized spectra. It is shown that in our microscopic study, both of the approaches are very useful to the determination of several free parameters of fermion residual interactions
Physical renormalization schemes and asymptotic safety in quantum gravity
Falls, Kevin
2017-12-01
The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.
A note on nonperturbative renormalization of effective field theory
Energy Technology Data Exchange (ETDEWEB)
Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China)
2009-08-28
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.
A note on nonperturbative renormalization of effective field theory
International Nuclear Information System (INIS)
Yang Jifeng
2009-01-01
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.
A simple perturbative renormalization scheme for supersymmetric gauge theories
International Nuclear Information System (INIS)
Foda, O.E.
1983-01-01
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.)
Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime
International Nuclear Information System (INIS)
Leen, T.K.
1983-01-01
In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space
Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED
International Nuclear Information System (INIS)
Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.
1992-01-01
We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)
Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain
International Nuclear Information System (INIS)
Chaves, C.M.; Koiller, B.
1983-03-01
Local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas are calculated. It envolves decimating alternate apins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range. (Author) [pt
Complete one-loop renormalization of the Higgs-electroweak chiral Lagrangian
Buchalla, G.; Catà, O.; Celis, A.; Knecht, M.; Krause, C.
2018-03-01
Employing background-field method and super-heat-kernel expansion, we compute the complete one-loop renormalization of the electroweak chiral Lagrangian with a light Higgs boson. Earlier results from purely scalar fluctuations are confirmed as a special case. We also recover the one-loop renormalization of the conventional Standard Model in the appropriate limit.
One-loop renormalization of a gravity-scalar system
Energy Technology Data Exchange (ETDEWEB)
Park, I.Y. [Philander Smith College, Department of Applied Mathematics, Little Rock, AR (United States)
2017-05-15
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector 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 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. (orig.)
One-loop renormalization of a gravity-scalar system
International Nuclear Information System (INIS)
Park, I.Y.
2017-01-01
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector 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 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. (orig.)
One-loop renormalization of a gravity-scalar system
Park, I. Y.
2017-05-01
Extending the renormalizability proposal of the physical sector of 4D Einstein gravity, we have recently proposed renormalizability of the 3D physical sector 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 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 scheme-invariant perturbation theory
International Nuclear Information System (INIS)
Dhar, A.
1983-01-01
A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)
Renormalization group theory of earthquakes
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H. Saleur
1996-01-01
Full Text Available We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995. The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated 'critical point', but is accompanied by an embedded set of 'critical points', its foreshocks and any subsequent shocks for which it may be a foreshock.
Scaling algebras and renormalization group in algebraic quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Verch, R.
1995-01-01
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.)
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Seiler, Christian; Evers, Ferdinand
2016-10-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.
Effective-field renormalization-group method for Ising systems
Fittipaldi, I. P.; De Albuquerque, D. F.
1992-02-01
A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.
Renormalization group treatment of nonrenormalizable interactions
International Nuclear Information System (INIS)
Kazakov, D I; Vartanov, G S
2006-01-01
The structure of the UV divergences in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergences (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. An explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms
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.)
Rota-Baxter algebras and the Hopf algebra of renormalization
International Nuclear Information System (INIS)
Ebrahimi-Fard, K.
2006-06-01
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.)
Energy Technology Data Exchange (ETDEWEB)
Kubo, R; Yokoyama, K
1974-11-01
The purpose of this work is to study the structure of c-number gauge transformation in connection with renormalization problem. In the wide theory of neutral vector fields, there is the gauge structure described essentially by free Lagrangian density. The c-number gauge transformation makes the Lagrangian invariant correspondingly to the usual case of quantum electrodynamics. The c-number transformation can be used to derive relationships among all relevant renormalization constants in the case of interacting fields. In the presence of interaction, total Lagrangian density L is written as L=L/sub 0/+L/sub 1/+L/sub 2/, where L/sub 1/ is given from matter-field Lagrangian density, and L/sub 2/ denotes necessary additional counter terms. In order to conserve the gauge structure, the form of L is invariant under the gauge transformation. Since L matter is self-adjoining, L/sub 1/ remains invariant by itself under the transformation. The form of L/sub 2/ is finally given from the observation that L/sub 3/ cannot contain wave-function renormalization constants. Since L/sub 2/ is invariant under q-number gauge transformation, this transformation in unrenormalized form makes the present L form-invariant. Therefore, together with the above results, auxiliary fields produce the q-number gauge transformation for renormalized fields.
Functional renormalization group approach to interacting three-dimensional Weyl semimetals
Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter
2018-03-01
We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.
Large neutrino mixing from renormalization group evolution
International Nuclear Information System (INIS)
Balaji, K.R.S.; Mohapatra, R.N.; Parida, M.K.; Paschos, E.A.
2000-10-01
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 ν μ - ν τ , if the ν μ and ν τ 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)
The quantum-field renormalization group in the problem of a growing phase boundary
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Antonov, N.V.; Vasil'ev, A.N.
1995-01-01
Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab
Renormalization group improved Yennie-Frautschi-Suura theory for Z0 physics
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Ward, B.F.L.
1987-06-01
Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z 0 physics at the SLC and LEP
Complex-mass shell renormalization of the higher-derivative electrodynamics
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Turcati, Rodrigo [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Universidade Federal do Espirito Santo, Departamento de Fisica e Quimica, Vitoria, ES (Brazil); Laboratorio de Fisica Experimental (LAFEX), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil); Neves, Mario Junior [Universidade Federal Rural do Rio de Janeiro, Departamento de Fisica, Rio de Janeiro (Brazil)
2016-08-15
We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron-positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed. (orig.)
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.)
Poissonian renormalizations, exponentials, and power laws.
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive "renormalization study" of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to "white noise" and to "1/f noise." Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
Renormalization group flow of scalar models in gravity
International Nuclear Information System (INIS)
Guarnieri, Filippo
2014-01-01
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.
Renormalization group and mayer expansions
International Nuclear Information System (INIS)
Mack, G.
1984-01-01
Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U (1) lattice gauge theory by Gopfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear σ-model, and elsewhere
Physical renormalization condition for de Sitter QED
Hayashinaka, Takahiro; Xue, She-Sheng
2018-05-01
We considered a new renormalization condition for the vacuum expectation values of the scalar and spinor currents induced by a homogeneous and constant electric field background in de Sitter spacetime. Following a semiclassical argument, the condition named maximal subtraction imposes the exponential suppression on the massive charged particle limit of the renormalized currents. The maximal subtraction changes the behaviors of the induced currents previously obtained by the conventional minimal subtraction scheme. The maximal subtraction is favored for a couple of physically decent predictions including the identical asymptotic behavior of the scalar and spinor currents, the removal of the IR hyperconductivity from the scalar current, and the finite current for the massless fermion.
Full counting statistics of level renormalization in electron transport through double quantum dots
International Nuclear Information System (INIS)
Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong; Jiao Hujun
2011-01-01
We examine the full counting statistics of electron transport through double quantum dots coupled in series, with particular attention being paid to the unique features originating from level renormalization. It is clearly illustrated that the energy renormalization gives rise to a dynamic charge blockade mechanism, which eventually results in super-Poissonian noise. Coupling of the double dots to an external heat bath leads to dephasing and relaxation mechanisms, which are demonstrated to suppress the noise in a unique way.
Renormalization group and Mayer expansions
International Nuclear Information System (INIS)
Mack, G.
1984-02-01
Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U(1) lattice gauge theory by Goepfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear sigma-model, and elsewhere. (orig.)
Superfield perturbation theory and renormalization
International Nuclear Information System (INIS)
Delbourgo, R.
1975-01-01
The perturbation theory graphs and divergences in super-symmetric Lagrangian models are studied by using superfield techniques. In super PHI 3 -theory very little effort is needed to arrive at the single infinite (wave function) renormalization counterterm, while in PHI 4 -theory the method indicates the counter-Lagrangians needed at the one-loop level and possibly beyond
International Nuclear Information System (INIS)
Maris, Th.A.J.
1976-01-01
The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt
Applications of the renormalization group approach to problems in quantum field theory
International Nuclear Information System (INIS)
Renken, R.L.
1985-01-01
The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical
Systematic renormalization of the effective theory of Large Scale Structure
International Nuclear Information System (INIS)
Abolhasani, Ali Akbar; Mirbabayi, Mehrdad; Pajer, Enrico
2016-01-01
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 large scale density contrast δ and momentum density π(k) scale as k 2 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.
Renormalization of three-quark operators for baryon distribution amplitudes
Energy Technology Data Exchange (ETDEWEB)
Gruber, Michael
2017-07-01
In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI{sup '}/SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.
Renormalization of three-quark operators for baryon distribution amplitudes
International Nuclear Information System (INIS)
Gruber, Michael
2017-01-01
In this thesis we design and study three-quark operators that are essential for the calculation of baryon distribution amplitudes. These nonperturbative objects grant insight into the internal structure of hadrons, but their renormalization patterns are nontrivial and need to be treated with care. With the application to lattice simulations in mind we discuss two renormalization schemes, MS and RI ' /SMOM, and connect them by calculating conversion factors. Armed with this knowledge we are able to extract phenomenologically relevant results from an accompanying lattice analysis.
Renormalization group evolution of Dirac neutrino masses
International Nuclear Information System (INIS)
Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas
2005-01-01
There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments
Poissonian renormalizations, exponentials, and power laws
Eliazar, Iddo
2013-05-01
This paper presents a comprehensive “renormalization study” of Poisson processes governed by exponential and power-law intensities. These Poisson processes are of fundamental importance, as they constitute the very bedrock of the universal extreme-value laws of Gumbel, Fréchet, and Weibull. Applying the method of Poissonian renormalization we analyze the emergence of these Poisson processes, unveil their intrinsic dynamical structures, determine their domains of attraction, and characterize their structural phase transitions. These structural phase transitions are shown to be governed by uniform and harmonic intensities, to have universal domains of attraction, to uniquely display intrinsic invariance, and to be intimately connected to “white noise” and to “1/f noise.” Thus, we establish a Poissonian explanation to the omnipresence of white and 1/f noises.
On the renormalization of string functionals
International Nuclear Information System (INIS)
Dietz, K.; Filk, T.
1982-09-01
We investigate analytic renormalization procedures for functional integrals, corresponding to field theories defined on compact manifolds, which arise e.g. from string functionals of the Nambu-Schild-Eguchi type. Although these models belong to the nonrenormalizable class of quantum field theories, we prove finiteness for a rectangular string shape up to three loop level, for circular boundary up to two loop order, and for a variety of graphs in higher order, thus indicating that the result might hold in general. From the explicit calculation of the two loop approximation we extract the first model dependent corrections to the qanti q - potential or the Casimir effect. The importance of dilation transformations for the properties of the renormalization procedure are investigated. We prove that under certain conditions, forced by symmetry properties, the association of finite values to divergent series is unique, independent of the regularization procedure. (orig.)
The renormalized action principle in quantum field theory
International Nuclear Information System (INIS)
Balasin, H.
1990-03-01
The renormalized action principle holds a central position in field theory, since it offers a variety of applications. The main concern of this work is the proof of the action principle within the so-called BPHZ-scheme of renormalization. Following the classical proof given by Lam and Lowenstein, some loopholes are detected and closed. The second part of the work deals with the application of the action principle to pure Yang-Mills-theories within the axial gauge (n 2 ≠ 0). With the help of the action principle we investigate the decoupling of the Faddeev-Popov-ghost-fields from the gauge field. The consistency of this procedure, suggested by three-graph approximation, is proven to survive quantization. Finally we deal with the breaking of Lorentz-symmetry caused by the presence of the gauge-direction n. Using BRST-like techniques and the semi-simplicity of the Lorentz-group, it is shown that no new breakings arise from quantization. Again the main step of the proof is provided by the action principle. (Author, shortened by G.Q.)
Comment on non-renormalization theorem in the four dimensional superstrings
International Nuclear Information System (INIS)
Soda, Jiro; Nakazawa, Naohito; Sakai, Kenji; Ojima, Shuichi.
1987-10-01
We discuss non-renormalization theorem in the context of the four dimensional superstrings. We explicitly demonstrate that the graviton 3-point one-loop amplitude does not vanish in contrast to the ten dimensional superstring theories. (author)
Covariant Derivatives and the Renormalization Group Equation
Dolan, Brian P.
The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.
Golden mean renormalization for a generalized Harper equation: The Ketoja-Satija orchid
International Nuclear Information System (INIS)
Mestel, B.D.; Osbaldestin, A.H.
2004-01-01
We provide a rigorous analysis of the fluctuations of localized eigenstates in a generalized Harper equation with golden mean flux and with next-nearest-neighbor interactions. For next-nearest-neighbor interaction above a critical threshold, these self-similar fluctuations are characterized by orbits of a renormalization operator on a universal strange attractor, whose projection was dubbed the ''orchid'' by Ketoja and Satija [Phys. Rev. Lett. 75, 2762 (1995)]. We show that the attractor is given essentially by an embedding of a subshift of finite type, and give a description of its periodic orbits
Probing renormalization group flows using entanglement entropy
International Nuclear Information System (INIS)
Liu, Hong; Mezei, Márk
2014-01-01
In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen
Two-loop renormalization of quantum gravity simplified
Bern, Zvi; Chi, Huan-Hang; Dixon, Lance; Edison, Alex
2017-02-01
The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when nondynamical three-forms are added to the theory, or when a pseudoscalar is replaced by the antisymmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences for renormalized scattering processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. We explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators.
Dynamic mass generation and renormalizations in quantum field theories
International Nuclear Information System (INIS)
Miransky, V.A.
1979-01-01
It is shown that the dynamic mass generation can destroy the multiplicative renormalization relations and lead to new type divergences in the massive phase. To remove these divergences the values of the bare coupling constants must be fixed. The phase diagrams of gauge theories are discussed
Renormalized powers of quantum white noise
International Nuclear Information System (INIS)
Accardi, L.; Boukas, A.
2009-01-01
Giving meaning to the powers of the creation and annihilation densities (quantum white noise) is an old and important problem in quantum field theory. In this paper we present an account of some new ideas that have recently emerged in the attempt to solve this problem. We emphasize the connection between the Lie algebra of the renormalized higher powers of quantum white noise (RHPWN), which can be interpreted as a suitably deformed (due to renormalization) current algebra over the 1-mode full oscillator algebra, and the current algebra over the centerless Virasoro (or Witt)-Zamolodchikov-ω ∞ Lie algebras of conformal field theory. Through a suitable definition of the action on the vacuum vector we describe how to obtain a Fock representation of all these algebras. We prove that the restriction of the vacuum to the abelian subalgebra generated by the field operators gives an infinitely divisible process whose marginal distribution is the beta (or continuous binomial). (authors)
Renormalization of spin excitations in hexagonal HoMnO3 by magnon-phonon coupling
Kim, Taehun; Leiner, Jonathan C.; Park, Kisoo; Oh, Joosung; Sim, Hasung; Iida, Kazuki; Kamazawa, Kazuya; Park, Je-Geun
2018-05-01
Hexagonal HoMnO3, a two-dimensional Heisenberg antiferromagnet, has been studied via inelastic neutron scattering. A simple Heisenberg model with a single-ion anisotropy describes most features of the spin-wave dispersion curves. However, there is shown to be a renormalization of the magnon energies located at around 11 meV. Since both the magnon-magnon interaction and magnon-phonon coupling can affect the renormalization in a noncollinear magnet, we have accounted for both of these couplings by using a Heisenberg XXZ model with 1 /S expansions [1] and the Einstein site phonon model [13], respectively. This quantitative analysis leads to the conclusion that the renormalization effect primarily originates from the magnon-phonon coupling, while the spontaneous magnon decay due to the magnon-magnon interaction is suppressed by strong two-ion anisotropy.
Renormalization and operator product expansion in theories with massless particles
International Nuclear Information System (INIS)
Anikin, S.A.; Smirnov, V.A.
1985-01-01
Renormalization procedure in theories including massless particles is presented. With the help of counterterm formalism the operator product expansion for arbitrary composite fields is derived. The coefficient functions are explicitly expressed in terms of certain Green's functions. (author)
Renormalized sum rules for structure functions of heavy meson decays
International Nuclear Information System (INIS)
Grozin, A.G.; Korchemsky, G.P.
1996-01-01
We consider the properties of the structure functions of inclusive heavy meson decays B→X c and treat the c quark mass as a free parameter. We show that in two extreme cases of heavy and light c quarks the structure functions of heavy-heavy and heavy-light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a timelike and a lightlike segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of the heavy-heavy transition is renormalized multiplicatively, while that of the heavy-light transition obeys the GLAP-type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the open-quote open-quote third close-quote close-quote sum rules) with a soft exponential factorization cutoff, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at u=1/2 are exactly canceled by a similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at u=1 are parametrized by the matrix element μ π 2 which is proportional to the heavy quark kinetic energy. copyright 1996 The American Physical Society
The large-Nc renormalization group
International Nuclear Information System (INIS)
Dorey, N.
1995-01-01
In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N c , limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N c , selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N c . We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ -1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ -1 . The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N c , renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞
Strong-Weak CP Hierarchy from Non-Renormalization Theorems
Energy Technology Data Exchange (ETDEWEB)
Hiller, Gudrun
2002-01-28
We point out that the hierarchy between the measured values of the CKM phase and the strong CP phase has a natural origin in supersymmetry with spontaneous CP violation and low energy supersymmetry breaking. The underlying reason is simple and elegant: in supersymmetry the strong CP phase is protected by an exact non-renormalization theorem while the CKM phase is not. We present explicit examples of models which exploit this fact and discuss corrections to the non-renormalization theorem in the presence of supersymmetry breaking. This framework for solving the strong CP problem has generic predictions for the superpartner spectrum, for CP and flavor violation, and predicts a preferred range of values for electric dipole moments.
Real space renormalization tecniques for disordered systems
International Nuclear Information System (INIS)
Anda, E.V.
1984-01-01
Real space renormalization techniques are applied to study different disordered systems, with an emphasis on the understanding of the electronic properties of amorphous matter, mainly semiconductors. (Authors) [pt
The renormalization group: scale transformations and changes of scheme
International Nuclear Information System (INIS)
Roditi, I.
1983-01-01
Starting from a study of perturbation theory, the renormalization group is expressed, not only for changes of scale but also within the original view of Stueckelberg and Peterman, for changes of renormalization scheme. The consequences that follow from using that group are investigated. Following a more general point of view a method to obtain an improvement of the perturbative results for physical quantities is proposed. The results obtained with this method are compared with those of other existing methods. (L.C.) [pt
Renormalization group flow of the Higgs potential.
Gies, Holger; Sondenheimer, René
2018-03-06
We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).
Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model
Energy Technology Data Exchange (ETDEWEB)
Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden)
2017-03-08
We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.
Tutchton, Roxanne; Marchbanks, Christopher; Wu, Zhigang
2018-05-01
The phonon-induced renormalization of electronic band structures is investigated through first-principles calculations based on the density functional perturbation theory for nine materials with various crystal symmetries. Our results demonstrate that the magnitude of the zero-point renormalization (ZPR) of the electronic band structure is dependent on both crystal structure and material composition. We have performed analysis of the electron-phonon-coupling-induced renormalization for two silicon (Si) allotropes, three carbon (C) allotropes, and four boron nitride (BN) polymorphs. Phonon dispersions of each material were computed, and our analysis indicates that materials with optical phonons at higher maximum frequencies, such as graphite and hexagonal BN, have larger absolute ZPRs, with the exception of graphene, which has a considerably smaller ZPR despite having phonon frequencies in the same range as graphite. Depending on the structure and material, renormalizations can be comparable to the GW many-body corrections to Kohn-Sham eigenenergies and, thus, need to be considered in electronic structure calculations. The temperature dependence of the renormalizations is also considered, and in all materials, the eigenenergy renormalization at the band gap and around the Fermi level increases with increasing temperature.
Real space renormalization techniques for disordered systems
International Nuclear Information System (INIS)
Anda, E.V.
1985-01-01
Real Space renormalization techniques are applied to study different disordered systems, with an emphasis on the under-standing of the electronic properties of amorphous matter, mainly semiconductors. (author) [pt
Functional renormalization group and Kohn-Sham scheme in density functional theory
Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo
2018-04-01
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
QCD: Renormalization for the practitioner
International Nuclear Information System (INIS)
Pascual, P.; Tarrach, R.
1984-01-01
These notes correspond to a GIFT (Grupo Interuniversitario de Fisica Teorica) course which was given by us in autumn 1983 at the University of Barcelona. Their main subject is renormalization in perturbative QCD and only the last chapter goes beyond perturbation theory. They are essentially self contained and their aim is to teach the student the techniques of perturbative QCD and the QCD sum rules. (orig./HSI)
Renormalization group and the superconducting susceptibility of a Fermi liquid
International Nuclear Information System (INIS)
Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.
2010-01-01
A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.
Running with rugby balls: bulk renormalization of codimension-2 branes
Williams, M.; Burgess, C. P.; van Nierop, L.; Salvio, A.
2013-01-01
We compute how one-loop bulk effects renormalize both bulk and brane effective interactions for geometries sourced by codimension-two branes. We do so by explicitly integrating out spin-zero, -half and -one particles in 6-dimensional Einstein-Maxwell-Scalar theories compactified to 4 dimensions on a flux-stabilized 2D geometry. (Our methods apply equally well for D dimensions compactified to D - 2 dimensions, although our explicit formulae do not capture all divergences when D > 6.) The renormalization of bulk interactions are independent of the boundary conditions assumed at the brane locations, and reproduce standard heat-kernel calculations. Boundary conditions at any particular brane do affect how bulk loops renormalize this brane's effective action, but not the renormalization of other distant branes. Although we explicitly compute our loops using a rugby ball geometry, because we follow only UV effects our results apply more generally to any geometry containing codimension-two sources with conical singularities. Our results have a variety of uses, including calculating the UV sensitivity of one-loop vacuum energy seen by observers localized on the brane. We show how these one-loop effects combine in a surprising way with bulk back-reaction to give the complete low-energy effective cosmological constant, and comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.
All-order renormalization of propagator matrix for Majorana fermions with inter-generation mixing
International Nuclear Information System (INIS)
Kniehl, Bernd A.
2014-04-01
We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.
A real-space renormalization approach to the Kubo-Greenwood formula in mirror Fibonacci systems
International Nuclear Information System (INIS)
Sanchez, Vicenta; Wang Chumin
2006-01-01
An exact real-space renormalization method is developed to address the electronic transport in mirror Fibonacci chains at a macroscopic scale by means of the Kubo-Greenwood formula. The results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra, contrary to the simple Fibonacci case. A length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour. For multidimensional quasiperiodic systems, a novel renormalization plus convolution method is proposed. This combined renormalization + convolution method has shown an extremely elevated computing efficiency, being able to calculate electrical conductance of a three-dimensional non-crystalline solid with 10 30 atoms. Finally, the dc and ac conductances of mirror Fibonacci nanowires are also investigated, where a quantized dc-conductance variation with the Fermi energy is found, as observed in gold nanowires
A perturbative study of two four-quark operators in finite volume renormalization schemes
Palombi, Filippo; Sint, S
2006-01-01
Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the $\\Delta F=1$ or $\\Delta F=2$ effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of ...
Renormalization-group study of the four-body problem
International Nuclear Information System (INIS)
Schmidt, Richard; Moroz, Sergej
2010-01-01
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
Distribution of the minimum path on percolation clusters: A renormalization group calculation
International Nuclear Information System (INIS)
Hipsh, Lior.
1993-06-01
This thesis uses the renormalization group for the research of the chemical distance or the minimal path on percolation clusters on a 2 dimensional square lattice. Our aims are to calculate analytically (iterative calculation) the fractal dimension of the minimal path. d min. , and the distributions of the minimum paths, l min for different lattice sizes and for different starting densities (including the threshold value p c ). For the distributions. We seek for an analytic form which describes them. The probability to get a minimum path for each linear size L is calculated by iterating the distribution of l min for the basic cell of size 2*2 to the next scale sizes, using the H cell renormalization group. For the threshold value of p and for values near to p c . We confirm a scaling in the form: P(l,L) =f1/l(l/(L d min ). L - the linear size, l - the minimum path. The distribution can be also represented in the Fourier space, so we will try to solve the renormalization group equations in this space. A numerical fitting is produced and compared to existing numerical results. In order to improve the agreement between the renormalization group and the numerical simulations, we also present attempts to generalize the renormalization group by adding more parameters, e.g. correlations between bonds in different directions or finite densities for occupation of bonds and sites. (author) 17 refs
On the renormalization of operator products: the scalar gluonic case
International Nuclear Information System (INIS)
Zoller, Max F.
2016-01-01
In this paper we study the renormalization of the product of two operators O 1 =−(1/4)G μν G μν in QCD. An insertion of two such operators O 1 (x)O 1 (0) into a Greens function produces divergent contact terms for x→0. In the course of the computation of the operator product expansion (OPE) of the correlator of two such operators i∫ d 4 x e iqx T{ O 1 (x)O 1 (0)} to three-loop order http://dx.doi.org/10.1007/JHEP12(2012)119; http://dx.doi.org/10.1007/JHEP10(2014)169 we discovered that divergent contact terms remain not only in the leading Wilson coefficient C 0 , which is just the VEV of the correlator, but also in the Wilson coefficient C 1 in front of O 1 . As this correlator plays an important role for example in QCD sum rules a full understanding of its renormalization is desireable. This work explains how the divergences encountered in higher orders of an OPE of this correlator should be absorbed in counterterms and derives an additive renormalization constant for C 1 from first principles and to all orders in perturnbation theory. The method to derive the renormalization of this operator product is an extension of the ideas of V. Spiridonov, Anomalous dimension of g μν 2 and β-function, Preprint IYAI-P-0378 (1984). and can be generalized to other cases.
International Nuclear Information System (INIS)
Anton, Luis; MartI, Jose M; Ibanez, Jose M; Aloy, Miguel A.; Mimica, Petar; Miralles, Juan A.
2010-01-01
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 wave front 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 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 numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.
Renormalization group invariance in the presence of an instanton
International Nuclear Information System (INIS)
Ross, D.A.
1987-01-01
A pure Yang-Mills theory which admits an instanton is under discussion. n=1 supersymmetric (SU-2) Yang-Mills theory, both in the Wess-zumino gauge and in manifestly supersymmetric supergauge is considered. Two-loop vacuum graphs are calculated. The way a renormalization group invariance works under conditions of fermionic zero mode elimination is shown
International Nuclear Information System (INIS)
Gulov, A.V.; Skalozub, V.V.
2000-01-01
In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives possibility to reduce the problem to the scattering of light particles on the external field substituting a heavy virtual state. Applications of the results to problem of searching new physics beyond the Standard Model are discussed [ru
Renormalization-group equations of neutrino masses and flavor mixing parameters in matter
Xing, Zhi-zhong; Zhou, Shun; Zhou, Ye-Ling
2018-05-01
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a≡ 2√{2}{G}F{N}_eE to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {\\tilde{m}}_i (for i = 1 , 2 , 3). Given the standard parametrization of V , the RGEs for {{\\tilde{θ}}_{12}, {\\tilde{θ}}_{13}, {\\tilde{θ}}_{23}, \\tilde{δ}} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ- τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.
PyR@TE. Renormalization group equations for general gauge theories
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Four loop wave function renormalization in the non-abelian Thirring model
International Nuclear Information System (INIS)
Ali, D.B.; Gracey, J.A.
2001-01-01
We compute the anomalous dimension of the fermion field with N f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d F abcd d F abcd , in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess-Zumino-Witten-Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored
Fine-grained entanglement loss along renormalization-group flows
International Nuclear Information System (INIS)
Latorre, J.I.; Rico, E.; Luetken, C.A.; Vidal, G.
2005-01-01
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
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Re-Normalization Method of Doppler Lidar Signal for Error Reduction
Energy Technology Data Exchange (ETDEWEB)
Park, Nakgyu; Baik, Sunghoon; Park, Seungkyu; Kim, Donglyul [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Kim, Dukhyeon [Hanbat National Univ., Daejeon (Korea, Republic of)
2014-05-15
In this paper, we presented a re-normalization method for the fluctuations of Doppler signals from the various noises mainly due to the frequency locking error for a Doppler lidar system. For the Doppler lidar system, we used an injection-seeded pulsed Nd:YAG laser as the transmitter and an iodine filter as the Doppler frequency discriminator. For the Doppler frequency shift measurement, the transmission ratio using the injection-seeded laser is locked to stabilize the frequency. If the frequency locking system is not perfect, the Doppler signal has some error due to the frequency locking error. The re-normalization process of the Doppler signals was performed to reduce this error using an additional laser beam to an Iodine cell. We confirmed that the renormalized Doppler signal shows the stable experimental data much more than that of the averaged Doppler signal using our calibration method, the reduced standard deviation was 4.838 Χ 10{sup -3}.
Renormalization of gauge theories in the background-field approach arXiv
Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.
Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.
Renormalization group fixed points of foliated gravity-matter systems
Energy Technology Data Exchange (ETDEWEB)
Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)
2017-05-17
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.
Renormalization effects and phonon density of states in high temperature superconductors
Directory of Open Access Journals (Sweden)
Vinod Ashokan
2013-02-01
Full Text Available Using the versatile double time thermodynamic Green's function approach based on many body theory the renormalized frequencies, phonon energy line widths, shifts and phonon density of states (PDOS are investigated via a newly formulated Hamiltonian (does not include BCS type Hamiltonian that includes the effects of electron-phonon, anharmonicities and that of isotopic impurities. The automatic appearance of pairons, temperature, impurity and electron-phonon coupling of renormalized frequencies, widths, shifts and PDOS emerges as a characteristic feature of present theory. The numerical investigations on PDOS for the YBa2Cu3O7 − δ crystal predicts several new feature of high temperature superconductors (HTS and agreements with experimental observations.
The renormalization of collective states and the improper initial or final states in NFT
International Nuclear Information System (INIS)
Bes, D.R.; Dussel, G.G.; Perazzo, R.P.J.; Sofia, H.M.
1978-01-01
The collective lines in a given diagram are renormalized by including higher order processes. The problem is cast into the form of a conventional linear algebraic matrix equation that allows a simple treatment of the normalization conditions. It is shown that the states entering in the renormalization of the phonons become improper initial or final states, if dressed phonons are used in the intermediate states. A simple extension of this argument allows one to justify one of the rules given in the formulation of the NFT. (Auth.)
Perturbative renormalization of composite operators via flow equations. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1992-09-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).
Perturbative renormalization of composite operators via flow equations. Pt. 1
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1992-01-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)
Exact renormalization group as a scheme for calculations
International Nuclear Information System (INIS)
Mack, G.
1985-10-01
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)
Functional-derivative study of the Hubbard model. III. Fully renormalized Green's function
International Nuclear Information System (INIS)
Arai, T.; Cohen, M.H.
1980-01-01
The functional-derivative method of calculating the Green's function developed earlier for the Hubbard model is generalized and used to obtain a fully renormalized solution. Higher-order functional derivatives operating on the basic Green's functions, G and GAMMA, are all evaluated explicitly, thus making the solution applicable to the narrow-band region as well as the wide-band region. Correction terms Phi generated from functional derivatives of equal-time Green's functions of the type delta/sup n/ /deltaepsilon/sup n/, etc., with n > or = 2. It is found that the Phi's are, in fact, renormalization factors involved in the self-energy Σ and that the structure of the Phi's resembles that of Σ and contains the same renormalization factors Phi. The renormalization factors Phi are shown to satisfy a set of equations and can be evaluated self-consistently. In the presence of the Phi's, all difficulties found in the previous results (papers I and II) are removed, and the energy spectrum ω can now be evaluated for all occupations n. The Schwinger relation is the only basic relation used in generating this fully self-consistent Green's function, and the Baym-Kadanoff continuity condition is automatically satisfied
Energy Technology Data Exchange (ETDEWEB)
Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2017-07-15
Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
International Nuclear Information System (INIS)
Green, Jeremy; Jansen, Karl; Steffens, Fernanda
2017-07-01
Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.
Energy Technology Data Exchange (ETDEWEB)
Blanchard, P [European Organization for Nuclear Research, Geneva (Switzerland); Seneor, R [European Organization for Nuclear Research, Geneva (Switzerland); Ecole Polytechnique, 75 - Paris (France). Centre de Physique Theorique)
1975-01-01
With the method of perturbative renormalization developed by Epstein and Glaser it is shown that Green's functions exist for theories with massless particles such as Q.E.D. and lambda:PHI/sup 2n/ theories. Growth properties are given in momentum space. In the case of Q.E.D., it is also shown that one can perform the physical mass renormalization.
Baumgarten, Lorenz; Kierfeld, Jan
2018-05-01
We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017), 10.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy
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.)
Singlet vs Nonsinglet Perturbative Renormalization factors of Staggered Fermion Bilinears
Panagopoulos, Haralambos; Spanoudes, Gregoris
2018-03-01
In this paper we present the perturbative computation of the difference between the renormalization factors of flavor singlet (Σfψ¯fΓψf', f : flavor index) and nonsinglet (ψ¯f1Γψf2,f1 ≠ f2) bilinear quark operators (where Γ = 𝟙, γ5, γ µ, γ5 γ µ, γ5 σµv on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, using Symanzik improved gluons and staggered fermions with twice stout-smeared links. The stout smearing procedure is also applied to the definition of bilinear operators. A significant part of this work is the development of a method for treating some new peculiar divergent integrals stemming from the staggered formalism. Our results can be combined with precise simulation results for the renormalization factors of the nonsinglet operators, in order to obtain an estimate of the renormalization factors for the singlet operators. The results have been published in Physical Review D [1].
Directory of Open Access Journals (Sweden)
Huan-Yu Bi
2015-09-01
Full Text Available The Principle of Maximum Conformality (PMC eliminates QCD renormalization scale-setting uncertainties using fundamental renormalization group methods. The resulting scale-fixed pQCD predictions are independent of the choice of renormalization scheme and show rapid convergence. The coefficients of the scale-fixed couplings are identical to the corresponding conformal series with zero β-function. Two all-orders methods for systematically implementing the PMC-scale setting procedure for existing high order calculations are discussed in this article. One implementation is based on the PMC-BLM correspondence (PMC-I; the other, more recent, method (PMC-II uses the Rδ-scheme, a systematic generalization of the minimal subtraction renormalization scheme. Both approaches satisfy all of the principles of the renormalization group and lead to scale-fixed and scheme-independent predictions at each finite order. In this work, we show that PMC-I and PMC-II scale-setting methods are in practice equivalent to each other. We illustrate this equivalence for the four-loop calculations of the annihilation ratio Re+e− and the Higgs partial width Γ(H→bb¯. Both methods lead to the same resummed (‘conformal’ series up to all orders. The small scale differences between the two approaches are reduced as additional renormalization group {βi}-terms in the pQCD expansion are taken into account. We also show that special degeneracy relations, which underly the equivalence of the two PMC approaches and the resulting conformal features of the pQCD series, are in fact general properties of non-Abelian gauge theory.
Renormalization Group Functional Equations
Curtright, Thomas L
2011-01-01
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.
Renormalization group and finite size effects in scalar lattice field theories
International Nuclear Information System (INIS)
Bernreuther, W.; Goeckeler, M.
1988-01-01
Binder's phenomenological renormalization group is studied in the context of the O(N)-symmetric euclidean lattice φ 4 theory in dimensions d ≤ 4. By means of the field theoretical formulation of the renormalization group we analyse suitable ratios of Green functions on finite lattices in the limit where the dimensionless lattice length L >> 1 and where the dimensionless bare mass approaches the critical point of the corresponding infinite volume model. If the infrared-stable fixed point which controls this limit is a simple zero of the β-function we are led to formulae which allow the extraction of the critical exponents ν and η. For the gaussian fixed point in four dimensions, discussed as a known example for a multiple zero of the β-function, we derive for these ratios the leading logarithmic corrections to mean field scaling. (orig.)
Self-similarity and scaling theory of complex networks
Song, Chaoming
Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.
The Kadanoff lower-bound variational renormalization group applied to an SU(2) lattice spin model
International Nuclear Information System (INIS)
Thorleifsson, G.; Damgaard, P.H.
1990-07-01
We apply the variational lower-bound Renormalization Group transformation of Kadanoff to an SU(2) lattice spin model in 2 and 3 dimensions. Even in the one-hypercube framework of this renormalization group transformation the present model is characterised by having an infinite basis of fundamental operators. We investigate whether the lower-bound variational renormalization group transformation yields results stable under truncations of this operator basis. Our results show that for this particular spin model this is not the case. (orig.)
Renormalization of period doubling in symmetric four-dimensional volume-preserving maps
International Nuclear Information System (INIS)
Mao, J.; Greene, J.M.
1987-01-01
We have determined three maps (truncated at quadratic terms) that are fixed under the renormalization operator of pitchfork period doubling in symmetric four-dimensional volume-preserving maps. Each of these contains the previously known two-dimensional area-preserving map that is fixed under the period-doubling operator. One of these three fixed maps consists of two uncoupled two-dimensional (nonlinear) area-preserving fixed maps. The other two contain also the two-dimensional area-preserving fixed map coupled (in general) with a linear two-dimensional map. The renormalization calculation recovers all numerical results for the pitchfork period doubling in the symmetric four-dimensional volume-preserving maps, reported by Mao and Helleman [Phys. Rev. A 35, 1847 (1987)]. For a large class of nonsymmetric four-dimensional volume-preserving maps, we found that the fixed maps are the same as those for the symmetric maps
A rigorous treatment of the lattice renormalization problem of f$_{B}$
Boucaud, P; Micheli, J; Pène, O; Rossi, G C; Boucaud, Ph.
1993-01-01
The $B$-meson decay constant can be measured on the lattice using a $1/m_b$ expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalization coefficient, $Z$, between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of $Z$. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point $B$-meson correlator in the limit of large $b$-quark mass, we prove that the two schemes give consistent results to order $\\alpha_s$. We show that there is, however, a renormalization prescription ambiguity that can have sizeable numerical consequences. This ambiguity can be resolved in the framework of an $O(a)$ improved calculation, and we describe the correct prescription in that case. Finally we give the numerical values of $Z$ t...
A non-renormalization theorem for conformal anomalies
International Nuclear Information System (INIS)
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 functions 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 contact terms saturate by free fields
New renormalization group approach to multiscale problems
Energy Technology Data Exchange (ETDEWEB)
Einhorn, M B; Jones, D R.T.
1984-02-27
A new renormalization group is presented which exploits invariance with respect to more than one scale. The method is illustrated by a simple model, and future applications to fields such as critical phenomena and supersymmetry are speculated upon.
Unraveling the interlayer-related phonon self-energy renormalization in bilayer graphene.
Araujo, Paulo T; Mafra, Daniela L; Sato, Kentaro; Saito, Riichiro; Kong, Jing; Dresselhaus, Mildred S
2012-01-01
In this letter, we present a step towards understanding the bilayer graphene (2LG) interlayer (IL)-related phonon combination modes and overtones as well as their phonon self-energy renormalizations by using both gate-modulated and laser-energy dependent inelastic scattering spectroscopy. We show that although the IL interactions are weak, their respective phonon renormalization response is significant. Particularly special, the IL interactions are mediated by Van der Waals forces and are fundamental for understanding low-energy phenomena such as transport and infrared optics. Our approach opens up a new route to understanding fundamental properties of IL interactions which can be extended to any graphene-like material, such as MoS₂, WSe₂, oxides and hydroxides. Furthermore, we report a previously elusive crossing between IL-related phonon combination modes in 2LG, which might have important technological applications.
Functional renormalization group approach to the two dimensional Bose gas
Energy Technology Data Exchange (ETDEWEB)
Sinner, A; Kopietz, P [Institut fuer Theoretische Physik, Universitaet Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt (Germany); Hasselmann, N [International Center for Condensed Matter Physics, Universidade de BrasIlia, Caixa Postal 04667, 70910-900 BrasIlia, DF (Brazil)], E-mail: hasselma@itp.uni-frankfurt.de, E-mail: sinner@itp.uni-frankfurt.de
2009-02-01
We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.
Introduction to the renormalization group study in relativistic quantum field theory
International Nuclear Information System (INIS)
Mignaco, J.A.; Roditi, I.
1985-01-01
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.) [pt
International Nuclear Information System (INIS)
Dias, S.A.
1985-01-01
The transformation law of truncated pertubation theory observables under changes of renormalization scheme is deduced. Based on this, a criticism of the calculus of the moments of structure functions in deep inelastic scattering, obtaining that the A 2 coefficient not renormalization group invariant is done. The PMS criterion is used to optimize the perturbative productions of the moments, truncated to 2nd order. (author) [pt
Renormalized perturbation theory: Vlasov-Poisson System, weak turbulence limit and gyrokinetics
International Nuclear Information System (INIS)
Zhang, Y.Z.; Mahajan, S.M.
1987-10-01
The Self-consistency of the renormalized perturbation theory is demonstrated by applying it to the Vlasov-Poisson System and showing that the theory has the correct weak turbulence limit. Energy conservation is proved to arbitrary high order for the electrostatic drift waves. The theory is applied to derive renormalized equations for a low-β gyrokinetic system. Comparison of our theory with other current theories is presented. 22 refs
Quark-mixing renormalization effects on the W-boson partial decay widths
International Nuclear Information System (INIS)
Almasy, A.A.; Kniehl, B.A.; Sirlin, A.
2008-10-01
We briefly review existing proposals for the renormalization of the Cabibbo- Kobayashi-Maskawa matrix and study their numerical effects on the W-boson partial decay widths. The differences between the decay widths predicted by the various renormalization schemes are generally negligible, while their deviations from the MS results are very small, except for W + → u anti b and W + →c anti b, where they reach approximately 4%. (orig.)
Carilli, Michael F.; Delaney, Kris T.; Fredrickson, Glenn H.
2018-02-01
Using the zero-temperature string method, we investigate nucleation of a stable lamellar phase from a metastable disordered phase of the renormalized Landau-Brazovskii model at parameters explicitly connected to those of an experimentally accessible diblock copolymer melt. We find anisotropic critical nuclei in qualitative agreement with previous experimental and analytic predictions; we also find good quantitative agreement with the predictions of a single-mode analysis. We conduct a thorough search for critical nuclei containing various predicted and experimentally observed defect structures. The predictions of the renormalized model are assessed by simulating the bare Landau-Brazovskii model with fluctuations. We find that the renormalized model makes reasonable predictions for several important quantities, including the order-disorder transition (ODT). However, the critical nucleus size depends sharply on proximity to the ODT, so even small errors in the ODT predicted by the renormalized model lead to large errors in the predicted critical nucleus size. We conclude that the renormalized model is a poor tool to study nucleation in the fluctuating Landau-Brazovskii model, and recommend that future studies work with the fluctuating bare model directly, using well-chosen collective variables to investigate kinetic pathways in the disorder → lamellar transition.
Two-and three-dimension Potts magnetism in the renormalization group approximation
International Nuclear Information System (INIS)
Silva, L.R. da.
1985-01-01
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) [pt
Perturbative renormalization of QED via flow equations
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1991-01-01
We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)
Renormalization schemes for the Two-Higgs-Doublet Model and applications to h → WW/ZZ → 4 fermions
DEFF Research Database (Denmark)
Altenkamp, Lukas; Dittmaier, Stefan; Rzehak, Heidi
2017-01-01
We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization conditions as far as possible and on M S ¯ prescriptions for th...
Regularization and renormalization of quantum field theory in curved space-time
International Nuclear Information System (INIS)
Bernard, C.; Duncan, A.
1977-01-01
It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x,t)/vertical bar/0 in greater than for t → + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t→ +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed
Closed-form irreducible differential formulations of the Wilson renormalization group
International Nuclear Information System (INIS)
Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.
1983-01-01
We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator
Energy Technology Data Exchange (ETDEWEB)
Guazzini, D.; Sommer, R. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Meyer, H. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics
2007-05-15
We carry out the non-perturbative renormalization of the chromo-magnetic operator in Heavy Quark Effective Theory. At order 1/m of the expansion, the operator is responsible for the mass splitting between the pseudoscalar and vector B mesons. We obtain its two-loop anomalous dimension in a Schroedinger functional scheme by successive oneloop conversions to the lattice MS scheme and the MS scheme. We then compute the scale evolution of the operator non-perturbatively in the N{sub f}=0 theory between {mu} {approx}0.3 GeV and {mu} {approx}100 GeV, where contact is made with perturbation theory. The overall renormalization factor that converts the bare lattice operator to its renormalization group invariant form is given for the Wilson gauge action and two standard discretizations of the heavy-quark action. As an application, we find that this factor brings the previous quenched predictions of the B{sup *}-B mass splitting closer to the experimental value than found with a perturbative renormalization. The same renormalization factor is applicable to the spin-dependent potentials of Eichten and Feinberg. (orig.)
Renormalized multiple-scattering theory of photoelectron diffraction
International Nuclear Information System (INIS)
Biagini, M.
1993-01-01
The current multiple-scattering cluster techniques for the calculation of x-ray photoelectron and Auger-electron diffraction patterns consume much computer time in the intermediate-energy range (200--1000 eV); in fact, because of the large value of the electron mean free path and of the large forward-scattering amplitude at such energies, the electron samples a relatively large portion of the crystal, so that the number of paths to be considered becomes dramatically high. An alternative method is developed in the present paper: instead of calculating the individual contribution from each single path, the scattering matrix of each plane parallel to the surface is calculated with a renormalization process that calculates every scattering event in the plane up to infinite order. Similarly the scattering between two planes is calculated up to infinite order, and the double-plane scattering matrix is introduced. The process may then be applied to the calculation of a larger set of atomic layers. The advantage of the method is that a relatively small number of internuclear vectors have been used to obtain convergence in the calculation
Perturbative renormalization of QED via flow equations
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))
1991-12-19
We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).
Finite size scaling and phenomenological renormalization
International Nuclear Information System (INIS)
Derrida, B.; Seze, L. de; Vannimenus, J.
1981-05-01
The basic equations of the phenomenological renormalization method are recalled. A simple derivation using finite-size scaling is presented. The convergence of the method is studied analytically for the Ising model. Using this method we give predictions for the 2d bond percolation. Finally we discuss how the method can be applied to random systems
Neutral currents and electromagnetic renormalization of the vector part of neutrino weak interaction
International Nuclear Information System (INIS)
Folomeshkin, V.N.
1976-01-01
The nature and properties of neutral currents in neutrino processes at high energies are theoretically investigated. Electronagmetic renormalization of diagonal ((νsub(e)e(νsub(e)e) and (νsub(μ)μ)(νsub(μ)μ)) and nondiagonal ((νsub(e)μ)(νsub(e)μ)) interactions is discussed in terms of the universal fourfermion interaction model. It is shown that electromagnetic renormalization of neutrino vector interaction caused an effective appearance of vector neutral currents with photon isotopic structure. The value for the interaction constant is unambigously defined by the ratio of the total cross-section for electron-positron annihilation into muonic pairs. Interaction (renormalization) constants for neutral currents are pointed out to be always smaller than interaction constants for charge currents
Renormalization-group decimation technique for spectra, wave-functions and density of states
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-09-01
The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)
Mutual information, neural networks and the renormalization group
Koch-Janusz, Maciej; Ringel, Zohar
2018-06-01
Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.
Renormalization group flows and continual Lie algebras
International Nuclear Information System (INIS)
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. 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, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund 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, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
Renormalization (and power counting) of effective field theories for the nuclear force
International Nuclear Information System (INIS)
Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.
2011-01-01
The most common scheme used to regularize the Lippman-Schwinger (LS) equation is to introduce a sharp or smooth regularizing function that suppresses the contributions from the potential matrix elements for momenta larger than a given cutoff scale, which separates high-energy/short-distance scales and low-energy/long-distance scales, thus eliminating the ultraviolet divergences in the momentum integrals. Then, one needs determine the strengths of the contact interactions, the so called low-energy constants (LEC), by fitting a set of low-energy scattering data. Once the LECs are fixed for a given cutoff, the LS equation can be solved to evaluate other observables. Such a procedure, motivated by Wilsons renormalization group, relies on the fundamental premise of EFT that physics at low-energy/long-distance scales is insensitive with respect to the details of the dynamics at high-energy/short-distance scales, i.e. the relevant high-energy/short- distance effects for describing the low-energy observables can be captured in the cutoff-dependent LECs. The NN interaction can be considered properly renormalized when the calculated observables are independent of the cutoff scale within the range of validity of the ChEFT or involves a small residual cutoff dependence due to the truncation of the chiral expansion. In the language of Wilsons renormalization group, this means that the LECs must run with the cutoff scale in such a way that the scattering amplitude becomes renormalization group invariant (RGI). Here we consider pionless EFT up to NNLO and chiral EFT up to NNLO and use a subtractive renormalization scheme to describe the NN scattering channels with. We fix the strength of the contact interactions at a reference scale, chosen to be the one the provides the best fit, and then evolve the driving terms with a non-relativistic Callan-Symanzik equation to slide the renormalization scale. By computing phase shift relative differences, we show that the method is RGI. We
One-loop renormalization of Lee-Wick gauge theory
International Nuclear Information System (INIS)
Grinstein, Benjamin; O'Connell, Donal
2008-01-01
We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
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
The density-matrix renormalization group: a short introduction.
Schollwöck, Ulrich
2011-07-13
The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.
Generalized Callan-Symanzik equations and the Renormalization Group
International Nuclear Information System (INIS)
MacDowell, S.W.
1975-01-01
A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg
Optimal renormalization scales and commensurate scale relations
International Nuclear Information System (INIS)
Brodsky, S.J.; Lu, H.J.
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 - 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 α V which is measurable in lattice gauge theory
International Nuclear Information System (INIS)
Brown, M.R.; Ottewill, A.C.
1986-01-01
We present the symmetric Hadamard representation for scalar and photon Feynman Green's functions. We use these representations to give a simple definition for their associated renormalized stress tensors. We investigate the connection between the accuracy of the WKB approximation and the vanishing of the trace anomaly for these fields. We show that, although for scalars there is a direct connection, this is not true for photons, and we discuss the relevance of these results to the approximation of renormalized stress tensors in static Einstein space-times
E-cigarette marketing and older smokers: road to renormalization.
Cataldo, Janine K; Petersen, Anne Berit; Hunter, Mary; Wang, Julie; Sheon, Nicolas
2015-05-01
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. 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. 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. 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.
Phenomenological renormalization of free nucleon-nucleon interaction
International Nuclear Information System (INIS)
Prakash, M.; Waghmare, Y.R.; Mehrotra, I.
1976-01-01
Low-lying spectra of 6 Li, 18 F, 18 O, 42 Sc, 42 Ca, 58 Ni and 92 Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly for T = 0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization fo the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lying T = 0 levels can be satisfactorily described if the SME in the 3 S 1 relative state are made (1+α) times their bare interaction value, where α is a constant to be determined from a comparison with experimental level energies. Similarly, for T = 1 levels, better agreement with the experimental results is obtained if a delta-function-plus-quadrupole interaction is added to the SME. (orig.) [de
Renormalization group procedure for potential −g/r2
Directory of Open Access Journals (Sweden)
S.M. Dawid
2018-02-01
Full Text Available Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.
International Nuclear Information System (INIS)
Manoukian, E.B.
1986-01-01
Generalized conditions (rules) are set up for the existence of the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space. These rules are generalizations of rules that have been set up earlier by us and hence are applicable to a larger class of graphs. The study is very general as the vanishing masses are led to vanish at different rates. All subtractions of renormalization are carried out directly in momentum space, about the origin, with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram
The Bogolyubov renormalization group in theoretical and mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1999-01-01
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part I) partially overlaps with corresponding text of my previous commemorative paper - see Ref. [6] in the list. At the same time the second part includes some fresh results in QFT (Sect. 2.1.) and summarizes (Sect. 2.4) an impressive recent progress of the 'QFT renormalization group' application in mathematical physics
Renormalization group aspects of 3-dimensional Pure U(1) lattice gauge theory
International Nuclear Information System (INIS)
Gopfert, M.; Mack, G.
1983-01-01
A few surprises in a recent study of the 3-dimensional pure U(1) lattice gauge theory model, from the point of view of the renormalization group theory, are discussed. Since the gauge group U(1) of this model is abelian, the model is subject to KramersWannier duality transformation. One obtains a ferromagnet with a global symmetry group Z. The duality transformation shows that the surface tension alpha of the model equals the strong tension of the U(1) gauge model. A theorem to represent the true asymptotic behaviour of alpha is derived. A second theorem considers the correlation functions. Discrepiancies between the theorems result in a solution that ''is regarded as a catastrophe'' in renormalization group theory. A lesson is drawn: To choose a good block spin in a renormalization group procedure, know what the low lying excitations of the theory are, to avoid integrating some of them by mischief
Improved Epstein-Glaser Renormalization in Coordinate Space I. Euclidean Framework
International Nuclear Information System (INIS)
Gracia-Bondia, Jose M.
2003-01-01
In a series of papers, we investigate the reformulation of Epstein-Glaser renormalization in coordinate space, both in analytic and (Hopf) algebraic terms. This first article deals with analytical aspects. Some of the (historically good) reasons for the divorces of the Epstein-Glaser method, both from mainstream quantum field theory and the mathematical literature on distributions, are made plain; and overcome
Supersymmetric renormalization prescription in N=4 super-Yang-Mills theory
International Nuclear Information System (INIS)
Baulieu, Laurent; Bossard, Guillaume
2006-01-01
Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry
Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory
2017-04-01
The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.
International Nuclear Information System (INIS)
Antonov, N V
2006-01-01
Recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field-theoretic renormalization group (RG) and operator product expansion (OPE). In that approach, the anomalous scaling is established as a consequence of the existence in the corresponding field-theoretic models of an infinite number of 'dangerous' composite fields (operators) with negative critical dimensions, which are identified with the anomalous exponents. This allows one to calculate the exponents in a systematic perturbation expansion, similar to the ε expansion in the theory of critical phenomena. The RG and OPE approach is presented in a self-contained way for the example of a passive scalar field (temperature, concentration of an impurity, etc) advected by a self-similar Gaussian velocity ensemble with vanishing correlation time, the so-called Kraichnan's rapid-change model, where the anomalous exponents are known up to order O(ε 3 ). Effects of anisotropy, compressibility and the correlation time of the velocity field are discussed. Passive advection by non-Gaussian velocity field governed by the stochastic Navier-Stokes equation and passively advected vector (e.g. magnetic) fields are considered
Energy Technology Data Exchange (ETDEWEB)
Palombi, F.
2007-06-15
We carry out the renormalization and the Symanzik O(a)-improvement programme for the static vector current in quenched lattice QCD. The scale independent ratio of the renormalization constants of the static vector and axial currents is obtained non-perturbatively from an axial Ward identity with Wilson-type light quarks and various lattice discretizations of the static action. The improvement coefficients c{sub V}{sup stat} and b{sub V}{sup stat} are obtained up to O(g{sub 4}{sup 0})-terms by enforcing improvement conditions respectively on the axial Ward identity and a three-point correlator of the static vector current. A comparison between the non-perturbative estimates and the corresponding one-loop results shows a non-negligible effect of the O(g{sub 4}{sup 0})-terms on the improvement coefficients but a good accuracy of the perturbative description of the ratio of the renormalization constants. (orig.)
Renormalization of Extended QCD2
International Nuclear Information System (INIS)
Fukaya, Hidenori; Yamamura, Ryo
2015-01-01
Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region
Renormalization-group flows and charge transmutation in string theory
International Nuclear Information System (INIS)
Orlando, D.; Petropoulos, P.M.; Sfetsos, K.
2006-01-01
We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Computing the effective action with the functional renormalization group
Energy Technology Data Exchange (ETDEWEB)
Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)
2016-04-15
The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 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. (orig.)
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-invariant 1/N corrections to nontrival φ4 theory
International Nuclear Information System (INIS)
Smekal, L.v.; Langfeld, K.; Reinhardt, H.; Langbein, R.F.
1994-01-01
In the framework of path integral linearization techniques, the effective potential and the master field equation for massless φ 4 theory, in the modified loop expansion around the mean field, are derived up to next to leading order. In the O(N)-symmetric theory, these equations are equivalent to a subsummation of O(N) and order 1 diagrams. A renormalization prescription is proposed which is manifestly renormalization group invariant. The numerical results for the potential in next to leading order agree qualitatively well with the leading order ones. In particular, the nontrivial phase structure remains unchanged. Quantitatively, the corrections ar small for N much-gt 8, but even for N as small as one their essential effect is to modify the scaling coefficient β 0 in the Callan-Symanzik β function, in accordance with conventional loop expansions. The numerical results are best parametrized by scaling improved mean field formulas. Dimensional transmutation renders the overall (physical) mass scale M 0 , generated by a dynamical breaking of scale invariance, the only adjustable parameter of the theory. Renormalization group invariance of the numerical results is explicitly verified
Renormalization of gauge theories
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1975-04-01
Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semi-simple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independant from the parameters which define the gauge function [fr
Absence of renormalization group pathologies near the critical temperature. Two examples
International Nuclear Information System (INIS)
Haller, K.; Kennedy, T.
1996-01-01
We consider real-space renormalization group transformations for Ising-type systems which are formally defined by where T(σ, σ') is a probability kernel, i.e., Σ σ' T(σ, σ') = 1, for every configuration σ. For each choice of the block spin configuration σ', let μ σ' , be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional to T(σ, σ') exp[ -H(σ)]. We give a condition which is sufficient to imply that the renormalized Hamiltonian H' is defined. Roughly speaking, the condition is that the collection of measures μ σ' is in the high-temperature phase uniformly in the block spin configuration σ'. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacing b = 2 on the square lattice with β c and the Kadanoff transformation with parameter p on the triangular lattice in a subset of the β, p plane that includes values of β greater than β c
Rose, F.; Dupuis, N.
2018-05-01
We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.
Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.
2017-12-01
The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.
Goh, Segun; Lee, Keumsook; Choi, Moo Young; Fortin, Jean-Yves
2014-01-01
Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare) bus stops are transformed into a (renormalized) "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.
Directory of Open Access Journals (Sweden)
Segun Goh
Full Text Available Social systems have recently attracted much attention, with attempts to understand social behavior with the aid of statistical mechanics applied to complex systems. Collective properties of such systems emerge from couplings between components, for example, individual persons, transportation nodes such as airports or subway stations, and administrative districts. Among various collective properties, criticality is known as a characteristic property of a complex system, which helps the systems to respond flexibly to external perturbations. This work considers the criticality of the urban transportation system entailed in the massive smart card data on the Seoul transportation network. Analyzing the passenger flow on the Seoul bus system during one week, we find explicit power-law correlations in the system, that is, power-law behavior of the strength correlation function of bus stops and verify scale invariance of the strength fluctuations. Such criticality is probed by means of the scaling and renormalization analysis of the modified gravity model applied to the system. Here a group of nearby (bare bus stops are transformed into a (renormalized "block stop" and the scaling relations of the network density turn out to be closely related to the fractal dimensions of the system, revealing the underlying structure. Specifically, the resulting renormalized values of the gravity exponent and of the Hill coefficient give a good description of the Seoul bus system: The former measures the characteristic dimensionality of the network whereas the latter reflects the coupling between distinct transportation modes. It is thus demonstrated that such ideas of physics as scaling and renormalization can be applied successfully to social phenomena exemplified by the passenger flow.
Renormalization theory of beam-beam interaction in electron-positron colliders
International Nuclear Information System (INIS)
Chin, Y.H.
1989-07-01
This note is devoted to explaining the essence of the renormalization theory of beam-beam interaction for carrying out analytical calculations of equilibrium particle distributions in electron-positron colliding beam storage rings. Some new numerical examples are presented such as for betatron tune dependence of the rms beam size. The theory shows reasonably good agreements with the results of computer simulations. 5 refs., 6 figs
International Nuclear Information System (INIS)
Groot Nibbelink, Stefan; Hillenbach, Mark
2005-01-01
We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S 1 /Z 2 . This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T 2 /Z N orbifolds using supergraph techniques in six dimensions. On general Z N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z 2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.
Pade expansion and the renormalization of nucleon-nucleon scattering
International Nuclear Information System (INIS)
Yang Jifeng; Huang Jianhua; Liu Dan
2006-01-01
The importance of imposing physical boundary conditions on the T-matrix to remove to nonperturbative renormalization prescription dependence is stressed and demonstrated in two diagonal channels 1 P 1 and 1 D 2 , with the help of Pade expansion. (authors)
On renormalization group flow in matrix model
International Nuclear Information System (INIS)
Gao, H.B.
1992-10-01
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
International Nuclear Information System (INIS)
Solin, J.
1988-01-01
The one-loop renormalization of the λφ 4 theory with a spontaneous breaking of its discrete (reflection) symmetry is analyzed. It is explicitly shown that it is not necessary to forcefully eliminate the linear counterterm in the shifted field (accomplished usually by shifting the vacuum expectation value of the field) in order to have the renormalized Lagrangian still formally invariant under the original discrete symmetry. It is further shown, using the normal-ordering procedure, that the renormalization carried out in the customary form completely wipes out the tadpole diagram contributions from the original Lagrangian. As a consequence, the same renormalized Lagrangian can be also obtained from the original bare Lagrangian which, however, has been normal-ordered and as such cannot cause the linear counterterm in the shifted field since now the tadpole diagrams are absent altogether. These analyses should support the view that the vacuum expectation value of the field is of a group-theoretical origin rather than a field-theoretical origin, and as such should not change independently of the shifted field in the course of renormalization
International Nuclear Information System (INIS)
Boyanovsky, Daniel; Vega, Hector J. de; Wang Shangyung
2003-01-01
The dc electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the real-time dependence of a dissipative kernel closely related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as secular terms that grow in time in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self-energy and vertex contributions to the collision term. We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling. This equation determines that the transport time scale is given by t tr =24 π/e 4 T ln(1/e). The solution of the Fokker-Planck equation approaches asymptotically the steady-state solution as ∼e -t/(4.038...t tr ) . The steady-state solution leads to the conductivity σ=15.698 T/e 2 ln(1/e) to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory
Renormalization group equations in the stochastic quantization scheme
International Nuclear Information System (INIS)
Pugnetti, S.
1987-01-01
We show that there exists a remarkable link between the stochastic quantization and the theory of critical phenomena and dynamical statistical systems. In the stochastic quantization of a field theory, the stochastic Green functions coverge to the quantum ones when the frictious time goes to infinity. We therefore use the typical techniques of the Renormalization Group equations developed in the framework of critical phenomena to discuss some features of the convergence of the stochastic theory. We are also able, in this way, to compute some dynamical critical exponents and give new numerical valuations for them. (orig.)
Renormalization of gauge fields models
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1974-01-01
A new approach to gauge field models is described. It is based on the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renormalization scheme making extensive use of the quantum action principle, and the Slavnov invariance. The quantum action principle being first summarized in the framework of the BPHZ is then applied to a global symmetry problem. The symmetry property of the gauge field Lagrangians in the tree approximation is exhibited, and the preservation of this property at the quantum level is discussed. The main results relative to the Abelian and SU(2) Higgs-Kibble models are briefly reviewed [fr
Energy Technology Data Exchange (ETDEWEB)
Johnston, S.; /Waterloo U. /SLAC; Lee, W.S.; /Stanford U., Geballe Lab. /SLAC; Nowadnick, E.A.; /SLAC /Stanford U., Phys. Dept.; Moritz, B.; /SLAC /North Dakota U.; Shen, Z.-X.; /Stanford U., Geballe Lab. /SLAC /Stanford U., Phys. Dept. /Stanford U., Appl. Phys. Dept.; Devereaux, T.P.; /Stanford U., Geballe Lab. /SLAC
2010-02-15
In this paper we present a review of bosonic renormalization effects on electronic carriers observed from angle-resolved photoemission spectra in the cuprates. Specifically, we discuss the viewpoint that these renormalizations represent coupling of the electrons to the lattice and review how materials dependence, such as the number of CuO{sub 2} layers, and doping dependence can be understood straightforwardly in terms of several aspects of electron-phonon coupling in layered correlated materials.
Quasi-renormalization of the axial vector model
International Nuclear Information System (INIS)
Schweda, M.
1979-01-01
Using the regulator-free BPHZL renormalization scheme the problem of anomalies in a massive axial vector meson model is reinvestigated. The Adler-Bardeen-Bell-Jackiw anomaly introduces some impressive modifications: the nontrivial self-energy and the counterterm of the longitudinal part of the axial vector field depend on the anomaly via the anomalous Ward identity. The investigations are based on a Fermi-type gauge. (author)
Quarkonia from charmonium and renormalization group equations
International Nuclear Information System (INIS)
Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.
1978-01-01
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.)
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
Renormalization group approach to causal bulk viscous cosmological models
International Nuclear Information System (INIS)
Belinchon, J A; Harko, T; Mak, M K
2002-01-01
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
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.
Renormalizing the kinetic energy operator in elementary quantum mechanics
International Nuclear Information System (INIS)
Coutinho, F A B; Amaku, M
2009-01-01
In this paper, we consider solutions to the three-dimensional Schroedinger equation of the form ψ(r) = u(r)/r, where u(0) ≠ 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.
The Bogolyubov renormalization group. Second English printing
International Nuclear Information System (INIS)
Shirkov, D.V.
1996-01-01
We begin with personal notes describing the atmosphere of 'Bogolyubov renormalization group' birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its application in mathematical physics. 58 refs
International Nuclear Information System (INIS)
Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua
2015-01-01
We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)
Holographic renormalization group and cosmology in theories with quasilocalized gravity
International Nuclear Information System (INIS)
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-01-01
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
Finite cluster renormalization group for disordered two-dimensional systems
International Nuclear Information System (INIS)
El Kenz, A.
1987-09-01
A new type of renormalization group theory using the generalized Callen identities is exploited in the study of the disordered systems. Bond diluted and frustrated Ising systems on a square lattice are analyzed with this new scheme. (author). 9 refs, 2 figs, 2 tabs
BPHZ renormalization in configuration space for the A4-model
Pottel, Steffen
2018-02-01
Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.
Renormalization ambiguities and conformal anomaly in metric-scalar backgrounds
International Nuclear Information System (INIS)
Asorey, M.; Berredo-Peixoto, G. de; Shapiro, I. L.
2006-01-01
We analyze the problem of the existing ambiguities in the conformal anomaly in theories with an external scalar field in curved backgrounds. In particular, we consider the anomaly of a self-interacting massive scalar field theory and of a Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of local nonminimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise
Energy Technology Data Exchange (ETDEWEB)
Ansel' m, A A; D' yakonov, D I [AN SSSR, Leningrad. Inst. Yadernoj Fiziki
1975-01-01
The mechanism of dynamic spontaneous breaking of the Coleman-Weinberg gauge invariance is discussed in which scalar fields assume nonzero mean values owing to quantum effects in higher orders of the perturbation theory. Group renormalization methods are used to study scalar electrodynamics and gauge theories similar to that of Yang and Mills; for these gauge theories it is established that by choosing proper constants it is possible to combine the acquisition of a mass by particles, owing to a dynamic violation of symmetry, with the asymptotic freedom of the theory. The symmetry violation is found to be closely related to infrared poles observed in effective charge for asymptotically free theories. The emerging masses of particles automatically cover these poles. It is proved that physical results due to symmetry violation do not depend, at least in the first non-trivial order of the perturbation theory, on the initial gauging of vector fields.
Phase structure of NJL model with weak renormalization group
Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi
2018-06-01
We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.
On Newton-Cartan local renormalization group and anomalies
Energy Technology Data Exchange (ETDEWEB)
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)
2016-11-28
Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.
On Newton-Cartan local renormalization group and anomalies
International Nuclear Information System (INIS)
Auzzi, Roberto; Baiguera, Stefano; Filippini, Francesco; Nardelli, Giuseppe
2016-01-01
Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.
Updated RENORM/MBR Predictions for Diffraction at the LHC
Goulianos, K
2015-01-01
Updated RENORM/MBR-model predictions of diffractive, total, and total-inelastic cross sections at the LHC are presented and compared with experimental results and predictions from other models. In addition, expectations for diffraction at the upcoming LHC run at √s = 13 TeV are discussed.
Perturbative renormalization and effective Langrangians in Φ44
International Nuclear Information System (INIS)
Keller, G.; Salmhofer, M.; Kopper, C.
1992-01-01
Polchinski's proof of the perturbative renormalizability of massive Euclidean Φ 4 4 is considerably simplified, in some respects clarified and extended to general renormalization conditions and Green's functions with arbitrary external momenta. Φ 3 4 and Φ 2 4 are also dealt with. Moreover we show that adding e.g. Φ≥ 5 type interactions to the bare Lagrangian, with coupling constants vanishing at least as some inverse power of the UV-cutoff, does not alter the Green's functions in the limit where the UV-cutoff is removed. Establishing the validity of the action principle in this formalism has not yet been possible, but some partial results are obtained. (orig.)
International Nuclear Information System (INIS)
Neves, A.G.M.
1988-01-01
The renormalization transformation e sup(-S 1) sup((B)) const. ζ e sup(-S o (A) - V(A)) δ (B-C sub(1) A) δ sub(Ax) (A)DA for the U(1) lattice gauge theory, where S sub(o) (A) is the gaussian fixed point of the transformation, V(A) is a gauge invariant perturbation, C sub(1) is the averaging operator and δ sub(Ax) (A) fixes the local axial gauge is studied via an equivalent renormalization transformation on the 2-forms F = dA. The transformation is linearized in the neighborhood of the fixed point and then diagonalized. (author)
International Nuclear Information System (INIS)
Cichy, Krzysztof; Adam Mickiewicz Univ., Poznan; Jansen, Karl; Korcyl, Piotr; Jagiellonian Univ., Krakow
2012-07-01
We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N f =2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
RENORMALIZATION FACTOR AND ODD-OMEGA GAP SINGLET SUPERCONDUCTIVITY
DOLGOV, OV; LOSYAKOV, VV
1994-01-01
Abrahams et al. [Phys. Rev. B 47 (1993) 513] have considered the possibility of a nonzero critical temperature of the superconductor transition to the state with odd-omega pp function and shown that the condition for it is the following inequality for the renormalization factor. Z (k, omega(n)) <1.
Renormalization of the Sine-Gordon model and nonconservation of the kink current
International Nuclear Information System (INIS)
Huang, K.; Polonyi, J.
1991-01-01
The authors of this paper renormalize the (1 + 1)-dimensional sine-Gordon model by placing it on a Euclidean lattice, and study the renormalization group flow. The authors start with a compactified theory with controllable vortex activity. In the continuum limit the theory has a phase in which the kink current is anomalous, with divergence given by the vortex density. The phase structure is quite complicated. Roughly speaking, the system is normal for small coupling T. At the Kosterlitz-Thouless point T = π/2, the current can become anomalous. At the Coleman point T = 8π either the current becomes anomalous or the theory becomes trivial
Propagators and renormalization transformations for lattice gauge theories. Pt. 2
International Nuclear Information System (INIS)
Balaban, T.
1984-01-01
We continue the studies of the Paper I and extend the results of this paper to operators defined by restrictions on different scales, or by renormalization transformations of different orders. (orig.)
International Nuclear Information System (INIS)
Lopez-Aguilar, F.; Costa-Quintana, J.
1992-01-01
In this paper, the authors give a method for obtaining the renormalized electronic structure of the Hubbard systems. The first step is the determination of the self-energy beyond the Hartree-Fock approximation. This self-energy is constructed from several dielectric response functions. The second step is the determination of the quasiparticle band structure calculation which is performed from an appropriate modification of the augmented plane wave method. The third step consists in the determination of the renormalized density of states deduced from the spectral functions. The analysis of the renormalized density of states of the strongly correlated systems leads to the conclusion that there exist three types of resonances in their electronic structures, the lower energy resonances (LER), the middle energy resonances (MER) and the upper energy resonances (UER). In addition, the authors analyze the conditions for which the Luttinger theorem is satisfied. All of these questions are determined in a characteristic example which allows to test the theoretical method
Zero Point Energy of Renormalized Wilson Loops
Hidaka, Yoshimasa; Pisarski, Robert D.
2009-01-01
The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero wh...
Dynamical renormalization group approach to relaxation in quantum field theory
International Nuclear Information System (INIS)
Boyanovsky, D.; Vega, H.J. de
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 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
On mass-shell parametric space renormalization of PHI3 theory in six dimensions
International Nuclear Information System (INIS)
Smith, A.W.
1977-05-01
An on mass shell, parametric space renormalization procedure for phi 3 theory in six dimensions is defined and its formal equivalence to the usual Lagrangian counter procedure demonstrated. Two loop contributions to the self-energy are used as an illustration of the method. (author)
Renormalization group analysis of the temperature dependent coupling constant in massless theory
International Nuclear Information System (INIS)
Yamada, Hirofumi.
1987-06-01
A general analysis of finite temperature renormalization group equations for massless theories is presented. It is found that in a direction where momenta and temperature are scaled up with their ratio fixed the coupling constant behaves in the same manner as in zero temperature and that asymptotic freedom at short distances is also maintained at finite temperature. (author)
International Nuclear Information System (INIS)
Bergstroem, Johannes; Ohlsson, Tommy; Zhang He
2011-01-01
We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Renormalization and scaling behaviour of eikonal perturbation theories. [Eikonal approximation
Energy Technology Data Exchange (ETDEWEB)
Din, A M [Chalmers Tekniska Hoegskola, Goeteborg (Sweden). Institutionen foer Teoretisk Fysik; Nielsen, N K [Aarhus Univ. (Denmark)
1975-01-04
Some observations on the renormalization and scaling behaviour of the charged-particle propagator in scalar quantum electrodynamics, in the ordinary eikonal approximation as well as in the eikonal perturbation theory, are reported. The conclusions indicate that scaling behaviour is not realized in the simple sense.
Fierz transformations and renormalization schemes for fourquark operators
Directory of Open Access Journals (Sweden)
Garron Nicolas
2018-01-01
Full Text Available It has been shown that the choice of renormalization scheme is crucial for four-quark operators, in particular for neutral kaon mixing beyond the Standard Model. In the context of SMOM schemes, the choice of projector is not unique and is part of the definition of the renormalisation scheme. I present the non-diagonal Fierz relations which relate some of these projectors.
Temperature renormalization group approach to spontaneous symmetry breaking
International Nuclear Information System (INIS)
Manesis, E.; Sakakibara, S.
1985-01-01
We apply renormalization group equations that describe the finite-temperature behavior of Green's functions to investigate thermal properties of spontaneous symmetry breaking. Specifically, in the O(N).O(N) symmetric model we study the change of symmetry breaking patterns with temperature, and show that there always exists the unbroken symmetry phase at high temperature, modifying the naive result of leading order in finite-temperature perturbation theory. (orig.)
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.
Momentum-subtraction renormalization techniques in curved space-time
International Nuclear Information System (INIS)
Foda, O.
1987-01-01
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
Matrix product density operators: Renormalization fixed points and boundary theories
Energy Technology Data Exchange (ETDEWEB)
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)
2017-03-15
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
International Nuclear Information System (INIS)
Monthus, Cécile
2015-01-01
For the quantum Ising chain, the self-dual block renormalization procedure of Fernandez-Pacheco (1979 Phys. Rev. D 19 3173) is known to reproduce exactly the location of the zero-temperature critical point and the correlation length exponent ν = 1. Recently, Miyazaki and Nishimori (2013 Phys. Rev. E 87 032154) have proposed to study the disordered quantum Ising model in dimensions d > 1 by applying the Fernandez-Pacheco procedure successively in each direction. To avoid the inequivalence of directions of their approach, we propose here an alternative procedure where the d directions are treated on the same footing. For the pure model, this leads to the correlation length exponents ν ≃ 0.625 in d = 2 (to be compared with the 3D classical Ising model exponent ν ≃ 0.63) and ν ≃ 0.5018 (to be compared with the 4D classical Ising model mean-field exponent ν = 1/2). For the disordered model in dimension d = 2, either ferromagnetic or spin-glass, the numerical application of the renormalization rules to samples of linear size L = 4096 yields that the transition is governed by an Infinite Disorder Fixed Point, with the activated exponent ψ ≃ 0.65, the typical correlation exponent ν typ ≃ 0.44 and the finite-size correlation exponent ν FS ≃ 1.25. We discuss the similarities and differences with the Strong Disorder Renormalization results. (paper)
Renormalized thermodynamic entropy of black holes in higher dimensions
International Nuclear Information System (INIS)
Kim, S.P.; Kim, S.K.; Soh, K.; Yee, J.H.
1997-01-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstroem black hole and compute the matter field contribution to the Bekenstein-Hawking entropy by using the Pauli-Villars regularization method. We find that the matter field contribution to the black hole entropy does not, in general, yield the correct renormalization of the gravitational coupling constants. In particular, we show that the matter field contribution in odd dimensions does not give the term proportional to the area of the black hole event horizon. copyright 1997 The American Physical Society
Dynamical renormalization group resummation of finite temperature infrared divergences
International Nuclear Information System (INIS)
Boyanovsky, D.; Vega, H.J. de; Boyanovsky, D.; Simionato, M.; Holman, R.; Simionato, M.
1999-01-01
We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e -αampersandhthinsp;Tampersandhthinsp;tampersandhthinsp;ln[t/t 0 ] for hard momentum charged excitations. This is in contrast with the usual quasiparticle interpretation of charged collective excitations at finite temperature in the sense of exponential relaxation of a narrow width resonance for which the width is the imaginary part of the self-energy on shell. In the case of narrow resonances away from thresholds, this approach leads to the usual exponential relaxation. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that transcends the conceptual limitations of the quasiparticle picture and other types of resummation schemes. copyright 1999 The American Physical Society
Renormalization group equations with multiple coupling constants
International Nuclear Information System (INIS)
Ghika, G.; Visinescu, M.
1975-01-01
The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given
Construction of renormalized coefficient functions of the Feynman diagrams by means of a computer
International Nuclear Information System (INIS)
Tarasov, O.V.
1978-01-01
An algorithm and short description of computer program, written in SCHOONSCHIP, are given. The program is assigned for construction of integrands of renormalized coefficient functions of the Feynman diagrams in scalar theories in the case of arbitrary subtraction point. For the given Feynman graph computer completely realizes the R-operation of Bogolubov-Parasjuk and gives the result as an integral over Feynman parameters. With the help of the program the time construction of the whole renormalized coefficient function is equal approximately 30 s on the CDC-6500 computer
Monthus, Cécile
2017-07-01
When random quantum spin chains are submitted to some periodic Floquet driving, the eigenstates of the time-evolution operator over one period can be localized in real space. For the case of periodic quenches between two Hamiltonians (or periodic kicks), where the time-evolution operator over one period reduces to the product of two simple transfer matrices, we propose a block-self-dual renormalization procedure to construct the localized eigenstates of the Floquet dynamics. We also discuss the corresponding strong disorder renormalization procedure, that generalizes the RSRG-X procedure to construct the localized eigenstates of time-independent Hamiltonians.
Nonthermal fixed points and the functional renormalization group
International Nuclear Information System (INIS)
Berges, Juergen; Hoffmeister, Gabriele
2009-01-01
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
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Renormalized plasma turbulence theory: A quasiparticle picture
International Nuclear Information System (INIS)
DuBois, D.F.
1981-01-01
A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation
Conditions for the absence of infinite renormalization in masses and coupling constants
International Nuclear Information System (INIS)
Terrab, E.S.C.
1985-01-01
A model of scalar, pseudo-scalar and spin 1/2 particle interaction is studied. After reformulation of the problem in function of auxiliary fields, perturbative calculations up to one loop are developed, finding out certain relations among characteristics constants of system, which assure (until the considered order) the absence of infinite renormalization in masses and coupling constants. (M.C.K.) [pt
Renormalization of self-consistent Schwinger-Dyson equations at finite temperature
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2002-01-01
We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (orig.)
Real-space renormalization group approach to driven diffusive systems
Energy Technology Data Exchange (ETDEWEB)
Hanney, T [SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ (United Kingdom); Stinchcombe, R B [Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2006-11-24
We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.
Real-space renormalization group approach to driven diffusive systems
International Nuclear Information System (INIS)
Hanney, T; Stinchcombe, R B
2006-01-01
We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase
A renormalization group study of persistent current in a quasiperiodic ring
Energy Technology Data Exchange (ETDEWEB)
Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)
2014-04-01
We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.
Practical algebraic renormalization
International Nuclear Information System (INIS)
Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias
2001-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage
1976-01-01
The transverse correlation range ξ and the susceptibility in the critical region has been measured by neutron scattering. A special technique required to resolve the superdiverging longitudinal correlation range has been utilized. The results for ξ together with existing specific-heat data are in...... are in remarkable agreement with the renormalization group theory of systems with marginal dimensionality. The ratio between the susceptibility amplitudes above and below Tc was found to be 2 in accordance with renormalization-group and meanfield theory....
Functional renormalization group study of fluctuation effects in fermionic superfluids
Energy Technology Data Exchange (ETDEWEB)
Eberlein, Andreas
2013-03-22
This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature
Hanasoge, Shravan; Agarwal, Umang; Tandon, Kunj; Koelman, J. M. Vianney A.
2017-09-01
Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.
On the perturbative renormalization of four-quark operators for new physics
Energy Technology Data Exchange (ETDEWEB)
Papinutto, M. [Roma Univ. (Italy). Dipt. di Fisica; INFN, Sezione di Roma (Italy); Pena, C. [Univ. Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC; Preti, D. [Univ. Autonoma de Madrid (Spain). Inst. de Fisica Teorica UAM-CSIC
2017-06-15
We discuss the renormalization properties of the full set of ΔF = 2 operators involved in BSM processes, including the definition of RGI versions of operators that exhibit mixing under RG transformations. As a first step for a fully non-perturbative determination of the scale-dependent renormalization factors and their runnings, we introduce a family of appropriate Schroedinger Functional schemes, and study them in perturbation theory. This allows, in particular, to determine the NLO anomalous dimensions of all ΔF = 1,2 operators in these schemes. Finally, we discuss the systematic uncertainties related to the use of NLO perturbation theory for the RG running of four-quark operators to scales in the GeV range, in both our SF schemes and standard MS and RI-MOM schemes. Large truncation effects are found for some of the operators considered. (orig.)
Renormalization group flow of entanglement entropy on spheres
Energy Technology Data Exchange (ETDEWEB)
Ben-Ami, Omer; Carmi, Dean [Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and Astronomy,Tel-Aviv University, Ramat-Aviv 69978 (Israel); Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)
2015-08-12
We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2,3,4. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal ‘area law’ for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.
Zero-temperature renormalization of the 2D transverse Ising model
International Nuclear Information System (INIS)
Kamieniarz, G.
1982-08-01
A zero-temperature real-space renormalization-group method is applied to the transverse Ising model on planar hexagonal, triangular and quadratic lattices. The critical fields and the critical exponents describing low-field large-field transition are calculated. (author)
Studies in the renormalization-prescription dependence of perturbative calculations
International Nuclear Information System (INIS)
Celmaster, W.; Sivers, D.
1981-01-01
Now that the quantitative testing of perturbative quantum chromodynamics (QCD) has become a major experimental and theoretical effort, it is important to understand the renormalization-prescription dependence of perturbative calculations. We stress the phenomenological importance of finding a definition of the QCD expansion parameter which reduces the magnitude of high-order corrections. We give explicit arguments suggesting that a choice of coupling based on momentum-space subtraction can be phenomenologically useful. Examples from QCD and QED are used to illustrate these arguments, and we also discuss possibilities for refining them
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.
Migdal-Kadanoff renormalization group for the Z(5) model
International Nuclear Information System (INIS)
Baltar, V.L.V.; Carneiro, G.M.; Pol, M.E.; Zagury, N.
1984-01-01
The Migdal-Kadanoff renormalization group methods is used to calculate the phase diagram of the AF Z(5) model. It is found that this scheme simulates a fixed line which it is interpreted as the locus of attraction of a critical phase. This result is in reasonable agreement with the predictions of Monte Carlo simulations. (Author) [pt
Renormalization group approach to Sudakov resummation in prompt photon production
International Nuclear Information System (INIS)
Bolzoni, Paolo; Forte, Stefano; Ridolfi, Giovanni
2005-01-01
We prove the all-order exponentiation of soft logarithmic corrections to prompt photon production in hadronic collisions, by generalizing an approach previously developed in the context of Drell-Yan production and deep-inelastic scattering. We show that all large logs in the soft limit can be expressed in terms of two dimensionful variables, and we use the renormalization group to resum them. The resummed results that we obtain are more general though less predictive than those proposed by other groups, in that they can accommodate for violations of Sudakov factorization
A renormalization group theory of cultural evolution
Fath, Gabor; Sarvary, Miklos
2003-01-01
We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequa...
Bulk renormalization and particle spectrum in codimension-two brane worlds
International Nuclear Information System (INIS)
Salvio, Alberto
2013-01-01
We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).
Renormalization as an extension problem on the Count our ordered formalism in FFTF
Energy Technology Data Exchange (ETDEWEB)
Franco, D.H.T. [Centro de Estudos de Fisica Teorica (CEFT), Belo Horizonte, MG (Brazil); Acebal, J.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Teoria de Campos e Particulas; Grupo de Fisica Teorica Jose Leite Lopes (GFT-JLL), Petropolis, RJ (Brazil)
2003-06-01
From a distributional-theoretical framework, we make efforts in order to fill a gap in the series of studies which discuss the inheritance of the renormalization behaviour of a finite temperature field theory (FTFT) from the analogous version in quantum field theory (QFT) at T=0. Renormalization is treated as a distributional extension problem having the mathematical structure disentangled as much as possible from the physical aspects. The purely technical details essential for the discussion are briefly reviewed in a handle manner for further theoretical physics applications. The analysis elucidates some qualitative and quantitative distinctions concerning the divergences in the perturbation series when it is considered the FTFT version associated to a given QFT. Despite the differences, it turns clear the reason why the leading ultraviolet behaviour keeps unaffected when it is considered the FTFT version associated to a given QFT. The study is model independent and the approach allows one to consider the FTFT both imaginary and real time formalism at once in a unified way in the contour ordered formalism. (author)
Blossier, BenoÃ®t.; Brinet, Mariane; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas
2015-06-01
We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator O44 are also presented.
Renormalization of the axial-vector current in QCD
International Nuclear Information System (INIS)
Chiu, C.B.; Pasupathy, J.; Wilson, S.L.
1985-01-01
Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant G/sub A/, as well as the Cabibbo coupling constants in the SU 3 -symmetric limit (m/sub s/ = 0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU 3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be roughly-equal0, or D/(F+D)roughly-equal(7/12). .AE
Gauge mediation scenario with hidden sector renormalization in MSSM
International Nuclear Information System (INIS)
Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika
2010-01-01
We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5 minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.
Gauge mediation scenario with hidden sector renormalization in MSSM
Arai, Masato; Kawai, Shinsuke; Okada, Nobuchika
2010-02-01
We study the hidden sector effects on the mass renormalization of a simplest gauge-mediated supersymmetry breaking scenario. We point out that possible hidden sector contributions render the soft scalar masses smaller, resulting in drastically different sparticle mass spectrum at low energy. In particular, in the 5+5¯ minimal gauge-mediated supersymmetry breaking with high messenger scale (that is favored by the gravitino cold dark matter scenario), we show that a stau can be the next lightest superparticle for moderate values of hidden sector self-coupling. This provides a very simple theoretical model of long-lived charged next lightest superparticles, which imply distinctive signals in ongoing and upcoming collider experiments.
Potts ferromagnet correlation length in hypercubic lattices: Renormalization - group approach
International Nuclear Information System (INIS)
Curado, E.M.F.; Hauser, P.R.
1984-01-01
Through a real space renormalization group approach, the q-state Potts ferromagnet correlation length on hierarchical lattices is calculated. These hierarchical lattices are build in order to simulate hypercubic lattices. The high-and-low temperature correlation length asymptotic behaviours tend (in the Ising case) to the Bravais lattice correlation length ones when the size of the hierarchical lattice cells tends to infinity. It is conjectured that the asymptotic behaviours several values of q and d (dimensionality) so obtained are correct. Numerical results are obtained for the full temperature range of the correlation length. (Author) [pt
Camargo, Manuel; Téllez, Gabriel
2008-04-07
The renormalized charge of a simple two-dimensional model of colloidal suspension was determined by solving the hypernetted chain approximation and Ornstein-Zernike equations. At the infinite dilution limit, the asymptotic behavior of the correlation functions is used to define the effective interactions between the components of the system and these effective interactions were compared to those derived from the Poisson-Boltzmann theory. The results we obtained show that, in contrast to the mean-field theory, the renormalized charge does not saturate, but exhibits a maximum value and then decays monotonically as the bare charge increases. The results also suggest that beyond the counterion layer near to the macroion surface, the ionic cloud is not a diffuse layer which can be handled by means of the linearized theory, as the two-state model claims, but a more complex structure is settled by the correlations between microions.
Energy Technology Data Exchange (ETDEWEB)
Zinn-Justin, J
2003-08-01
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.)
Nezir, Veysel; Mustafa, Nizami
2017-04-01
In 2008, P.K. Lin provided the first example of a nonreflexive space that can be renormed to have fixed point property for nonexpansive mappings. This space was the Banach space of absolutely summable sequences l1 and researchers aim to generalize this to c0, Banach space of null sequences. Before P.K. Lin's intriguing result, in 1979, Goebel and Kuczumow showed that there is a large class of non-weak* compact closed, bounded, convex subsets of l1 with fixed point property for nonexpansive mappings. Then, P.K. Lin inspired by Goebel and Kuczumow's ideas to give his result. Similarly to P.K. Lin's study, Hernández-Linares worked on L1 and in his Ph.D. thesis, supervisored under Maria Japón, showed that L1 can be renormed to have fixed point property for affine nonexpansive mappings. Then, related questions for c0 have been considered by researchers. Recently, Nezir constructed several equivalent norms on c0 and showed that there are non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings. In this study, we construct a family of equivalent norms containing those developed by Nezir as well and show that there exists a large class of non-weakly compact closed, bounded, convex subsets of c0 with fixed point property for affine nonexpansive mappings.
Energy Technology Data Exchange (ETDEWEB)
Cichy, Krzysztof [DESY, Zeuthen (Germany). NIC; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [DESY, Zeuthen (Germany). NIC; Korcyl, Piotr [DESY, Zeuthen (Germany). NIC; Jagiellonian Univ., Krakow (Poland). M. Smoluchowski Inst. of Physics
2012-07-15
We present results of a lattice QCD application of a coordinate space renormalization scheme for the extraction of renormalization constants for flavour non-singlet bilinear quark operators. The method consists in the analysis of the small-distance behaviour of correlation functions in Euclidean space and has several theoretical and practical advantages, in particular: it is gauge invariant, easy to implement and has relatively low computational cost. The values of renormalization constants in the X-space scheme can be converted to the MS scheme via 4-loop continuum perturbative formulae. Our results for N{sub f}=2 maximally twisted mass fermions with tree-level Symanzik improved gauge action are compared to the ones from the RI-MOM scheme and show full agreement with this method. (orig.)
Renormalization effects on neutrino--electron scattering in the Weinberg-Salam theory of leptons
International Nuclear Information System (INIS)
Salomonson, P.; Ueda, Y.
1975-01-01
The renormalization program for nu-bar/sub mu/-e (or ν/sub mu/-e) scattering is formulated in the Weinberg-Salam theory. The explicit calculation is carried out in the one-loop approximation. With the aid of the continuous-dimension regularization method, both ultraviolet and infrared divergences can be removed in the unitary gauge. Numerical results are discussed
Ding, Mingnan; Lu, Bing-Sui; Xing, Xiangjun
2016-10-01
Self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a m:-n electrolyte. A perturbation series is developed in terms of g=4πκb, where band1/κ are Bjerrum length and bare Debye length, respectively. To the zeroth order, we obtain the nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes (m≠n), the first order (one-loop) correction to mean potential contains a secular term, which indicates the breakdown of the regular perturbation method. Using a renormalizaton group transformation, we remove the secular term and obtain a globally well-behaved one-loop approximation with a renormalized Debye length and a renormalized surface charge density. Furthermore, we find that if the counterions are multivalent, the surface charge density is renormalized substantially downwards and may undergo a change of sign, if the bare surface charge density is sufficiently large. Our results agrees with large MC simulation even when the density of electrolytes is relatively high.
Renormalization group summation of Laplace QCD sum rules for scalar gluon currents
Directory of Open Access Journals (Sweden)
Farrukh Chishtie
2016-03-01
Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.
Simultaneous analysis in renormalization and factorization scheme dependences in perturbative QCD
International Nuclear Information System (INIS)
Nakkagawa, Hisao; Niegawa, Akira.
1983-01-01
Combined and thorough investigations of both the factorization and the renormalization scheme dependences of perturbative QCD calculations are given. Our findings are that (i) by introducing a multiscale-dependent coupling the simultaneous parametrization of both scheme-dependences can be accomplished, (ii) Stevenson's optimization method works quite well so that it gives a remarkable prediction which forces us to exponentiate ''everything'' with uncorrected subprocess cross sections, and (iii) the perturbation series in QCD may converge when Stevenson's principle of minimal sensitivity is taken into account at each order of perturbative approximation. (author)
Renormalization and radiative corrections to masses in a general Yukawa model
Fox, M.; Grimus, W.; Löschner, M.
2018-01-01
We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields φa, general Yukawa couplings and a ℤ4 symmetry that forbids linear and trilinear terms in the scalar potential. Moreover, fermions become massive only after spontaneous symmetry breaking of the ℤ4 symmetry by vacuum expectation values (VEVs) of the φa. Introducing the shifted fields ha whose VEVs vanish, MS¯ renormalization of the parameters of the unbroken theory suffices to make the theory finite. However, in this way, beyond tree level it is necessary to perform finite shifts of the tree-level VEVs, induced by the finite parts of the tadpole diagrams, in order to ensure vanishing one-point functions of the ha. Moreover, adapting the renormalization scheme to a situation with many scalars and VEVs, we consider the physical fermion and scalar masses as derived quantities, i.e. as functions of the coupling constants and VEVs. Consequently, the masses have to be computed order by order in a perturbative expansion. In this scheme, we compute the self-energies of fermions and bosons and show how to obtain the respective one-loop contributions to the tree-level masses. Furthermore, we discuss the modification of our results in the case of Dirac fermions and investigate, by way of an example, the effects of a flavor symmetry group.
Cosmological constant problem and renormalized vacuum energy density in curved background
Energy Technology Data Exchange (ETDEWEB)
Kohri, Kazunori [Theory Center, IPNS, KEK, Tsukuba 305-0801, Ibaraki (Japan); Matsui, Hiroki, E-mail: kohri@post.kek.jp, E-mail: matshiro@post.kek.jp [The Graduate University of Advanced Studies (Sokendai), Tsukuba 305-0801, Ibaraki (Japan)
2017-06-01
The current vacuum energy density observed as dark energy ρ{sub dark}≅ 2.5×10{sup −47} GeV{sup 4} is unacceptably small compared with any other scales. Therefore, we encounter serious fine-tuning problem and theoretical difficulty to derive the dark energy. However, the theoretically attractive scenario has been proposed and discussed in literature: in terms of the renormalization-group (RG) running of the cosmological constant, the vacuum energy density can be expressed as ρ{sub vacuum}≅ m {sup 2} H {sup 2} where m is the mass of the scalar field and rather dynamical in curved spacetime. However, there has been no rigorous proof to derive this expression and there are some criticisms about the physical interpretation of the RG running cosmological constant. In the present paper, we revisit the RG running effects of the cosmological constant and investigate the renormalized vacuum energy density in curved spacetime. We demonstrate that the vacuum energy density described by ρ{sub vacuum}≅ m {sup 2} H {sup 2} appears as quantum effects of the curved background rather than the running effects of cosmological constant. Comparing to cosmological observational data, we obtain an upper bound on the mass of the scalar fields to be smaller than the Planck mass, m ∼< M {sub Pl}.
General renormalized statistical approach with finite cross-field correlations
International Nuclear Information System (INIS)
Vakulenko, M.O.
1992-01-01
The renormalized statistical approach is proposed, accounting for finite correlations of potential and magnetic fluctuations. It may be used for analysis of a wide class of nonlinear model equations describing the cross-correlated plasma states. The influence of a cross spectrum on stationary potential and magnetic ones is investigated. 10 refs. (author)
The functional renormalization group for interacting quantum systems with spin-orbit interaction
International Nuclear Information System (INIS)
Grap, Stephan Michael
2013-01-01
We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer
Renormalization of loop functions for all loops
International Nuclear Information System (INIS)
Brandt, R.A.; Neri, F.; Sato, M.
1981-01-01
It is shown that the vacuum expectation values W(C 1 ,xxx, C/sub n/) of products of the traces of the path-ordered phase factors P exp[igcontour-integral/sub C/iA/sub μ/(x)dx/sup μ/] are multiplicatively renormalizable in all orders of perturbation theory. Here A/sub μ/(x) are the vector gauge field matrices in the non-Abelian gauge theory with gauge group U(N) or SU(N), and C/sub i/ are loops (closed paths). When the loops are smooth (i.e., differentiable) and simple (i.e., non-self-intersecting), it has been shown that the generally divergent loop functions W become finite functions W when expressed in terms of the renormalized coupling constant and multiplied by the factors e/sup -K/L(C/sub i/), where K is linearly divergent and L(C/sub i/) is the length of C/sub i/. It is proved here that the loop functions remain multiplicatively renormalizable even if the curves have any finite number of cusps (points of nondifferentiability) or cross points (points of self-intersection). If C/sub γ/ is a loop which is smooth and simple except for a single cusp of angle γ, then W/sub R/(C/sub γ/) = Z(γ)W(C/sub γ/) is finite for a suitable renormalization factor Z(γ) which depends on γ but on no other characteristic of C/sub γ/. This statement is made precise by introducing a regularization, or via a loop-integrand subtraction scheme specified by a normalization condition W/sub R/(C-bar/sub γ/) = 1 for an arbitrary but fixed loop C-bar/sub γ/. Next, if C/sub β/ is a loop which is smooth and simple except for a cross point of angles β, then W(C/sub β/) must be renormalized together with the loop functions of associated sets S/sup i//sub β/ = ]C/sup i/ 1 ,xxx, C/sup i//sub p/i] (i = 2,xxx,I) of loops C/sup i//sub q/ which coincide with certain parts of C/sub β/equivalentC 1 1 . Then W/sub R/(S/sup i//sub β/) = Z/sup i/j(β)W(S/sup j//sub β/) is finite for a suitable matrix Z/sup i/j
Angle, J. Scott; McGrath, Stephen P.; Chaney, Rufus L.
1991-01-01
A new growth medium which closely approximates the composition of the soil solution is presented. This soil solution equivalent (SSE) medium contains the following components (millimolar): NO3, 2.5; NH4, 2.5; HPO4, 0.005; Na, 2.5; Ca, 4.0; Mg, 2.0; K, 0.503; Cl, 4.0; SO4, 5.0; ethylenediamine-di(o-hydroxyphenylacetic acid), 0.02; and MES [2-(N-morpholino)ethanesulfonic acid] (to maintain the pH at 6.0), 10, plus 0.1% arabinose. The advantages of the SSE medium are discussed. PMID:16348614
Renormalization and applications of baryon distribution amplitudes in QCD
International Nuclear Information System (INIS)
Rohrwild, Juergen Holger
2009-01-01
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 * (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 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.)
International Nuclear Information System (INIS)
Werner, Gerhard
2013-01-01
The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations
Energy Technology Data Exchange (ETDEWEB)
Ma, Hong -Hao [Chongqing Univ., Chongqing (People' s Republic of China); Wu, Xing -Gang [Chongqing Univ., Chongqing (People' s Republic of China); Ma, Yang [Chongqing Univ., Chongqing (People' s Republic of China); Brodsky, Stanley J. [Stanford Univ., Stanford, CA (United States); Mojaza, Matin [KTH Royal Inst. of Technology and Stockholm Univ., Stockholm (Sweden)
2015-05-26
A key problem in making precise perturbative QCD (pQCD) predictions is how to set the renormalization scale of the running coupling unambiguously at each finite order. The elimination of the uncertainty in setting the renormalization scale in pQCD will greatly increase the precision of collider tests of the Standard Model and the sensitivity to new phenomena. Renormalization group invariance requires that predictions for observables must also be independent on the choice of the renormalization scheme. The well-known Brodsky-Lepage-Mackenzie (BLM) approach cannot be easily extended beyond next-to-next-to-leading order of pQCD. Several suggestions have been proposed to extend the BLM approach to all orders. In this paper we discuss two distinct methods. One is based on the “Principle of Maximum Conformality” (PMC), which provides a systematic all-orders method to eliminate the scale and scheme ambiguities of pQCD. The PMC extends the BLM procedure to all orders using renormalization group methods; as an outcome, it significantly improves the pQCD convergence by eliminating renormalon divergences. An alternative method is the “sequential extended BLM” (seBLM) approach, which has been primarily designed to improve the convergence of pQCD series. The seBLM, as originally proposed, introduces auxiliary fields and follows the pattern of the β0-expansion to fix the renormalization scale. However, the seBLM requires a recomputation of pQCD amplitudes including the auxiliary fields; due to the limited availability of calculations using these auxiliary fields, the seBLM has only been applied to a few processes at low orders. In order to avoid the complications of adding extra fields, we propose a modified version of seBLM which allows us to apply this method to higher orders. As a result, we then perform detailed numerical comparisons of the two alternative scale-setting approaches by investigating their predictions for the annihilation cross section ratio R
The analytic renormalization group
Directory of Open Access Journals (Sweden)
Frank Ferrari
2016-08-01
Full Text Available 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=2πk/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.
On the renormalization group flow in two dimensional superconformal models
International Nuclear Information System (INIS)
Ahn, Changrim; Stanishkov, Marian
2014-01-01
We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM p for p≫1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow the renormalization scheme proposed in [1]. As a result we obtained the anomalous dimensions of certain NS and Ramond fields. It turns out that the linear combination expressing the infrared limit of these fields in term of the IR theory SM p−2 is exactly the same as those of the nonsupersymmetric minimal theory
Source Localization by Entropic Inference and Backward Renormalization Group Priors
Directory of Open Access Journals (Sweden)
Nestor Caticha
2015-04-01
Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.
Chaotic renormalization group approach to disordered systems
International Nuclear Information System (INIS)
Oliveira, P.M.C. de; Continentino, M.A.; Makler, S.S.; Anda, E.V.
1984-01-01
We study the eletronic properties of the disordered linear chain using a technique previously developed by some of the authors for an ordered chain. The equations of motion for the one electron Green function are obtained and the configuration average is done according to the GK scheme. The dynamical problem is transformed, using a renormalization group procedure, into a bidimensional map. The properties of this map are investigated and related to the localization properties of the eletronic system. (Author) [pt
Phenomenological renormalization of free nucleon-nucleon interaction. [Sussex matrix elements
Energy Technology Data Exchange (ETDEWEB)
Prakash, M; Waghmare, Y R [Indian Inst. of Tech., Kanpur. Dept. of Physics; Mehrotra, I [Allahabad Univ. (India). Dept. of Physics
1976-08-01
Low-lying spectra of /sup 6/Li, /sup 18/F, /sup 18/O, /sup 42/Sc, /sup 42/Ca, /sup 58/Ni and /sup 92/Zr are studied with Sussex matrix elements (SME) and their central, spin-orbit and tensor components. It is observed that major contribution to level energies comes from the central part, while the tensor part provides the finer details of spectra, particularly for T = 0 levels. The spin-orbit part does not make any appreciable contribution to level energies. A phenomenological renormalization fo the SME is carried out to improve the agreement with the experimental results. It turns out that some of the low-lying T = 0 levels can be satisfactorily described if the SME in the /sup 3/S/sub 1/ relative state are made (1+..cap alpha..) times their bare interaction value, where ..cap alpha.. is a constant to be determined from a comparison with experimental level energies. Similarly, for T = 1 levels, better agreement with the experimental results is obtained if a delta-function-plus-quadrupole interaction is added to the SME.
Effective field renormalization group approach for Ising lattice spin systems
Fittipaldi, Ivon P.
1994-03-01
A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.
Evaluation of spectral zeta-functions with the renormalization group
International Nuclear Information System (INIS)
Boettcher, Stefan; Li, Shanshan
2017-01-01
We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal–Kadanoff bond moving scheme from regular lattices. As possible applications of these results we mention quantum search algorithms as well as synchronization, which we discuss in more detail. (paper)
Asymptotic behavior of composite-particle form factors and the renormalization group
International Nuclear Information System (INIS)
Duncan, A.; Mueller, A.H.
1980-01-01
Composite-particle form factors are studied in the limit of large momentum transfer Q. It is shown that in models with spinor constituents and either scalar or gauge vector gluons, the meson electromagnetic form factor factorizes at large Q 2 and is given by independent light-cone expansions on the initial and final meson legs. The coefficient functions are shown to satisfy a Callan-Symanzik equation. When specialized to quantum chromodynamics, this equation leads to the asymptotic formula of Brodsky and Lepage for the pion electromagnetic form factor. The nucleon form factors G/sub M/(Q 2 ), G/sub E/(Q 2 ) are also considered. It is shown that momentum flows which contribute to subdominant logarithms in G/sub M/(Q 2 ) vitiate a conventional renormalization-group interpretation for this form factor. For large Q 2 , the electric form factor G/sub E/(Q 2 ) fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case
Matsuno, Genki; Kobayashi, Akito
2018-05-01
We evaluate the uniform spin susceptibility in an extended Hubbard model describing α-(BEDT-TTF)2I3. Employing the Fock-type self-energy with the long-range Coulomb interaction and the random phase approximation with the on-site Coulomb interaction, it is clarified that the characteristic energy scales at which ferrimagnetic fluctuation and velocity renormalization emerge are different. This is why these phenomena coexist while the ferrimagnetic fluctuation is disturbed by the velocity renormalization. In addition, it is found that screening effect to the self-energy is irrelevant in the presence of a strong on-site Coulomb interaction U.
Ultracold atoms and the Functional Renormalization Group
International Nuclear Information System (INIS)
Boettcher, Igor; Pawlowski, Jan M.; Diehl, Sebastian
2012-01-01
We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context, we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition. The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field.
A simple proof of renormalization group equation in the minimal subtraction scheme
International Nuclear Information System (INIS)
Chetyrkin, K.G.
1989-04-01
We give a simple combinatorial proof of the renormalization group equation in the minimal subtraction scheme. Being mathematically rigorous, the proof avoids both the notorious complexity of techniques using parametric representations of Feynman diagrams and heuristic arguments of usual ''proofs'' calling up bare fields living in the space-time of complex dimension. It also copes easily with the general case of Green functions of arbitrary number of composite fields. (author). 24 refs
Renormalization group, principle of invariance and functional automodelity
International Nuclear Information System (INIS)
Shirkov, D.V.
1981-01-01
There exists a remarkable identity of functional equations describing the property of functional automodelity in diverse branches of physics: renormalization group equations in quantum field theory, functional equations of the invariance principle of the one-dimensional transport theory and some others. The origin of this identity is investigated. It is shown that the structure of these equations reflects the simple and general property of transitivity with respect to the way of fixatio of initial on effective degrees of freedom [ru
How to resolve the factorization- and the renormalization-scheme ambiguities simultaneously
International Nuclear Information System (INIS)
Nakkagawa, H.; Niegawa, A.
1982-01-01
A combined investigation of both the factorization- and renormalization-scheme dependences of perturbative QCD calculations is reported. Applyong Stevenson's optimization method, we get a remarkable result, which forces us to exponentiate 'everything' with uncorrected subprocess cross sections. (orig.)
Renormalization and Central limit theorem for critical dynamical systems with weak external noise
Diaz-Espinosa, O
2006-01-01
We study of the effect of weak noise on critical one dimensional maps; that is, maps with a renormalization theory. We establish a one dimensional central limit theorem for weak noises and obtain Berry--Esseen estimates for the rate of this convergence. We analyze in detail maps at the accumulation of period doubling and critical circle maps with golden mean rotation number. Using renormalization group methods, we derive scaling relations for several features of the effective noise after long times. We use these scaling relations to show that the central limit theorem for weak noise holds in both examples. We note that, for the results presented here, it is essential that the maps have parabolic behavior. They are false for hyperbolic orbits.
Indefinite metric fields and the renormalization group
International Nuclear Information System (INIS)
Sherry, T.N.
1976-11-01
The renormalization group equations are derived for the Green functions of an indefinite metric field theory. In these equations one retains the mass dependence of the coefficient functions, since in the indefinite metric theories the masses cannot be neglected. The behavior of the effective coupling constant in the asymptotic and infrared limits is analyzed. The analysis is illustrated by means of a simple model incorporating indefinite metric fields. The model scales at first order, and at this order also the effective coupling constant has both ultra-violet and infra-red fixed points, the former being the bare coupling constant
Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus
2015-01-28
We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.
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.
A density matrix renormalization group study of low-lying excitations ...
Indian Academy of Sciences (India)
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 ...
Renormalization group equation for interacting Thirring fields in dimensional regularization scheme
International Nuclear Information System (INIS)
Chowdhury, A.R.; Roy, T.; Kar, S.
1976-01-01
The dynamics of two interacting Thirring fields has been investigated within the dimensional regularization framework. The coupling constants are renormalized in the same way as observed in the non-perturbative approach of Ansel'm et al (Sov. Phys. - JETP 36: 608 (1959)). Functionsβsub(i)(g 1 , g 2 , g 3 ) and γsub(i)(g 1 , g 2 , g 3 ), pertaining to the stability and anomalous behaviour of the problem, are computed up to a third order in the coupling parameters. With the help of these, subsidiary non-linear differential equations of the renormalization group are studied in 2-epsilon dimension. The results show up some peculiar features of the theory: a zero of βsub(i)(g 1 , g 2 , g 3 ) corresponding to g 2 approximately α√epsilon, a characteristic of phi theory. The scale invariant limit is reached when g 2 → 0 (i.e. the two Thirring fields are decoupled) and also when g 1 = xg 2 = g 3 , where x is a root of 2x 3 + 2x 2 - 1 = 0. The branch-point zero makes the transition to the epsilon tends to 0 limit non-unique. The anomalous dimensions are obtained and seen to match that of the Dashen-Frishman model (Phys. Lett.; 46B 439 (1973)). The existence of a non-trivial scale invariant limit distinguishes the model from many simple field theories. (author)
Renormalization group decimation technique for disordered binary harmonic chains
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-10-01
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)
International Nuclear Information System (INIS)
Busa, J.; Ajryan, Eh.A.; Jurcisinova, E.; Jurcisin, M.; Remecky, R.
2009-01-01
Using the field-theoretic renormalization group, the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passive transverse vector field advected by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and the borderline spatial dimension d e (1,3] below which the stability of the scaling regime is not present is found as a function of anisotropy parameters
Zero point energy of renormalized Wilson loops
International Nuclear Information System (INIS)
Hidaka, Yoshimasa; Pisarski, Robert D.
2009-01-01
The quark-antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.
de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.
2009-10-01
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
Energy Technology Data Exchange (ETDEWEB)
Albuquerque, Douglas F. de [Departamento de Matematica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil)], E-mail: douglas@ufs.br; Santos-Silva, Edimilson [Departamento de Matematica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil); Moreno, N.O. [Departamento de Fisica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil)
2009-10-15
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents {nu} for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
International Nuclear Information System (INIS)
Albuquerque, Douglas F. de; Santos-Silva, Edimilson; Moreno, N.O.
2009-01-01
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
Directory of Open Access Journals (Sweden)
Nikos Irges
2017-11-01
Full Text Available We perform an old school, one-loop renormalization of the Abelian–Higgs model in the Unitary and Rξ gauges, focused on the scalar potential and the gauge boson mass. Our goal is to demonstrate in this simple context the validity of the Unitary gauge at the quantum level, which could open the way for an until now (mostly avoided framework for loop computations. We indeed find that the Unitary gauge is consistent and equivalent to the Rξ gauge at the level of β-functions. Then we compare the renormalized, finite, one-loop Higgs potential in the two gauges and we again find equivalence. This equivalence needs not only a complete cancellation of the gauge fixing parameter ξ from the Rξ gauge potential but also requires its ξ-independent part to be equal to the Unitary gauge result. We follow the quantum behavior of the system by plotting Renormalization Group trajectories and Lines of Constant Physics, with the former the well known curves and with the latter, determined by the finite parts of the counter-terms, particularly well suited for a comparison with non-perturbative studies.
Renormalization of NN scattering: Contact potential
International Nuclear Information System (INIS)
Yang Jifeng; Huang Jianhua
2005-01-01
The renormalization of the T matrix for NN scattering with a contact potential is re-examined in a nonperturbative regime through rigorous nonperturbative solutions. Based on the underlying theory, it is shown that the ultraviolet divergences in the nonperturbative solutions of the T matrix should be subtracted through 'endogenous' counterterms, which in turn leads to a nontrivial prescription dependence. Moreover, employing the effective range expansion, the importance of imposing physical boundary conditions to remove the nontrivial prescription dependence, especially before making any physical claims, is discussed and highlighted. As by-products, some relations between the effective range expansion parameters are derived. We also discuss the power counting of the couplings for the nucleon-nucleon interactions and other subtle points related to the EFT framework beyond perturbative treatment
Gauge field theories. Part three. Renormalization
International Nuclear Information System (INIS)
Frampon, P.H.
1978-01-01
The renormalization of nonabelian gauge theories both with exact symmetry and with spontaneous symmetry breaking is discussed. The method of dimensional regularization is described and used in the ensuing discussion. Triangle anomalies and their implications and the method for cancellation of anomalies in an SU(2) x U(1) theory, introduction of the BRS form of local gauge transformation and its use for the iterative proof of renormalizability to all orders for pure Yang--Mills and with fermion and scalar matter fields are considered. Lastly for massive vectors arising from spontaneous breaking, the demonstration of renormalizability is given, using the 't Hooft gauges introduced first in 1971. While the treatment is not totally rigorous, all the principle steps are given. 108 references
Non-renormalization theorems andN=2 supersymmetric backgrounds
International Nuclear Information System (INIS)
Butter, Daniel; Wit, Bernard de; Lodato, Ivano
2014-01-01
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
Entanglement renormalization, quantum error correction, and bulk causality
Energy Technology Data Exchange (ETDEWEB)
Kim, Isaac H. [IBM T.J. Watson Research Center,1101 Kitchawan Rd., Yorktown Heights, NY (United States); Kastoryano, Michael J. [NBIA, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen (Denmark)
2017-04-07
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated by a local Hamiltonian.
Renormalization, conformal ward identities and the origin of a conformal anomaly pole
Corianò, Claudio; Maglio, Matteo Maria
2018-06-01
We investigate the emergence of a conformal anomaly pole in conformal field theories in the case of the TJJ correlator. We show how it comes to be generated in dimensional renormalization, using a basis of 13 form factors (the F-basis), where only one of them requires renormalization (F13), extending previous studies. We then combine recent results on the structure of the non-perturbative solutions of the conformal Ward identities (CWI's) for the TJJ in momentum space, expressed in terms of a minimal set of 4 form factors (A-basis), with the properties of the F-basis, and show how the singular behaviour of the corresponding form factors in both basis can be related. The result proves the centrality of such massless effective interactions induced by the anomaly, which have recently found realization in solid state, in the theory of topological insulators and of Weyl semimetals. This pattern is confirmed in massless abelian and nonabelian theories (QED and QCD) investigated at one-loop.
The Obstruction criterion for non existence of Invariant Circles and Renormalization.
De la Llave, R
2003-01-01
We formulate a conjecture which supplements the standard renormalization scenario for the breakdown of golden circle in twist maps. We show rigorously that if the conjecture was true then: a) The stable manifold of the non-trivial fixed point would indeed be a boundary between the existence of smooth invariant tori and hyperbolic orbits with golden mean rotation number. In particular, the boundary of the set of twist maps with a torus with a golden mean rotation number would include a smooth submanifold in the space of analytic mappings. b) The obstruction criterion of [Olvera-Simo] would be sharp in the universality class of the renormalization group. c) The criterion of [Greene-79] for existence of invariant circles if and only if there the residues of approximating orbits are finite would be valid for maps in the universality class. d) If there is no invariant circle, there are hyperbolic sets with golden mean rotation number. We also provide numerical evidence which suggests that the conjecture is true an...
Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.
2018-03-01
In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.
Kjellander, Roland
2018-05-01
A unified treatment of oscillatory and monotonic exponential decays of interactions in electrolytes is displayed, which highlights the role of dielectric response of the fluid in terms of renormalized (effective) dielectric permittivity and charges. An exact, but physically transparent statistical mechanical formalism is thereby used, which is presented in a systematic, pedagogical manner. Both the oscillatory and monotonic behaviors are given by an equation for the decay length of screened electrostatic interactions that is very similar to the classical expression for the Debye length. The renormalized dielectric permittivities, which have similar roles for electrolytes as the dielectric constant has for pure polar fluids, consist in general of several entities with different physical meanings. They are connected to dielectric response of the fluid on the same length scale as the decay length of the screened interactions. Only in cases where the decay length is very long, these permittivities correspond approximately to a dielectric response in the long-wavelength limit, like the dielectric constant for polar fluids. Experimentally observed long-range exponentially decaying surface forces are analyzed as well as the oscillatory forces observed for short to intermediate surface separations. Both occur in some ionic liquids and in concentrated as well as very dilute electrolyte solutions. The coexisting modes of decay are in general determined by the bulk properties of the fluid and not by the solvation of the surfaces; in the present cases, they are given by the behavior of the screened Coulomb interaction of the bulk fluid. The surface-fluid interactions influence the amplitudes and signs or phases of the different modes of the decay, but not their decay lengths and wavelengths. The similarities between some ionic liquids and very dilute electrolyte solutions as regards both the long-range monotonic and the oscillatory decays are analyzed.
Quantum gravity and the functional renormalization group the road towards asymptotic safety
Reuter, Martin
2018-01-01
During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering thi...
Miyake, Kazumasa; Tsuruta, Atsushi
2015-01-01
On the basis of the Luttinger-Ward formalism for the thermodynamic potential, the specific heat of single-component interacting fermion systems with fixed chemical potential is compactly expressed in terms of the fully renormalized Matsubara Green function.