Screening of heterogeneous surfaces: charge renormalization of Janus particles.
Boon, N; Carvajal Gallardo, E; Zheng, S; Eggen, E; Dijkstra, M; van Roij, R
2010-03-17
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadrupolar, etc, including 'mode couplings'. Our novel scheme is generally applicable to large classes of surface heterogeneities, and is explicitly applied here to Janus spheres with differently charged upper and lower hemispheres, revealing strong renormalization effects for all multipoles.
Screening of heterogeneous surfaces: Charge renormalization of Janus particles
Boon, N.; Carvajal Gallardo, E.; Zheng, S.; Eggen, E.; Dijkstra, M.; Van Roij, R.
2010-01-01
Nonlinear ionic screening theory for heterogeneously charged spheres is developed in terms of a mode decomposition of the surface charge. A far-field analysis of the resulting electrostatic potential leads to a natural generalization of charge renormalization from purely monopolar to dipolar, quadru
Energy Technology Data Exchange (ETDEWEB)
Sarmento, R.G. [Departamento de Fisica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Fulco, U.L. [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Albuquerque, E.L., E-mail: eudenilson@gmail.com [Departamento de Biofisica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN (Brazil); Caetano, E.W.S. [Instituto Federal de Educacao, Ciencia e Tecnologia do Ceara, 60040-531 Fortaleza, CE (Brazil); Freire, V.N. [Departamento de Fisica, Universidade Federal do Ceara, 60455-760 Fortaleza, CE (Brazil)
2011-10-31
Highlights: → One-step renormalization approach to describe the DBL-DNA molecule. → Electronic tight-binding Hamiltonian model. → A quasiperiodic sequence to mimic the DNA nucleotides arrangement. → Electronic transmission spectra. → I-V characteristics. -- Abstract: We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.
Large counterions boost the solubility and renormalized charge of suspended nanoparticles.
Guerrero-García, Guillermo Iván; González-Mozuelos, Pedro; Olvera de la Cruz, Monica
2013-11-26
Colloidal particles are ubiquitous in biology and in everyday products such as milk, cosmetics, lubricants, paints, or drugs. The stability and aggregation of colloidal suspensions are of paramount importance in nature and in diverse nanotechnological applications, including the fabrication of photonic materials and scaffolds for biological assemblies, gene therapy, diagnostics, targeted drug delivery, and molecular labeling. Electrolyte solutions have been extensively used to stabilize and direct the assembly of colloidal particles. In electrolytes, the effective electrostatic interactions among the suspended colloids can be changed over various length scales by tuning the ionic concentration. However, a major limitation is gelation or flocculation at high salt concentrations. This is explained by classical theories, which show that the electrostatic repulsion among charged colloids is significantly reduced at high electrolyte concentrations. As a result, these screened colloidal particles are expected to aggregate due to short-range attractive interactions or dispersion forces as the salt concentration increases. We discuss here a robust, tunable mechanism for colloidal stability by which large counterions prevent highly charged nanoparticles from aggregating in salt solutions with concentrations up to 1 M. Large counterions are shown to generate a thicker ionic cloud in the proximity of each charged colloid, which strengthens short-range repulsions among colloidal particles and also increases the corresponding renormalized colloidal charge perceived at larger separation distances. These effects thus provide a reliable stabilization mechanism in a broad range of biological and synthetic colloidal suspensions.
Sarmento, R. G.; Fulco, U. L.; Albuquerque, E. L.; Caetano, E. W. S.; Freire, V. N.
2011-10-01
We study the charge transport properties of a dangling backbone ladder (DBL)-DNA molecule focusing on a quasiperiodic arrangement of its constituent nucleotides forming a Rudin-Shapiro (RS) and Fibonacci (FB) Poly (CG) sequences, as well as a natural DNA sequence (Ch22) for the sake of comparison. Making use of a one-step renormalization process, the DBL-DNA molecule is modeled in terms of a one-dimensional tight-binding Hamiltonian to investigate its transmissivity and current-voltage (I-V) profiles. Beyond the semiconductor I-V characteristics, a striking similarity between the electronic transport properties of the RS quasiperiodic structure and the natural DNA sequence was found.
Directory of Open Access Journals (Sweden)
V. Bacsó
2015-12-01
Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.
Deng, Yanbin; Huang, Changyu; Huang, Yong-Chang
2016-08-01
It was suggested by dimensional analysis that there exists a limit called the Planck energy scale coming close to which the gravitational effects of physical processes would inflate and struggle for equal rights so as to spoil the validity of pure nongravitational physical theories that governed well below the Planck energy. Near the Planck scale, the Planck charges, Planck currents, or Planck parameters can be defined and assigned to physical quantities such as the single particle electric charge and magnetic charge as the ceiling value obeyed by the low energy ordinary physics. The Dirac electric-magnetic charge quantization relation as one form of electric-magnetic duality dictates that, the present low value electric charge corresponds to a huge magnetic charge value already passed the Planck limit so as to render theories of magnetic monopoles into the strong coupling regime, and vice versa, that small and tractable magnetic charge values correspond to huge electric charge values. It suggests that for theoretic models in which the renormalization group equation provides rapid growth for the running electric coupling constant, it is easier for the dual magnetic monopoles to emerge at lower energy scales. Allowing charges to vary with the Dirac electric-magnetic charge quantization relation while keeping values under the Planck limit informs that the magnetic charge value drops below the Planck ceiling value into the manageable region when the electric coupling constant grows to one fourth at a model dependent energy scale, and continues dropping toward half the value of the Planck magnetic charge as the electric coupling constant continues growing at the model dependent rate toward one near Planck energy scale.
Tsiper, Eugene
2006-03-01
A renormalization procedure is designed to find a subspace of high relevance in a many-body Hilbert space. Substantial reduction in the basis size can be achieved while approaching the exact diagonalization results. The idea is to search for a set of many-particle configurations that contribute the largest weight to the exact solution of the many-body Schrödinger equation, without actually computing the exact solution. We start with some suitable set of K configurations and find the ground state of the Hamiltonian in the many-body subspace that they span. We then retain K'elements with those retained. When repeated, the procedure converges after several iterations and yields some optimal set of configurations. The resulting truncation of the Hilbert space is essentially many-body, and cannot be achieved by truncating or rotating the single-particle basis. I will discuss an application of CSR to model resonant tunneling between the edges in the fractional quantum Hall regime, which has been used to experimentally observe fractional quantization of electric charge. Clusters large enough to contain two unconnected edges are modeled. The results suggest fractional quantization of the quasiparticle charge in units of e/3 and e/5 at fillings 1/3 and 2/5.
Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms
Gravejat, Philippe; Sere, Eric
2007-01-01
We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant $\\alpha$. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an $L^1$ function and compute the effective charge of the system, re...
Dutta, Tirthankar; Ramasesha, S.
2012-01-01
In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)x-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)x-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)x-A, systems in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a “quasi-static” state.
Wave function and CKM renormalization
Espriu, Doménec
2002-01-01
In this presentation we clarify some aspects of the LSZ formalism and wave function renormalization for unstable particles in the presence of electroweak interactions when mixing and CP violation are considered. We also analyze the renormalization of the CKM mixing matrix which is closely related to wave function renormalization. The effects due to the electroweak radiative corrections that are described in this work are small, but they will need to be considered when the precision in the measurement of the charged current sector couplings reaches the 1% level. The work presented here is done in collaboration with Julian Manzano and Pere Talavera.
Lavrov, P. M.; Shapiro, I. L.
2012-09-01
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.
Holographic renormalization and supersymmetry
Genolini, Pietro Benetti; Cassani, Davide; Martelli, Dario; Sparks, James
2017-02-01
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.
Renormalization Scheme Dependence and Renormalization Group Summation
McKeon, D G C
2016-01-01
We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter mu cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher order radiative corrections is absorbed by the behaviour of the running coupling.
Gover, A Rod
2016-01-01
For any conformally compact manifold with hypersurface boundary we define a canonical renormalized volume functional and compute an explicit, holographic formula for the corresponding anomaly. For the special case of asymptotically Einstein manifolds, our method recovers the known results. The anomaly does not depend on any particular choice of regulator, but the coefficients of divergences do. We give explicit formulae for these divergences valid for any choice of regulating hypersurface; these should be relevant to recent studies of quantum corrections to entanglement entropies. The anomaly is expressed as a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. We show that the variation of these energy functionals is exactly the obstruction to solving a singular Yamabe type problem with boundary data along the...
Holographic Renormalization in Dense Medium
Directory of Open Access Journals (Sweden)
Chanyong Park
2014-01-01
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.
Renormalized action improvements
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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.
Gies, Holger; Jaeckel, Joerg
2004-09-01
We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral-symmetry-breaking (χSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the χSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.
Renormalization of Dirac's Polarized Vacuum
Lewin, Mathieu
2010-01-01
We review recent results on a mean-field model for relativistic electrons in atoms and molecules, which allows to describe at the same time the self-consistent behavior of the polarized Dirac sea. We quickly derive this model from Quantum Electrodynamics and state the existence of solutions, imposing an ultraviolet cut-off $\\Lambda$. We then discuss the limit $\\Lambda\\to\\infty$ in detail, by resorting to charge renormalization.
Lee, Myoung-Jae; Jung, Young-Dae
2016-01-01
The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.
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Lee, Myoung-Jae [Department of Physics and Research Institute for Natural Sciences, Hanyang University, Seoul 04763 (Korea, Republic of); Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States)
2016-01-15
The influence of renormalization shielding on the Wannier threshold law for the double-electron escapes by the electron-impact ionization is investigated in partially ionized dense plasmas. The renormalized electron charge and Wannier exponent are obtained by considering the equation of motion in the Wannier-ridge including the renormalization shielding effect. It is found that the renormalization shielding effect reduces the magnitude of effective electron charge, especially, within the Bohr radius in partially ionized dense plasmas. The maximum position of the renormalized electron charge approaches to the center of the target atom with an increase of the renormalization parameter. In addition, the Wannier exponent increases with an increase of the renormalization parameter. The variations of the renormalized electron charge and Wannier exponent due to the renormalization shielding effect are also discussed.
Renormalization: an advanced overview
Gurau, Razvan; Sfondrini, Alessandro
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.
Renormalization for Philosophers
Butterfield, Jeremy
2014-01-01
We have two aims. The main one is to expound the idea of renormalization in quantum field theory, with no technical prerequisites (Sections 2 and 3). Our motivation is that renormalization is undoubtedly one of the great ideas, and great successes, of twentieth-century physics. Also it has strongly influenced in diverse ways, how physicists conceive of physical theories. So it is of considerable philosophical interest. Second, we will briefly relate renormalization to Ernest Nagel's account of inter-theoretic relations, especially reduction (Section 4). One theme will be a contrast between two approaches to renormalization. The old approach, which prevailed from ca. 1945 to 1970, treated renormalizability as a necessary condition for being an acceptable quantum field theory. On this approach, it is a piece of great good fortune that high energy physicists can formulate renormalizable quantum field theories that are so empirically successful. But the new approach to renormalization (from 1970 onwards) explains...
Renormalization and effective lagrangians
Polchinski, Joseph
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 λø 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.
The renormalization; La normalisation
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Rivasseau, V. [Paris-6 Univ., Lab. de Physique Theorique, 91 - Orsay (France); Gallavotti, G. [Universita di Roma, La Sapienza, Fisica, Roma (Italy); Zinn-Justin, J. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique Theorique, 91- Gif sur Yvette (France); Connes, A. [College de France, 75 - Paris (France)]|[Institut des Hautes Etudes Scientifiques - I.H.E.S., 91 - Bures sur Yvette (France); Knecht, M. [Centre de Physique Theorique, CNRS-Luminy, 13 - Marseille (France); Mansoulie, B. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique des Particules, 91- Gif sur Yvette (France)
2002-07-01
This document gathers 6 articles. In the first article the author reviews the theory of perturbative renormalization, discusses its limitations and gives a brief introduction to the powerful point of view of the renormalization group, which is necessary to go beyond perturbation theory and to define renormalization in a constructive way. The second article is dedicated to renormalization group methods by illustrating them with examples. The third article describes the implementation of renormalization ideas in quantum field theory. The mathematical aspects of renormalization are given in the fourth article where the link between renormalization and the Riemann-Hilbert problem is highlighted. The fifth article gives an overview of the main features of the theoretical calculations that have been done in order to obtain accurate predictions for the anomalous magnetic moments of the electron and of the muon within the standard model. The challenge is to make theory match the unprecedented accuracy of the last experimental measurements. The last article presents how ''physics beyond the standard model'' will be revealed at the large hadron collider (LHC) at CERN. This accelerator will be the first to explore the 1 TeV energy range directly. Supersymmetry, extra-dimensions and Higgs boson will be the different challenges. It is not surprising that all theories put forward today to subtend the electro-weak breaking mechanism, predict measurable or even spectacular signals at LHC. (A.C.)
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Renormalization of Wilson operators in Minkowski space
Andra, A
1996-01-01
We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge renormalization does not work in a simple graph-by-graph way; but does work when certain graphs are added together. We also verify that, in a simple example of a smooth loop in Minkowski space, the existence of pairs of points which are light-like separated does not cause any extra divergences.
Renormalization of fermion mixing
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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
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Carvalho, Vanuildo S de [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Freire, Hermann, E-mail: hfreire@mit.edu [Instituto de Física, Universidade Federal de Goiás, 74.001-970, Goiânia-GO (Brazil); Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 2139 (United States)
2014-09-15
The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t{sup ′} Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.
Renormalizing Entanglement Distillation.
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T; Eisert, Jens
2016-01-15
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics-ideas from renormalization and matrix-product states and operators-with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
Compressive Spectral Renormalization Method
Bayindir, Cihan
2016-01-01
In this paper a novel numerical scheme for finding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the governing equation is transformed into Fourier domain, but the iterations are performed for far fewer number of spectral components (M) than classical versions of the these methods with higher number of spectral components (N). After the converge criteria is achieved for M components, N component signal is reconstructed from M components by using the l1 minimization technique of the compressive sampling. This method can be named as compressive spectral renormalization (CSRM) method. The main advantage of the CSRM is that, it is capable of finding the sparse self-localized states of the evolution equation(s) with many spectral data missing.
Lavrov, Peter M
2010-01-01
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST symmetry after renormalization is preserved. The advantage of the Sp(2)-method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)- scalars.
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Lavrov, Peter M., E-mail: lavrov@tspu.edu.r [Department of Mathematical Analysis, Tomsk State Pedagogical University, Kievskaya St. 60, Tomsk 634061 (Russian Federation)
2011-08-11
The renormalization of general gauge theories on flat and curved space-time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge-invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST-symmetry after renormalization is preserved. The advantage of the Sp(2) method compared to the standard Batalin-Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)-scalars.
Renormalized Cosmological Perturbation Theory
Crocce, M
2006-01-01
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams constructed in terms of three objects: the initial conditions (e.g. perturbation spectrum), the vertex (describing non-linearities) and the propagator (describing linear evolution). We show that loop corrections to the linear power spectrum organize themselves into two classes of diagrams: one corresponding to mode-coupling effects, the other to a renormalization of the propagator. Resummation of the latter gives rise to a quantity that measures the memory of perturbations to initial conditions as a function of scale. As a result of this, we show that a well-defined (renormalized) perturbation theory follows, in the sense that each term in the remaining mode-coupling series dominates at some characteristic scale and is subdominant otherwise. This is unlike standard perturbatio...
Renormalizing Partial Differential Equations
Bricmont, J.; Kupiainen, A.
1994-01-01
In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.
Renormalization on noncommutative torus
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D' Ascanio, D.; Pisani, P. [Universidad Nacional de La Plata, Instituto de Fisica La Plata-CONICET, La Plata (Argentina); Vassilevich, D.V. [Universidade Federal do ABC, CMCC, Santo Andre, SP (Brazil); Tomsk State University, Department of Physics, Tomsk (Russian Federation)
2016-04-15
We study a self-interacting scalar φ{sup 4} theory on the d-dimensional noncommutative torus. We determine, for the particular cases d = 2 and d = 4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ. (orig.)
Renormalization on noncommutative torus
D'Ascanio, D; Vassilevich, D V
2016-01-01
We study a self-interacting scalar $\\varphi^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the nonlocal counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points towards the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $\\theta$.
Renormalization on noncommutative torus
D'Ascanio, D.; Pisani, P.; Vassilevich, D. V.
2016-04-01
We study a self-interacting scalar \\varphi ^4 theory on the d-dimensional noncommutative torus. We determine, for the particular cases d=2 and d=4, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the ultraviolet/infrared mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix θ.
Battle, G A
1999-01-01
WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the F 4 3 quantum field theory is presented. It is due to Battle and
Renormalization of composite operators
Polonyi, J
2001-01-01
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\\phi^3$ theory in dimension $d=6$.
Renormalized Volumes with Boundary
Gover, A Rod
2016-01-01
We develop a general regulated volume expansion for the volume of a manifold with boundary whose measure is suitably singular along a separating hypersurface. The expansion is shown to have a regulator independent anomaly term and a renormalized volume term given by the primitive of an associated anomaly operator. These results apply to a wide range of structures. We detail applications in the setting of measures derived from a conformally singular metric. In particular, we show that the anomaly generates invariant (Q-curvature, transgression)-type pairs for hypersurfaces with boundary. For the special case of anomalies coming from the volume enclosed by a minimal hypersurface ending on the boundary of a Poincare--Einstein structure, this result recovers Branson's Q-curvature and corresponding transgression. When the singular metric solves a boundary version of the constant scalar curvature Yamabe problem, the anomaly gives generalized Willmore energy functionals for hypersurfaces with boundary. Our approach ...
Renormalizing an initial state
Collins, Hael; Vardanyan, Tereza
2014-01-01
The intricate machinery of perturbative quantum field theory has largely been devoted to the 'dynamical' side of the theory: simple states are evolved in complicated ways. This article begins to address this lopsided treatment. Although it is rarely possible to solve for the eigenstates of an interacting theory exactly, a general state and its evolution can nonetheless be constructed perturbatively in terms of the propagators and structures defined with respect to the free theory. The detailed form of the initial state in this picture is fixed by imposing suitable `renormalization conditions' on the Green's functions. This technique is illustrated with an example drawn from inflation, where the presence of nonrenormalizable operators and where an expansion that naturally couples early times with short distances make the ability to start the theory at a finite initial time especially desirable.
Gutzwiller renormalization group
Lanatà, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Wang, Cai-Zhuang; Ho, Kai-Ming; Kotliar, Gabriel
2016-01-01
We develop a variational scheme called the "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.
Practical Algebraic Renormalization
Grassi, P A; Steinhauser, M
1999-01-01
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 illustra...
Tensor Network Renormalization.
Evenbly, G; Vidal, G
2015-10-30
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz
Evenbly, G.; Vidal, G.
2015-11-01
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e-β H for infinite β . This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β , produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Renormalization Group Invariance and Optimal QCD Renormalization Scale-Setting
Wu, Xing-Gang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J; Mojaza, Matin
2014-01-01
A valid prediction from quantum field theory for a physical observable 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 truncated perturbation series do not automatically satisfy the requirements of the renormalization group. Two distinct approaches for satisfying the RGI principle have been suggested in the literature. One is the "Principle of Maximum Conformality" (PMC) in which the terms associated with the $\\beta$-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 deta...
Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz.
Evenbly, G; Vidal, G
2015-11-13
We show how to build a multiscale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed tensor network renormalization [G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)] to the Euclidean time evolution operator e(-βH) for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows tensor network renormalization with a renormalization group flow in the space of wave functions and Hamiltonians (and not merely in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.
Fifty years of the renormalization group
Shirkov, D V
2001-01-01
Renormalization was the breakthrough that made quantum field theory respectable in the late 1940s. Since then, renormalization procedures, particularly the renormalization group method, have remained a touchstone for new theoretical developments. This work relates the history of the renormalization group. (17 refs).
Renormalization automated by Hopf algebra
Broadhurst, D J
1999-01-01
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a finite renormalized expression for any Feynman diagram. We thus verify a representation of the operator product expansion, which generalizes Chen's lemma for iterated integrals. The subset of diagrams whose forest structure entails a unique primitive subdivergence provides a representation of the Hopf algebra ${\\cal H}_R$ of undecorated rooted trees. Our undecorated Hopf algebra program is designed to process the 24,213,878 BPHZ contributions to the renormalization of 7,813 diagrams, with up to 12 loops. We consider 10 models, each in 9 renormalization schemes. The two simplest models reveal a notable feature of the subalgebra of Connes and Moscovici, corresponding to the commutative part of the Hopf ...
Differential renormalization of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab
The analytic renormalization group
Ferrari, Frank
2016-08-01
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k ∈ Z, associated with the Matsubara frequencies νk = 2 πk / β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct "Analytic Renormalization Group" linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk | < μ (with the possible exception of the zero mode G0), together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk | ≥ μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.
Cluster functional renormalization group
Reuther, Johannes; Thomale, Ronny
2014-01-01
Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a free expansion point of the action, the flow of the RG parameter Λ allows us to trace the evolution of the effective one- and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-1/2 bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.
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.
Renormalization group analysis of graphene with a supercritical Coulomb impurity
Nishida, Yusuke
2016-08-01
We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial-wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power-law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.
Renormalization group analysis of graphene with a supercritical Coulomb impurity
Nishida, Yusuke
2016-01-01
We develop a field theoretical approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov-Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.
Full counting statistics of level renormalization in electron transport through double quantum dots.
Luo, JunYan; Jiao, HuJun; Shen, Yu; Cen, Gang; He, Xiao-Ling; Wang, Changrong
2011-04-13
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.
Full counting statistics of level renormalization in electron transport through double quantum dots
Energy Technology Data Exchange (ETDEWEB)
Luo Junyan; Shen Yu; Cen Gang; He Xiaoling; Wang Changrong [School of Science, Zhejiang University of Science and Technology, Hangzhou 310023 (China); Jiao Hujun, E-mail: jyluo@zust.edu.cn [Department of Physics, Shanxi University, Taiyuan, Shanxi 030006 (China)
2011-04-13
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.
Energy Technology Data Exchange (ETDEWEB)
Baikov, P.A. [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 1(2), Leninskie gory, Moscow 119234 (Russian Federation); Chetyrkin, K.G.; Kuehn, J.H. [Institut fuer Theoretische Teilchenphysik, Universitaet Karlsruhe, D-76128 Karlsruhe (Germany); Sturm, C., E-mail: sturm@mpp.mpg.de [Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Foehringer Ring 6, D-80805 Muenchen (Germany)
2013-02-11
In this paper we compute the four-loop corrections to the QED photon self-energy {Pi}(Q{sup 2}) in the two limits of q=0 and Q{sup 2}{yields}{infinity}. These results are used to explicitly construct the conversion relations between the QED charge renormalized in on-shell (OS) and MS{sup Macron} scheme. Using these relations and results of Baikov et al. [1] we construct the momentum dependent part of {Pi}(Q{sup 2},m,{alpha}) at large Q{sup 2} at five loops in both MS{sup Macron} and OS schemes. As a direct consequence we arrive at the full result for the QED {beta}-function in the OS scheme at five loops. These results are applied, in turn, to analytically evaluate a class of asymptotic contributions to the muon anomaly at five and six loops.
A Constraint on Defect and Boundary Renormalization Group Flows
Jensen, Kristan
2015-01-01
A conformal field theory (CFT) in dimension $d\\geq 3$ coupled to a planar, two-dimensional, conformal defect is characterized in part by a "central charge" $b$ that multiplies the Euler density in the defect's Weyl anomaly. For defect renormalization group flows, under which the bulk remains critical, we use reflection positivity to show that $b$ must decrease or remain constant from ultraviolet to infrared. Our result applies also to a CFT in $d=3$ flat space with a planar boundary.
Lecture Notes on Holographic Renormalization
Skenderis, K
2002-01-01
We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, of holographic Ward identities, anomalies and RG equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown-York stress energy tensor of de Sitter spacetime is equal, up to a dimension dependent sign, to the Brown-York stress energy tensor of an associated AdS spacetime.
Allès, B; Di Giacomo, Adriano; Pica, C
2006-01-01
A Ginsparg-Wilson based calibration of the topological charge is used to calculate the renormalization constants which appear in the field-theoretical determination of the topological susceptibility on the lattice. A systematic comparison is made with calculations based on cooling. The two methods agree within present statistical errors (3%-4%). We also discuss the independence of the multiplicative renormalization constant Z from the background topological charge used to determine it.
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Fukushima, Noboru, E-mail: noboru.fukushima@gmail.com [Motomachi 13-23, Sanjo, Niigata 955-0072 (Japan)
2011-02-18
Renormalization of non-magnetic and magnetic impurities due to electron double-occupancy prohibition is derived analytically by an improved Gutzwiller approximation. Non-magnetic impurities are effectively weakened by the same renormalization factor as that for the hopping amplitude, whereas magnetic impurities are strengthened by the square root of the spin-exchange renormalization factor, in contrast to results by the conventional Gutzwiller approximation. We demonstrate it by showing that transition matrix elements of number operators between assumed excited states and between an assumed ground state and excited states are renormalized differently than diagonal matrix elements. Deviation from such simple renormalization with a factor is also discussed. In addition, as a related calculation, we correct an error in treatment of the renormalization of charge interaction in the literature. Namely, terms from the second order of the transition matrix elements are strongly suppressed. Since all these results do not depend on the signs of impurity potential or the charge interaction parameter, they are valid both in attractive and repulsive cases.
Algebraic Lattices in QFT Renormalization
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Concepts of renormalization in physics.
Alexandre, Jean
2005-01-01
A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic phase transition, and then show how similar ideas appear in particle physics. This short review is written for non-particle physicists and/or students aiming at studying particle physics.
Dynamical renormalization group resummation of finite temperature infrared divergences
Boyanovsky, D; 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 applied 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 $e^{-\\alpha T t \\ln[t/t_0]}$ which prevents a quasiparticle interpretation of charged collective excitations at finite temperature. 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 trascends the conceptual limitations of the quasiparticle picture and other type of resummation schemes. We derive a simple criterion for establishing the validity of the quasiparticle picture to lowest order.
Renormalization and asymptotic expansion of Dirac's polarized vacuum
Gravejat, Philippe; Séré, Eric
2010-01-01
We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no `real' electron. We show that it admits an asymptotic expansion to any order in powers of the physical coupling constant $\\alphaph$, provided that the ultraviolet cut-off behaves as $\\Lambda\\sim e^{3\\pi(1-Z_3)/2\\alphaph}\\gg1$. The renormalization parameter $0
Constraining differential renormalization in abelian gauge theories
del Águila, F; Tapia, R M; Pérez-Victoria, M
1998-01-01
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.
Renormalization of Extended QCD$_2$
Fukaya, Hidenori
2015-01-01
Extended QCD (XQCD) proposed by Kaplan [1] 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 two-dimensional (X)QCD, which is solvable in the limit of large number of colors Nc, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low energy region.
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
Hewson, A. C.
2016-11-01
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
Renormalization of Lepton Mixing for Majorana Neutrinos
Broncano, A; Jenkins, E; Jenkins, Elizabeth
2005-01-01
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
Renormalization of lepton mixing for Majorana neutrinos
Energy Technology Data Exchange (ETDEWEB)
Broncano, A. [Departamento de Fisica Teorica, C-XI, and IFT, C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)]. E-mail: alicia.broncano@uam.es; Gavela, M.B. [Departamento de Fisica Teorica, C-XI, and IFT, C-XVI, Facultad de Ciencias, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid (Spain)]. E-mail: gavela@delta.ft.uam.es; Jenkins, Elizabeth [Department of Physics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)]. E-mail: ejenkins@ucsd.edu
2005-01-17
We discuss the one-loop electroweak renormalization of the leptonic mixing matrix in the case of Majorana neutrinos, and establish its relationship with the renormalization group evolution of the dimension five operator responsible for the light Majorana neutrino masses. We compare our results in the effective theory with those in the full seesaw theory.
Combinatorics of renormalization as matrix calculus
Energy Technology Data Exchange (ETDEWEB)
Ebrahimi-Fard, Kurusch [Physics Institute, Bonn University, Nussallee 12, Bonn 53115 (Germany)]. E-mail: fard@th.physik.uni-bonn.de; Gracia-Bondia, Jose M. [Departamento de Fisica Teorica I, Universidad Complutense, Madrid 28040 (Spain); Guo, Li [Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102 (United States); Varilly, Joseph C. [Departamento de Matematicas, Universidad de Costa Rica, San Jose 2060 (Costa Rica)
2006-01-19
We give a simple presentation of the combinatorics of renormalization in perturbative quantum field theory in terms of triangular matrices. The prescription, that may be of calculational value, is derived from first principles, to wit, the 'Birkhoff decomposition' in the Hopf-algebraic description of renormalization by Connes and Kreimer.
Improved system identification with Renormalization Group.
Wang, Qing-Guo; Yu, Chao; Zhang, Yong
2014-09-01
This paper proposes an improved system identification method with Renormalization Group. Renormalization Group is applied to a fine data set to obtain a coarse data set. The least squares algorithm is performed on the coarse data set. The theoretical analysis under certain conditions shows that the parameter estimation error could be reduced. The proposed method is illustrated with examples.
Renormalization of dimension 6 gluon operators
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HyungJoo Kim
2015-09-01
Full Text Available We identify the independent dimension 6 twist 4 gluon operators and calculate their renormalization in the pure gauge theory. By constructing the renormalization group invariant combinations, we find the scale invariant condensates that can be estimated in nonperturbative calculations and used in QCD sum rules for heavy quark systems in medium.
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Energy Technology Data Exchange (ETDEWEB)
Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)
2013-08-01
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).
Perturbative entanglement thermodynamics for AdS spacetime: Renormalization
Mishra, Rohit
2015-01-01
We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that `boosted' AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately `renormalized' at the second order due to the corrections. We work in the perturbative regime where $T_{thermal}\\ll T_E$.
Renormalizing the NN interaction with multiple subtractions
Energy Technology Data Exchange (ETDEWEB)
Timoteo, V.S. [Faculdade de Tecnologia, Universidade Estadual de Campinas, 13484-332 Limeira, SP (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, Comando de Tecnologia Aeroespacial, 12228-900 Sao Jose dos Campos, SP (Brazil); Delfino, A. [Departamento de Fisica, Universidade Federal Fluminense, 24210-150 Niteroi, RJ (Brazil); Tomio, L. [Instituto de Fisica Teorica, Universidade Estadual Paulista, 01140-070 Sao Paulo, SP (Brazil); Szpigel, S.; Duraes, F.O. [Centro de Ciencias e Humanidades, Universidade Presbiteriana Mackenzie, 01302-907 Sao Paulo, SP (Brazil)
2010-02-15
The aim of this work is to show how to renormalize the nucleon-nucleon interaction at next-to-next-to-leading order using a systematic subtractive renormalization approach with multiple subtractions. As an example, we calculate the phase shifts for the partial waves with total angular momentum J=2. The intermediate driving terms at each recursive step as well as the renormalized T-matrix are also shown. We conclude that our method is reliable for singular potentials such as the two-pion exchange and derivative contact interactions.
Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
Energy Technology Data Exchange (ETDEWEB)
Gallavotti, G.
1985-04-01
A self-contained analysis is given of the simplest quantum fields from the renormalization group point of view: multiscale decomposition, general renormalization theory, resummations of renormalized series via equations of the Callan-Symanzik type, asymptotic freedom, and proof of ultraviolet stability for sine-Gordon fields in two dimensions and for other super-renormalizable scalar fields. Renormalization in four dimensions (Hepp's theorem and the De Calan--Rivasseau nexclamation bound) is presented and applications are made to the Coulomb gases in two dimensions and to the convergence of the planar graph expansions in four-dimensional field theories (t' Hooft--Rivasseau theorem).
Improved Monte Carlo Renormalization Group Method
Gupta, R.; Wilson, K. G.; Umrigar, C.
1985-01-01
An extensive program to analyze critical systems using an Improved Monte Carlo Renormalization Group Method (IMCRG) being undertaken at LANL and Cornell is described. Here we first briefly review the method and then list some of the topics being investigated.
Efimov physics from a renormalization group perspective
Hammer, Hans-Werner; Platter, Lucas
2011-01-01
We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.
Efimov physics from a renormalization group perspective.
Hammer, Hans-Werner; Platter, Lucas
2011-07-13
We discuss the physics of the Efimov effect from a renormalization group viewpoint using the concept of limit cycles. Furthermore, we discuss recent experiments providing evidence for the Efimov effect in ultracold gases and its relevance for nuclear systems.
Lectures on the functional renormalization group method
Polonyi, J
2001-01-01
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained in a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed poin...
Towards Holographic Renormalization of Fake Supergravity
Borodatchenkova, Natalia; Mueck, Wolfgang
2008-01-01
A step is made towards generalizing the method of holographic renormalization to backgrounds which are not asymptotically AdS, corresponding to a dual gauge theory which has logarithmically running couplings even in the ultraviolet. A prime example is the background of Klebanov-Strassler (KS). In particular, a recipe is given how to calculate renormalized two-point functions for the operators dual to the bulk scalars. The recipe makes use of gauge-invariant variables for the fluctuations around the background and works for any bulk theory of the fake supergravity type. It elegantly incorporates the renormalization scheme dependence of local terms in the correlators. Before applying the method to the KS theory, it is verified that known results in asymptotically AdS backgrounds are reproduced. Finally, some comments on the calculation of renormalized vacuum expectation values are made.
Renormalization-group improved inflationary scenarios
Pozdeeva, E O
2016-01-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
Renormalization-group improved inflationary scenarios
Pozdeeva, E. O.; Vernov, S. Yu.
2017-03-01
The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of quantum field models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameters values. The scalar electrodynamics inflationary scenario thus obtained are seen to be in good agreement with the most recent observational data.
Higher loop renormalization of fermion bilinear operators
Skouroupathis, A
2007-01-01
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\\bar\\psi\\Gamma\\psi$, where $\\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_\\psi$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. A longer write-up of the present work, including the conversion of our results to the MSbar scheme and a generalization to arbitrary fermion representations, can be found in arXiv:0707.2906 .
Euclidean Epstein-Glaser renormalization
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Keller, Kai J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2009-03-15
In the framework of perturbative Algebraic Quantum Field Theory (pAQFT) I give a general construction of so-called 'Euclidean time-ordered products', i.e. algebraic versions of the Schwinger functions, for scalar quantum eld theories on spaces of Euclidean signature. This is done by generalizing the recursive construction of time-ordered products by Epstein and Glaser, originally formulated for quantum field theories on Minkowski space (MQFT). An essential input of Epstein-Glaser renormalization is the causal structure of Minkowski space. The absence of this causal structure in the Euclidean framework makes it necessary to modify the original construction of Epstein and Glaser at two points. First, the whole construction has to be performed with an only partially defined product on (interaction-) functionals. This is due to the fact that the fundamental solutions of the Helmholtz operator (-{delta}+m{sup 2}) of EQFT have a unique singularity structure, i.e. they are unique up to a smooth part. Second, one needs to (re-)introduce a (rather natural) 'Euclidean causality' condition for the recursion of Epstein and Glaser to be applicable. (orig.)
Oono, Y.; Freed, Karl F.
1981-07-01
A conformation space renormalization group is developed to describe polymer excluded volume in single polymer chains. The theory proceeds in ordinary space in terms of position variables and the contour variable along the chain, and it considers polymers of fixed chain length. The theory is motivated along two lines. The first presents the renormalization group transformation as the means for extracting the macroscopic long wavelength quantities from the theory. An alternative viewpoint shows how the renormalization group transformation follows as a natural consequence of an attempt to correctly treat the presence of a cut-off length scale. It is demonstrated that the current configuration space renormalization method has a one-to-one correspondence with the Wilson-Fisher field theory formulation, so our method is valid to all orders in ɛ = 4-d where d is the spatial dimensionality. This stands in contrast to previous attempts at a configuration space renormalization approach which are limited to first order in ɛ because they arbitrarily assign monomers to renormalized ''blobs.'' In the current theory the real space chain conformations dictate the coarse graining transformation. The calculations are presented to lowest order in ɛ to enable the development of techniques necessary for the treatment of dynamics in Part II. The theory is presented both in terms of the simple delta function interaction as well as using realistic-type interaction potentials. This illustrates the renormalization of the interactions, the emergence of renormalized many-body interactions, and the complexity of the theta point.
Contractor renormalization group and the Haldane conjecture
Energy Technology Data Exchange (ETDEWEB)
Weinstein, Marvin
2001-05-01
The contractor renormalization group formalism (CORE) is a real-space renormalization group method which is the Hamiltonian analogue of the Wilson exact renormalization group equations. In an earlier paper [Phys. Rev. D 61, 034505 (2000)] I showed that the CORE method could be used to map a theory of free quarks and quarks interacting with gluons into a generalized frustrated Heisenberg antiferromagnet (HAF) and proposed using CORE methods to study these theories. Since generalizations of HAF's exhibit all sorts of subtle behavior which, from a continuum point of view, are related to topological properties of the theory, it is important to know that CORE can be used to extract this physics. In this paper I show that despite the folklore which asserts that all real-space renormalization group schemes are necessarily inaccurate, simple CORE computations can give highly accurate results even if one only keeps a small number of states per block and a few terms in the cluster expansion. In addition I argue that even very simple CORE computations give a much better qualitative understanding of the physics than naive renormalization group methods. In particular I show that the simplest CORE computation yields a first-principles understanding of how the famous Haldane conjecture works for the case of the spin-1/2 and spin-1 HAF.
Renormalized vacuum polarization of rotating black holes
Ferreira, Hugo R C
2015-01-01
Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2+1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization (and, more importantly, the renormalized stress-energy tensor), for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.
Foundations and Applications of Entanglement Renormalization
Evenbly, Glen
2011-01-01
Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence of the difficultly of the so-called many-body problem, many exotic quantum phenomena involving extended systems, such as high temperature superconductivity, remain not well understood on a theoretical level. Entanglement renormalization is a recently proposed numerical method for the simulation of many-body systems which draws together ideas from the renormalization group and from the field of quantum information. By taking due care of the quantum entanglement of a system, entanglement renormalization has the potential to go beyond the limitations of previous numerical methods and to provide new insight to quantum collective phenomena. This thesis comprises a significant portion of the research development of ER following its initial proposal. This includes exploratory stud...
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.
Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Wu, Xing-Gang [Chongqing Univ. (China); SLAC National Accelerator Lab., Menlo Park, CA (United States)
2012-08-07
In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {β^{R}_{i}}-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.
Renormalization of the charged scalar field in curved space
Herman, R; Herman, Rhett; Hiscock, William A
1996-01-01
The DeWitt-Schwinger proper time point-splitting procedure is applied to a massive complex scalar field with arbitrary curvature coupling interacting with a classical electromagnetic field in a general curved spacetime. The scalar field current is found to have a linear divergence. The presence of the external background gauge field is found to modify the stress-energy tensor results of Christensen for the neutral scalar field by adding terms of the form (eF)^2 to the logarithmic counterterms. These results are shown to be expected from an analysis of the degree of divergence of scalar quantum electrodynamics.
Higher loop renormalization of a supersymmetric field theory
Energy Technology Data Exchange (ETDEWEB)
Bellon, Marc P. [CEFIMAS, Av. Santa Fe 1145, 1069 Capital Federal (Argentina); Departamento de Fisica, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina); Lozano, Gustavo [Departamento de Fisica, FCEyN, Universidad de Buenos Aires, Pab. I, Ciudad Universitaria, 1428 Buenos Aires (Argentina); Schaposnik, Fidel A. [CEFIMAS, Av. Santa Fe 1145, 1069 Capital Federal (Argentina) and Departamento de Fisica, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata (Argentina)]. E-mail: fidel@fisica.unlp.edu.ar
2007-07-05
Using Dyson-Schwinger equations within an approach developed by Broadhurst and Kreimer and the renormalization group, we show how high loop order of the renormalization group coefficients can be efficiently computed in a supersymmetric model.
Novel formulations of CKM matrix renormalization
Kniehl, B A
2009-01-01
We review two recently proposed on-shell schemes for the renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix in the Standard Model. One first constructs gauge-independent mass counterterm matrices for the up- and down-type quarks complying with the hermiticity of the complete mass matrices. Diagonalization of the latter then leads to explicit expressions for the CKM counterterm matrix, which are gauge independent, preserve unitarity, and lead to renormalized amplitudes that are non-singular in the limit in which any two quarks become mass degenerate. One of the schemes also automatically satisfies flavor democracy.
Renormalized Effective QCD Hamiltonian Gluonic Sector
Robertson, D G; Szczepaniak, A P; Ji, C R; Cotanch, S R
1999-01-01
Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.
Renormalization Group independence of Cosmological Attractors
Fumagalli, Jacopo
2016-01-01
The large class of inflationary models known as $\\alpha$- and $\\xi$-attractors give identical predictions at tree level (at leading order in inverse power of the number of efolds). Working with the renormalization group improved action, we show that these predictions are robust under quantum corrections. This result follows once the field dependence of the renormalization scale, fixed by demanding the leading log correction to vanish, satisfies a quite generic condition. In Higgs inflation this is indeed the case; in the more general attractor models this is still ensured by the renormalizability of the theory in the effective field theory sense.
Exact Renormalization Group for Point Interactions
Eröncel, Cem
2014-01-01
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble non-abelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Automating Renormalization of Quantum Field Theories
Kennedy, A D; Rippon, T
2007-01-01
We give an overview of state-of-the-art multi-loop Feynman diagram computations, and explain how we use symbolic manipulation to generate renormalized integrals that are then evaluated numerically. We explain how we automate BPHZ renormalization using "henges" and "sectors", and give a brief description of the symbolic tensor and Dirac gamma-matrix manipulation that is required. We shall compare the use of general computer algebra systems such as Maple with domain-specific languages such as FORM, highlighting in particular memory management issues.
Relativistic causality and position space renormalization
Todorov, Ivan
2016-11-01
The paper gives a historical survey of the causal position space renormalization with a special attention to the role of Raymond Stora in the development of this subject. Renormalization is reduced to subtracting the pole term in analytically regularized primitively divergent Feynman amplitudes. The identification of residues with "quantum periods" and their relation to recent developments in number theory are emphasized. We demonstrate the possibility of integration over internal vertices (that requires control over the infrared behavior) in the case of the massless φ4 theory and display the dilation and the conformal anomaly.
Renormalized dissipation in plasmas with finite collisionality
Energy Technology Data Exchange (ETDEWEB)
Parker, S.E. [Princeton Plasma Physics Lab., NJ (United States); Carati, D. [Universite Libre de Bruxelles (Belgium). Service de Physique Statistique
1995-05-01
A nonlinear truncation procedure for Fourier-Hermite expansion of Boltzmann-type plasma equations is presented which eliminates fine velocity scale, taking into account its effect on coarser scales. The truncated system is then transformed back to (x, v) space which results in a renormalized Boltzmann equation. The resulting equation may allow for coarser velocity space resolution in kinetic simulations while reducing to the original Boltzmann equation when fine velocity scales are resolved. To illustrate the procedure, renormalized equations are derived for one dimensional electrostatic plasmas in which collisions are modeled by the Lenard-Bernstein operator.
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.
Bonini, M; Marchesini, G
1993-01-01
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the ``relevant'' vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.
Bonini, M.; D'Attanasio, M.; Marchesini, G.
1993-11-01
A new proof of perturbative renormalizability and infrared finiteness for a scalar massless theory is obtained from a formulation of renormalized field theory based on the Wilson renormalization group. The loop expansion of the renormalized Green functions is deduced from the Polchinski equation of renormalization group. The resulting Feynman graphs are organized in such a way that the loop momenta are ordered. It is then possible to analyse their ultraviolet and infrared behaviours by iterative methods. The necessary subtractions and the corresponding counterterms are automatically generated in the process of fixing the physical conditions for the "relevant" vertices at the normalization point. The proof of perturbative renormalizability and infrared finiteness is simply based on dimensional arguments and does not require the usual analysis of topological properties of Feynman graphs.
Enhancement of field renormalization in scalar theories via functional renormalization group
Zappalà, Dario
2012-01-01
The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, to determine the effective potential and the renormalization function of the field in the broken phase. The flow equations of these quantities are derived from a reduction of the full flow of the effective action onto a set of equations for the n-point vertices of the theory. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.
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.)
Complete renormalization of QCD at five loops
Luthe, Thomas; Maier, Andreas; Marquard, Peter; Schröder, York
2017-03-01
We present new analytical five-loop Feynman-gauge results for the anomalous dimensions of ghost field and -vertex, generalizing the known values for SU(3) to a general gauge group. Together with previously published results on the quark mass and -field anomalous dimensions and the Beta function, this completes the 5-loop renormalization program of gauge theories in that gauge.
RENORMALIZED ENERGY WITH VORTICES PINNING EFFECT
Institute of Scientific and Technical Information of China (English)
Ding Shijin
2000-01-01
This paper is a continuation of the previous paper in the Journal of Partial Differential Equations [1]. We derive in this paper the renormalized energy to further determine the locations of vortices in some case for the variational problem related to the superconducting thin films having variable thickness.
Renormalized entropies in a de Sitter spacetime
Xiang, Li; Shen, You-Gen
2005-07-01
The quantum entropies due to the scalar and Dirac fields are investigated in a pure de Sitter spacetime. The leading divergent terms in both cases are regularized by the Pauli-Villars scheme. It is shown that the explosive entropies can be renormalized according to the Bekenstein-Hawking formula.
Basis Optimization Renormalization Group for Quantum Hamiltonian
Sugihara, Takanori
2001-01-01
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.
Renormalization Group Equations for the CKM matrix
Kielanowski, P; Montes de Oca Y, J H
2008-01-01
We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs extension and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle $\\alpha$ of the unitarity triangle. For the special case of the Standard Model and its extensions with $v_{1}\\approx v_{2}$ we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters $\\bar{\\rho}=(1-{1/2}\\lambda^{2})\\rho$ and $\\bar{\\eta}=(1-{1/2}\\lambda^{2})\\eta$ are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix mi...
Composite operators in lattice QCD nonperturbative renormalization
Göckeler, M; Oelrich, H; Perlt, H; Petters, D; Rakow, P; Schäfer, A; Schierholz, G; Schiller, A
1999-01-01
We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of hadronic structure functions. The computations are based on Monte Carlo simulations using quenched Wilson fermions.
Biswas, P K; Gogonea, V
2005-10-22
We describe a regularized and renormalized electrostatic coupling Hamiltonian for hybrid quantum-mechanical (QM)-molecular-mechanical (MM) calculations. To remedy the nonphysical QM/MM Coulomb interaction at short distances arising from a point electrostatic potential (ESP) charge of the MM atom and also to accommodate the effect of polarized MM atom in the coupling Hamiltonian, we propose a partial-wave expansion of the ESP charge and describe the effect of a s-wave expansion, extended over the covalent radius r(c), of the MM atom. The resulting potential describes that, at short distances, large scale cancellation of Coulomb interaction arises intrinsically from the localized expansion of the MM point charge and the potential self-consistently reduces to 1r(c) at zero distance providing a renormalization to the Coulomb energy near interatomic separations. Employing this renormalized Hamiltonian, we developed an interface between the Car-Parrinello molecular-dynamics program and the classical molecular-dynamics simulation program Groningen machine for chemical simulations. With this hybrid code we performed QM/MM calculations on water dimer, imidazole carbon monoxide (CO) complex, and imidazole-heme-CO complex with CO interacting with another imidazole. The QM/MM results are in excellent agreement with experimental data for the geometry of these complexes and other computational data found in literature.
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
Gu, Zheng-Cheng; Wen, Xiao-Gang
2009-10-01
We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the tensors in the tensor network has a nice fixed-point structure. The isolated fixed-point tensors Tinv plus the symmetry group Gsym of the tensors (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D quantum spin-1/2 and spin-1 models. In particular, using such a (Gsym,Tinv) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (Gsym,Tinv) characterization is more general than the characterizations based on the boundary spins and string order parameters. The tensor renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point tensors at those critical points.
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.)
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
Information loss along the renormalization flow
Energy Technology Data Exchange (ETDEWEB)
Beny, Cedric; Osborne, Tobias [Leibniz Universitaet Hannover (Germany)
2013-07-01
Our ability to probe the real world is always limited by experimental constraints such as the precision of our instruments. It is remarkable that the resulting imperfect data nevertheless contains regularities which can be understood in terms of effective laws. The renormalization group (RG) aims to formalize the relationship between effective theories summarizing the behaviour of a single system probed at different length scales. An important feature of the RG is its tendency to converge to few universal effective field theories at large scale. We explicitly model the change of resolution at which a quantum lattice system is probed as a completely positive semigroup on density operators, i.e., a family of quantum channels, and derive from it a renormalization ''group'' on effective theories. This formalism suggests a family of finite distinguishability metrics which contract under the RG, hence identifying the information that is lost on the way to universal RG fixed points.
Holographic renormalization and the electroweak precision parameters
Round, Mark
2010-09-01
We study the effects of holographic renormalization on an AdS/QCD inspired description of dynamical electroweak symmetry breaking. Our model is a 5D slice of AdS5 geometry containing a bulk scalar and SU(2)×SU(2) gauge fields. The scalar field obtains a vacuum expectation value (VEV) which represents a condensate that triggers electroweak symmetry breaking. Fermion fields are constrained to live on the UV brane and do not propagate in the bulk. The two-point functions are holographically renormalized through the addition of boundary counterterms. Measurable quantities are then expressed in terms of well-defined physical parameters, free from any spurious dependence on the UV cutoff. A complete study of the precision parameters is carried out and bounds on physical quantities derived. The large-N scaling of results is discussed.
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 of Magnetic Excitations in Praseodymium
DEFF Research Database (Denmark)
Lindgård, Per-Anker
1975-01-01
The magnetic exciton renormalization and soft-mode behaviour as the temperature approaches zero of the singlet-doublet magnet (dhcp)pr are accounted for by a selfconsistent rpa theory with no adjustable parameters. The crystal-field splitting between the ground state and the doublet is d=3.74 mev...... and the ratio between the exchange interaction and d is very close to unity. However, zero-point motion prevents the system from ordering.......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...
Accurate renormalization group analyses in neutrino sector
Energy Technology Data Exchange (ETDEWEB)
Haba, Naoyuki [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Kaneta, Kunio [Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8568 (Japan); Takahashi, Ryo [Graduate School of Science and Engineering, Shimane University, Matsue 690-8504 (Japan); Yamaguchi, Yuya [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)
2014-08-15
We investigate accurate renormalization group analyses in neutrino sector between ν-oscillation and seesaw energy scales. We consider decoupling effects of top quark and Higgs boson on the renormalization group equations of light neutrino mass matrix. Since the decoupling effects are given in the standard model scale and independent of high energy physics, our method can basically apply to any models beyond the standard model. We find that the decoupling effects of Higgs boson are negligible, while those of top quark are not. Particularly, the decoupling effects of top quark affect neutrino mass eigenvalues, which are important for analyzing predictions such as mass squared differences and neutrinoless double beta decay in an underlying theory existing at high energy scale.
A Hopf algebra deformation approach to renormalization
Ionescu, L M; Ionescu, Lucian M.; Marsalli, Michael
2003-01-01
We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and double Lie algebras/Lie bialgebras, via r-matrices. It is suggested that the QFTs obtained via deformation quantization and renormalization correspond to each other in the sense of Kontsevich/Cattaneo-Felder.
Renormalization of QCD under longitudinal rescaling
Xiao, Jing
2009-01-01
The form of the quantum Yang-Mills action, under a longitudinal rescaling is determined using a Wilsonian renormalization group. The high-energy limit, is the extreme limit of such a rescaling. We compute the anomalous dimensions and discuss the validity of the high-energy limit. This thesis is an expanded version of joint work with P. Orland, which appeared in arXiv:0901.2955.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
Dense nucleonic matter and the renormalization group
Drews, Matthias; Klein, Bertram; Weise, Wolfram
2013-01-01
Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.
Dense nucleonic matter and the renormalization group
Directory of Open Access Journals (Sweden)
Drews Matthias
2014-03-01
Full Text Available Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase diagram of QCD. We find good agreement with results from chiral effective field theory. Moreover, the results show a separation of the chemical freeze-out line and chiral symmetry restoration at large baryon chemical potentials.
Disordered Holographic Systems I: Functional Renormalization
Adams, Allan
2011-01-01
We study quenched disorder in strongly correlated systems via holography, focusing on the thermodynamic effects of mild electric disorder. Disorder is introduced through a random potential which is assumed to self-average on macroscopic scales. Studying the flow of this distribution with energy scale leads us to develop a holographic functional renormalization scheme. We test this scheme by computing thermodynamic quantities and confirming that the Harris criterion for relevance, irrelevance or marginality of quenched disorder holds.
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...
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...... Schro¨dinger equation is an occasion for physics-oriented considerations and unveils the potential of photonic crystal waveguides for the study of new nonlinear propagation phenomena....
Integrable Renormalization II: the general case
Ebrahimi-Fard, K; Kreimer, D; Ebrahimi-Fard, Kurusch; Guo, Li; Kreimer, Dirk
2004-01-01
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the Birkhoff decomposition of renormalization theory is derived by using the Rota-Baxter double construction, respectively Atkinson's theorem. We also outline the extension to the Hopf algebra of Feynman graphs via decorated rooted trees.
A shape dynamical approach to holographic renormalization
Energy Technology Data Exchange (ETDEWEB)
Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2015-01-01
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)
Renormalization persistency of tensor force in nuclei
Tsunoda, Naofumi; Tsukiyama, Koshiroh; Hjorth-Jensen, Morten
2011-01-01
In this work we analyze the tensor-force component of effective interactions appropriate for nuclear shell-model studies, with particular emphasis on the monopole term of the interactions. Standard nucleon-nucleon ($NN$) interactions such as AV8' and $\\chi$N$^3$LO are tailored to shell-model studies by employing $V_{low k}$ techniques to handle the short-range repulsion of the $NN$ interactions and by applying many-body perturbation theory to incorporate in-medium effects. We show, via numerical studies of effective interactions for the $sd$ and $pf$ shells, that the tensor-force contribution to the monopole term of the effective interaction is barely changed by these renormalization procedures, resulting in almost the same monopole term as the one of the bare $NN$ interactions. We propose to call this feature {\\it Renormalization Persistency} of the tensor force, as it is a remarkable property of the renormalization and should have many interesting consequences in nuclear systems. For higher multipole terms,...
Renormalization, Hopf algebras and Mellin transforms
Panzer, Erik
2014-01-01
This article aims to give a short introduction into Hopf-algebraic aspects of renormalization, enjoying growing attention for more than a decade by now. As most available literature is concerned with the minimal subtraction scheme, we like to point out properties of the kinematic subtraction scheme which is also widely used in physics (under the names of MOM or BPHZ). In particular we relate renormalized Feynman rules $\\phi_R$ in this scheme to the universal property of the Hopf algebra $H_R$ of rooted trees, exhibiting a refined renormalization group equation which is equivalent to $\\phi_R: H_R \\rightarrow K[x]$ being a morphism of Hopf algebras to the polynomials in one indeterminate. Upon introduction of analytic regularization this results in efficient combinatorial recursions to calculate $\\phi_R$ in terms of the Mellin transform. We find that different Feynman rules are related by a distinguished class of Hopf algebra automorphisms of $H_R$ that arise naturally from Hochschild cohomology. Also we recall...
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, T; Kawai, H; Ninomiya, M
1994-01-01
We study quantum gravity in 2+\\epsilon dimensions in such a way to preserve the volume preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for matter central charge 0
Renormalization of the graphene dispersion velocity determined from scanning tunneling spectroscopy.
Chae, Jungseok; Jung, Suyong; Young, Andrea F; Dean, Cory R; Wang, Lei; Gao, Yuanda; Watanabe, Kenji; Taniguchi, Takashi; Hone, James; Shepard, Kenneth L; Kim, Phillip; Zhitenev, Nikolai B; Stroscio, Joseph A
2012-09-14
In graphene, as in most metals, electron-electron interactions renormalize the properties of electrons but leave them behaving like noninteracting quasiparticles. Many measurements probe the renormalized properties of electrons right at the Fermi energy. Uniquely for graphene, the accessibility of the electrons at the surface offers the opportunity to use scanned probe techniques to examine the effect of interactions at energies away from the Fermi energy, over a broad range of densities, and on a local scale. Using scanning tunneling spectroscopy, we show that electron interactions leave the graphene energy dispersion linear as a function of excitation energy for energies within ±200 meV of the Fermi energy. However, the measured dispersion velocity depends on density and increases strongly as the density approaches zero near the charge neutrality point, revealing a squeezing of the Dirac cone due to interactions.
Renormalization of multiple infinities and the renormalization group in string loops
Russo, J.; Tseytlin, A. A.
1990-08-01
There is a widespread belief that string loop massles divergences may be absorbed into a renormalization of σ-model couplings (space-time metric and dilaton). The crucial property for this idea to be consistently implemented to arbitrary order in string loops should be the renormalizability of the generating functional for string amplitudes. We make several non-trivial checks of the renormalizability by explicit calculations at genus 1, 2 and 3. The renormalizability becomes non-trivial at the log 2ɛ order. We show that the log 2 ɛ counterterms are universal (e.g. the same counterterms provide finiteness both of two-loop scattering amplitudes and of the three-loop partition function) and are related to the log ɛ counterterms (β-functions) in the standard way dictated by the renormalization group. This checks the consistency of the Fischler-Susskind mechanism and implies that the renormalization group acts properly at the string loop level.
Hilbert space renormalization for the many-electron problem
Li, Zhendong
2015-01-01
Renormalization is a powerful concept in the many-body problem. Inspired by the highly successful density matrix renormalization group (DMRG) algorithm, and the quantum chemical graphical representation of configuration space, we introduce a new theoretical tool: Hilbert space renormalization, to describe many-electron correlations. While in DMRG, the many-body states in nested Fock subspaces are successively renormalized, in Hilbert space renormalization, many-body states in nested Hilbert subspaces undergo renormalization. This provides a new way to classify and combine configurations. The underlying wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS), has a very rich and flexible mathematical structure. It provides low-rank tensor approximations to any configuration interaction (CI) space through restricting either the 'physical indices' or the coupling rules in the HS-MPS. Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to a family of size-extensive wav...
Gauge and Scheme Dependence of Mixing Matrix Renormalization
Pilaftsis, Apostolos
2002-01-01
We revisit the issue of mixing matrix renormalization in theories that include Dirac or Majorana fermions. We show how a gauge-variant on-shell renormalized mixing matrix can be related to a manifestly gauge-independent one within a generalized ${\\bar {\\rm MS}}$ scheme of renormalization. This scheme-dependent relation is a consequence of the fact that in any scheme of renormalization, the gauge-dependent part of the mixing-matrix counterterm is ultra-violet safe and has a pure dispersive form. Employing the unitarity properties of the theory, we can successfully utilize the afore-mentioned scheme-dependent relation to preserve basic global or local symmetries of the bare Lagrangian through the entire process of renormalization. As an immediate application of our study, we derive the gauge-independent renormalization-group equations of mixing matrices in a minimal extension of the Standard Model with isosinglet neutrinos.
Improved Epstein–Glaser renormalization in x-space versus differential renormalization
Directory of Open Access Journals (Sweden)
José M. Gracia-Bondía
2014-09-01
Full Text Available Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
Improved Epstein–Glaser renormalization in x-space versus differential renormalization
Energy Technology Data Exchange (ETDEWEB)
Gracia-Bondía, José M. [Department of Theoretical Physics, Universidad de Zaragoza, 50009 Zaragoza (Spain); BIFI Research Center, Universidad de Zaragoza, 50018 Zaragoza (Spain); Department of Physics, Universidad de Costa Rica, San José 11501 (Costa Rica); Gutiérrez, Heidy [Department of Physics, Universidad de Costa Rica, San José 11501 (Costa Rica); Várilly, Joseph C., E-mail: joseph.varilly@ucr.ac.cr [Department of Mathematics, Universidad de Costa Rica, San José 11501 (Costa Rica)
2014-09-15
Renormalization of massless Feynman amplitudes in x-space is reexamined here, using almost exclusively real-variable methods. We compute a wealth of concrete examples by means of recursive extension of distributions. This allows us to show perturbative expansions for the four-point and two-point functions at several loop order. To deal with internal vertices, we expound and expand on convolution theory for log-homogeneous distributions. The approach has much in common with differential renormalization as given by Freedman, Johnson and Latorre; but differs in important details.
An algebraic Birkhoff decomposition for the continuous renormalization group
Girelli, F; Martinetti, P
2004-01-01
This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited.
Renormalization in general theories with inter-generation mixing
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Sirlin, Alberto [New York Univ., NY (United States). Dept. of Physics
2011-11-15
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.)
Applications of noncovariant gauges in the algebraic renormalization procedure
Boresch, A; Schweda, Manfred
1998-01-01
This volume is a natural continuation of the book Algebraic Renormalization, Perturbative Renormalization, Symmetries and Anomalies, by O Piguet and S P Sorella, with the aim of applying the algebraic renormalization procedure to gauge field models quantized in nonstandard gauges. The main ingredient of the algebraic renormalization program is the quantum action principle, which allows one to control in a unique manner the breaking of a symmetry induced by a noninvariant subtraction scheme. In particular, the volume studies in-depth the following quantized gauge field models: QED, Yang-Mills t
Summation of Higher Order Effects using the Renormalization Group Equation
Elias, V; Sherry, T N
2004-01-01
The renormalization group (RG) is known to provide information about radiative corrections beyond the order in perturbation theory to which one has calculated explicitly. We first demonstrate the effect of the renormalization scheme used on these higher order effects determined by the RG. Particular attention is payed to the relationship between bare and renormalized quantities. Application of the method of characteristics to the RG equation to determine higher order effects is discussed, and is used to examine the free energy in thermal field theory, the relationship between the bare and renormalized coupling and the effective potential in massless scalar electrodynamics.
Renormalization group circuits for gapless states
Swingle, Brian; McGreevy, John; Xu, Shenglong
2016-05-01
We show that a large class of gapless states are renormalization group fixed points in the sense that they can be grown scale by scale using local unitaries. This class of examples includes some theories with a dynamical exponent different from one, but does not include conformal field theories. The key property of the states we consider is that the ground-state wave function is related to the statistical weight of a local statistical model. We give several examples of our construction in the context of Ising magnetism.
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.)
Renormalization of Hierarchically Interacting Isotropic Diffusions
den Hollander, F.; Swart, J. M.
1998-10-01
We study a renormalization transformation arising in an infinite system of interacting diffusions. The components of the system are labeled by the N-dimensional hierarchical lattice ( N≥2) and take values in the closure of a compact convex set bar D subset {R}^d (d ≥slant 1). Each component starts at some θ ∈ D and is subject to two motions: (1) an isotropic diffusion according to a local diffusion rate g: bar D to [0,infty ] chosen from an appropriate class; (2) a linear drift toward an average of the surrounding components weighted according to their hierarchical distance. In the local mean-field limit N→∞, block averages of diffusions within a hierarchical distance k, on an appropriate time scale, are expected to perform a diffusion with local diffusion rate F ( k) g, where F^{(k)} g = (F_{c_k } circ ... circ F_{c_1 } ) g is the kth iterate of renormalization transformations F c ( c>0) applied to g. Here the c k measure the strength of the interaction at hierarchical distance k. We identify F c and study its orbit ( F ( k) g) k≥0. We show that there exists a "fixed shape" g* such that lim k→∞ σk F ( k) g = g* for all g, where the σ k are normalizing constants. In terms of the infinite system, this property means that there is complete universal behavior on large space-time scales. Our results extend earlier work for d = 1 and bar D = [0,1], resp. [0, ∞). The renormalization transformation F c is defined in terms of the ergodic measure of a d-dimensional diffusion. In d = 1 this diffusion allows a Yamada-Watanabe-type coupling, its ergodic measure is reversible, and the renormalization transformation F c is given by an explicit formula. All this breaks down in d≥2, which complicates the analysis considerably and forces us to new methods. Part of our results depend on a certain martingale problem being well-posed.
Functional renormalization group approach to neutron matter
Directory of Open Access Journals (Sweden)
Matthias Drews
2014-11-01
Full Text Available The chiral nucleon-meson model, previously applied to systems with equal number of neutrons and protons, is extended to asymmetric nuclear matter. Fluctuations are included in the framework of the functional renormalization group. The equation of state for pure neutron matter is studied and compared to recent advanced many-body calculations. The chiral condensate in neutron matter is computed as a function of baryon density. It is found that, once fluctuations are incorporated, the chiral restoration transition for pure neutron matter is shifted to high densities, much beyond three times the density of normal nuclear matter.
The exact renormalization group and approximation solutions
Morris, T R
1994-01-01
We investigate the structure of Polchinski's formulation of the flow equations for the continuum Wilson effective action. Reinterpretations in terms of I.R. cutoff greens functions are given. A promising non-perturbative approximation scheme is derived by carefully taking the sharp cutoff limit and expanding in `irrelevancy' of operators. We illustrate with two simple models of four dimensional $\\lambda \\varphi^4$ theory: the cactus approximation, and a model incorporating the first irrelevant correction to the renormalized coupling. The qualitative and quantitative behaviour give confidence in a fuller use of this method for obtaining accurate results.
A comment on the relationship between differential and dimensional renormalization
Dunne, G; Dunne, Gerald; Rius, Nuria
1992-01-01
We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension.
Feynman graph solution to Wilson's exact renormalization group
Sonoda, H
2003-01-01
We introduce a new prescription for renormalizing Feynman diagrams. The prescription is similar to BPHZ, but it is mass independent, and works in the massless limit as the MS scheme with dimensional regularization. The prescription gives a diagrammatic solution to Wilson's exact renormalization group differential equation.
Goldberger-treiman relation in the renormalized sigma model
Strubbe, H.J.
1972-01-01
The regularization and renormalization of the full sigma model is worked out explicitly in the tree and one-loop approximation. Various renormalized quantities relevant for chiral symmetry breaking are listed. The numerically calculated Goldberger-Treiman relation is also compared with experiment.
Holographic Entanglement Renormalization of Topological Insulators
Wen, Xueda; Lopes, Pedro L S; Gu, Yingfei; Qi, Xiao-Liang; Ryu, Shinsei
2016-01-01
We study the real-space entanglement renormalization group flows of topological band insulators in (2+1) dimensions by using the continuum multi-scale entanglement renormalization ansatz (cMERA). Given the ground state of a Chern insulator, we construct and study its cMERA by paying attention, in particular, to how the bulk holographic geometry and the Berry curvature depend on the topological properties of the ground state. It is found that each state defined at different energy scale of cMERA carries a nonzero Berry flux, which is emanated from the UV layer of cMERA, and flows towards the IR. Hence, a topologically nontrivial UV state flows under the RG to an IR state, which is also topologically nontrivial. On the other hand, we found that there is an obstruction to construct the exact ground state of a topological insulator with a topologically trivial IR state. I.e., if we try to construct a cMERA for the ground state of a Chern insulator by taking a topologically trivial IR state, the resulting cMERA do...
Two-Loop Renormalization in the Standard Model
Actis, S; Passarino, G; Passera, M
2006-01-01
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.
Kazinski, P. O.; Lyakhovich, S. L.; Sharapov, A. A.
2002-07-01
The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.
Conformal invariance and renormalization group in quantum gravity near two dimensions
Aida, Toshiaki; Kitazawa, Yoshihisa; Kawai, Hikaru; Ninomiya, Masao
1994-09-01
We study quantum gravity in 2 + ɛ dimensions in such a way as to preserve the volume-preserving diffeomorphism invariance. In such a formulation, we prove the following trinity: the general covariance, the conformal invariance and the renormalization group flow to the Einstein theory at long distance. We emphasize that the consistent and macroscopic universes like our own can only exist for a matter central charge 0 effect and universes are found to bounce back from the big crunch. Our formulation may be viewed as a Ginzburg-Landau theory which can describe both the broken and the unbroken phase of quantum gravity and the phase transition between them.
Kazinski, P O; Sharapov, A A
2002-01-01
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.
Holographic interpretations of the renormalization group
Balasubramanian, Vijay; Lawrence, Albion
2012-01-01
In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $\\Delta \
VLES Modelling with the Renormalization Group
Institute of Scientific and Technical Information of China (English)
Chris De Langhe; Bart Merci; Koen Lodefier; Erik Dick
2003-01-01
In a Very-Large-Eddy Simulation (VLES), the filterwidth-wavenumber can be outside the inertial range, and simple subgrid models have to be replaced by more complicated ('RANS-like') models which can describe the transport of the biggest eddies. One could approach this by using a RANS model in these regions, and modify the lengthscale in the model for the LES-regions[1～3]. The problem with these approaches is that these models are specifically calibrated for RANS computations, and therefore not suitable to describe inertial range quantities. We investigated the construction of subgrid viscosity and transport equations without any calibrated constants, but these are calculated directly form the Navier-Stokes equation by means of a Renormalization Group (RG)procedure. This leads to filterwidth dependent transport equations and effective viscosity with the right limiting behaviour (DNS and RANS limits).
Spin connection and renormalization of teleparallel action
Energy Technology Data Exchange (ETDEWEB)
Krššák, Martin, E-mail: krssak@ift.unesp.br; Pereira, J. G., E-mail: jpereira@ift.unesp.br [Instituto de Física Teórica, Universidade Estadual Paulista, R. Dr. Bento Teobaldo Ferraz 271, 01140-070, São Paulo, SP (Brazil)
2015-10-31
In general relativity, inertia and gravitation are both included in the Levi–Civita connection. As a consequence, the gravitational action, as well as the corresponding energy–momentum density, are in general contaminated by spurious contributions coming from inertial effects. In teleparallel gravity, on the other hand, because the spin connection represents inertial effects only, it is possible to separate inertia from gravitation. Relying on this property, it is shown that to each tetrad there is naturally associated a spin connection that locally removes the inertial effects from the action. The use of the appropriate spin connection can be viewed as a renormalization process in the sense that the computation of energy and momentum naturally yields the physically relevant values. A self-consistent method for solving field equations and determining the appropriate spin connection is presented.
Renormalization group theory impact on experimental magnetism
Köbler, Ulrich
2010-01-01
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...
Renormalization of QED near Decoupling Temperature
Masood, Samina S
2014-01-01
We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron selfmass, {\\delta}m/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.
Fermionic functional integrals and the renormalization group
Feldman, Joel; Trubowitz, Eugene
2002-01-01
This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...
Development of renormalization group analysis of turbulence
Smith, L. M.
1990-01-01
The renormalization group (RG) procedure for nonlinear, dissipative systems is now quite standard, and its applications to the problem of hydrodynamic turbulence are becoming well known. In summary, the RG method isolates self similar behavior and provides a systematic procedure to describe scale invariant dynamics in terms of large scale variables only. The parameterization of the small scales in a self consistent manner has important implications for sub-grid modeling. This paper develops the homogeneous, isotropic turbulence and addresses the meaning and consequence of epsilon-expansion. The theory is then extended to include a weak mean flow and application of the RG method to a sequence of models is shown to converge to the Navier-Stokes equations.
Integrable Renormalization I: the Ladder Case
Ebrahimi-Fard, K; Kreimer, D; Ebrahimi-Fard, Kurusch; Guo, Li; Kreimer, Dirk
2004-01-01
In recent years a Hopf algebraic structure underlying the process of renormalization in quantum field theory was found. It led to a Birkhoff factorization for (regularized) Hopf algebra characters, i.e. for Feynman rules. In this work we would like to show that this Birkhoff factorization finds its natural formulation in terms of a classical r-matrix, coming from a Rota-Baxter structure underlying the target space of the regularized Hopf algebra characters. Working in the rooted tree Hopf algebra, the simple case of the Hopf subalgebra of ladder trees is treated in detail. The extension to the general case, i.e. the full Hopf algebra of rooted trees or Feynman graphs is briefly outlined.
Renormalization group improved Higgs inflation with a running kinetic term
Takahashi, Fuminobu; Takahashi, Ryo
2016-09-01
We study a Higgs inflation model with a running kinetic term, taking account of the renormalization group evolution of relevant coupling constants. Specifically we study two types of the running kinetic Higgs inflation, where the inflaton potential is given by the quadratic or linear term potential in a frame where the Higgs field is canonically normalized. We solve the renormalization group equations at two-loop level and calculate the scalar spectral index and the tensor-to-scalar ratio. We find that, even if the renormalization group effects are included, the quadratic inflation is ruled out by the CMB observations, while the linear one is still allowed.
Ward identities and Wilson renormalization group for QED
Bonini, M; Marchesini, G
1994-01-01
We analyze a formulation of QED based on the Wilson renormalization group. Although the ``effective Lagrangian'' used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's functions correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski's renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponding counterterms are generated in the process of fixing the physical conditions.
Ward identities and Wilson renormalization group for QED
Bonini, M.; D'Attanasio, M.; Marchesini, G.
1994-04-01
We analyze a formulation of QED based on the Wilson renormalization group. Although the "effective lagrangian" used at any given scale does not have simple gauge symmetry, we show that the resulting renormalized Green's function correctly satisfies Ward identities to all orders in perturbation theory. The loop expansion is obtained by solving iteratively the Polchinski renormalization group equation. We also give a new simple proof of perturbative renormalizability. The subtractions in the Feynman graphs and the corresponing counter-terms are generated in the process of fixing the physical conditions.
On the Renormalization of Heavy Quark Effective Field Theory
Kilian, W
1994-01-01
The construction of heavy quark effective field theory (HqEFT) is extended to arbitrary order in both expansion parameters $\\alpha_s$ and $1/m_q$. Matching conditions are discussed for the general case, and it is verified that this approach correctly reproduces the infrared behaviour of full QCD. Choosing a renormalization scheme in the full theory fixes the renormalization scheme in the effective theory except for the scale of the heavy quark field. Explicit formulae are given for the effective Lagrangian, and one--loop matching renormalization constants are computed for the operators of order $1/m$. Finally, the multiparticle sector of HqEFT is considered.
Anton, L; Marti, J M; Ibanez, J M; Aloy, M A; Mimica, P
2009-01-01
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numeric...
Reductive renormalization of the phase-field crystal equation.
Oono, Y; Shiwa, Y
2012-12-01
It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods. Reductive renormalization was proposed to make this unification practically accessible; actually, this reductive perturbation is far simpler than most reduction methods, such as the rather standard scaling expansion. However, a rather cryptic exposition of the method seems to have been the cause of some trouble. Here, an explicit demonstration of the consistency of the reductive renormalization-group procedure is given for partial differentiation equations (of a certain type, including time-evolution semigroup type equations). Then, the procedure is applied to the reduction of a phase-field crystal equation to illustrate the streamlined reduction method. We conjecture that if the original system is structurally stable, the reductive renormalization-group result and that of the original equation are diffeomorphic.
The Role of Renormalization Group in Fundamental Theoretical Physics
Shirkov, Dmitri V.
1997-01-01
General aspects of fundamental physics are considered. We comment the Wigner's logical scheme and modify it to adjust to modern theoretical physics. Then, we discuss the role and indicate the place of renormalization group in the logic of fundamental physics.
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
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.
Renormalization and power counting of chiral nuclear forces
Energy Technology Data Exchange (ETDEWEB)
Long, Bingwei [JLAB
2013-08-01
I discuss the progress we have made on modifying Weinberg's prescription for chiral nuclear forces, using renormalization group invariance as the guideline. Some of the published results are presented.
Dimensional regularization and renormalization of non-commutative QFT
Gurau, R
2007-01-01
Using the recently introduced parametric representation of non-commutative quantum field theory, we implement here the dimensional regularization and renormalization of the vulcanized $\\Phi^{\\star 4}_4$ model on the Moyal space.
Theory of temperature dependent phonon-renormalized properties
Monserrat, Bartomeu; Conduit, G. J.; Needs, R. J.
2013-01-01
We present a general harmonic theory for the temperature dependence of phonon-renormalized properties of solids. Firstly, we formulate a perturbation theory in phonon-phonon interactions to calculate the phonon renormalization of physical quantities. Secondly, we propose two new schemes for extrapolating phonon zero-point corrections from temperature dependent data that improve the accuracy by an order of magnitude compared to previous approaches. Finally, we consider the low-temperature limi...
Supergravity corrections to $(g-2)_l$ in differential renormalization
del Águila, F; Muñoz-Tàpia, R; Pérez-Victoria, M
1997-01-01
The method of differential renormalization is extended to the calculati= on of the one-loop graviton and gravitino corrections to $(g-2)_l$ in unbroken supergravity. Rewriting the singular contributions of all the diagrams in= terms of only one singular function, U(1) gauge invariance and supersymmetry ar= e preserved. We compare this calculation with previous ones which made use = of momentum space regularization (renormalization) methods.
Higher covariant derivative regulators and non-multiplicative renormalization
Energy Technology Data Exchange (ETDEWEB)
Martin, C.P. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica; Ruiz Ruiz, F. [Nationaal Inst. voor Kernfysica en Hoge-Energiefysica (NIKHEF), Amsterdam (Netherlands). Sectie H
1994-12-31
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with dimensional regularization to obtain a consistent renormalized 4-dimensional Yang-Mills theory at the one-loop level. This shows that hybrid regularization methods can be applied not only to finite theories, like e.g. Chern-Simons, but also to divergent theories. (orig.).
The local renormalization of super-Yang-Mills theories
Gillioz, Marc
2016-01-01
We show how to consistently renormalize $\\mathcal{N} = 1$ and $\\mathcal{N} = 2$ super-Yang-Mills theories in flat space with a local (i.e. space-time-dependent) renormalization scale in a holomorphic scheme. The action gets enhanced by a term proportional to derivatives of the holomorphic coupling. In the $\\mathcal{N} = 2$ case, this new action is exact at all orders in perturbation theory.
Cohomology and Renormalization of BFYM Theory in three Dimensions
Accardi, A; Martellini, M; Zeni, M; Accardi, Alberto; Belli, Andrea; Martellini, Maurizio; Zeni, Mauro
1997-01-01
The first order formalism for 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 cohomology and renormalization for 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.
Renormalization of the energy-momentum tensor on the lattice
Pepe, Michele
2015-01-01
We present the calculation of the non-perturbative renormalization constants of the energy-momentum tensor in the SU(3) Yang-Mills theory. That computation is carried out in the framework of shifted boundary conditions, where a thermal quantum field theory is formulated in a moving reference frame. The non-perturbative renormalization factors are then used to measure the Equation of State of the SU(3) Yang-Mills theory. Preliminary numerical results are presented and discussed.
Renormalization theory in four dimensional scalar fields. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Gallavotti, G.; Nicolo, F.
1985-08-01
We present a renormalization group appraoch to the renormalization thoery of PHI/sub 4//sup 4/ using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the Schwinger functions. The main aim of this paper is to show how one can in this way obtain the n-bounds.
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.
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
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, will be discussed in p...
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.
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.)
Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei
2016-01-01
The Multiscale Entanglement Renormalization Ansatz (MERA) is a tensor network based variational ansatz that is capable of capturing many of the key physical properties of strongly correlated ground states such as criticality and topological order. MERA also shares many deep relationships with the AdS/CFT (gauge-gravity) correspondence by realizing a UV complete holographic duality within the tensor networks framework. Motivated by this, we have re-purposed the MERA tensor network as an analysis tool to study the real-time evolution of the 1D transverse Ising model in its low energy excited state sector. We performed this analysis by allowing the ancilla qubits of the MERA tensor network to acquire quantum fluctuations, which yields a unitary transform between the physical (boundary) and ancilla qubit (bulk) Hilbert spaces. This then defines a reversible quantum circuit which is used as a `holographic transform' to study excited states and their real-time dynamics from the point of the bulk ancillae. In the ga...
Renormalization of QED Near Decoupling Temperature
Directory of Open Access Journals (Sweden)
Samina S. Masood
2014-01-01
Full Text Available We study the effective parameters of QED near decoupling temperatures and show that the QED perturbative series is convergent, at temperatures below the decoupling temperature. The renormalization constant of QED acquires different values if a system cools down from a hotter system to the electron mass temperature or heats up from a cooler system to the same temperature. At T = m, the first order contribution to the electron self-mass, δm/m is 0.0076 for a heating system and 0.0115 for a cooling system and the difference between two values is equal to 1/3 of the low temperature value and 1/2 of the high temperature value around T~m. This difference is a measure of hot fermion background at high temperatures. With the increase in release of more fermions at hotter temperatures, the fermion background contribution dominates and weak interactions have to be incorporated to understand the background effects.
General Covariance from the Quantum Renormalization Group
Shyam, Vasudev
2016-01-01
The Quantum renormalization group (QRG) is a realisation of holography through a coarse graining prescription that maps the beta functions of a quantum field theory thought to live on the `boundary' of some space to holographic actions in the `bulk' of this space. A consistency condition will be proposed that translates into general covariance of the gravitational theory in the $D + 1$ dimensional bulk. This emerges from the application of the QRG on a planar matrix field theory living on the $D$ dimensional boundary. This will be a particular form of the Wess--Zumino consistency condition that the generating functional of the boundary theory needs to satisfy. In the bulk, this condition forces the Poisson bracket algebra of the scalar and vector constraints of the dual gravitational theory to close in a very specific manner, namely, the manner in which the corresponding constraints of general relativity do. A number of features of the gravitational theory will be fixed as a consequence of this form of the Po...
Functional renormalization group methods in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Braun, J.
2006-12-18
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
Renormalization of aperiodic model lattices: spectral properties
Kroon, L
2003-01-01
Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schroedinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubli...
Theories of Matter: Infinities and Renormalization
Kadanoff, Leo P
2010-01-01
This paper looks at the theory underlying the science of materials from the perspectives of physics, the history of science, and the philosophy of science. We are particularly concerned with the development of understanding of the thermodynamic phases of matter. The question is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) rise from a pot of heated water. The nature of the phases is brought into the sharpest focus in phase transitions: abrupt changes from one phase to another and hence changes from one behavior to another. This article starts with the development of mean field theory as a basis for a partial understanding of phase transition phenomena. It then goes on to the limitations of mean field theory and the development of very different supplementary understanding through the renormalization group concept. Throughout, the behavior at the phase transition is illuminated by an "extende...
Nonlinear dynamics in combinatorial games: Renormalizing Chomp
Friedman, Eric J.; Landsberg, Adam Scott
2007-06-01
We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to transform a combinatorial game like Chomp into a type of dynamical system. Not only does this provide powerful insights into the game of Chomp (yielding a complete probabilistic description of optimal play in Chomp and an answer to a longstanding question about the nature of the winning opening move), but more generally, it offers a mathematical framework for exploring this unexpected relationship between combinatorial games and modern dynamical systems theory.
Renormalization group approach to superfluid neutron matter
Energy Technology Data Exchange (ETDEWEB)
Hebeler, K.
2007-06-06
In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)
Renormalized Wick expansion for a modified PQCD
de Oca, Alejandro Cabo Montes
2007-01-01
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered, by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counter-terms are allowed in this mass less theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and to masses $m_q$ and $m_g$ associated to quarks and gluons respectively. This procedure allows to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters $m_q$ and $m_g$ is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential, is evaluated in more detail in the case when only the quark condensate is retained. This lowest order...
Renormalized Wick expansion for a modified PQCD
Energy Technology Data Exchange (ETDEWEB)
Cabo Montes de Oca, Alejandro [Instituto de Cibernetica, Matematica y Fisica, Group of Theoretical Physics, Vedado, La Habana (Cuba); Abdus Salam International Centre for Theoretical Physics, Trieste (Italy)
2008-05-15
The renormalization scheme for the Wick expansion of a modified version of the perturbative QCD introduced in previous works is discussed. Massless QCD is considered by implementing the usual multiplicative scaling of the gluon and quark wave functions and vertices. However, also massive quark and gluon counterterms are allowed in this massless theory since the condensates are expected to generate masses. A natural set of expansion parameters of the physical quantities is introduced: the coupling itself and the two masses m{sub q} and m{sub g} associated to quarks and gluons, respectively. This procedure allows one to implement a dimensional transmutation effect through these new mass scales. A general expression for the new generating functional in terms of the mass parameters m{sub q} and m{sub g} is obtained in terms of integrals over arbitrary but constant gluon or quark fields in each case. Further, the one loop potential is evaluated in more detail in the case when only the quark condensate is retained. This lowest order result again indicates the dynamical generation of quark condensates in the vacuum. (orig.)
Holographic renormalization as a canonical transformation
Papadimitriou, Ioannis
2010-01-01
The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in asymptotically AdS spaces these problems are systematically addressed by the method of holographic renormalization. We argue that this class of a priori ill defined variational problems extends far beyond the realm of holographic dualities. As we show, exactly the same issues arise in gravity in non asymptotically AdS spaces, in point particles with certain unbounded from below potentials, and even fundamental strings in flat or AdS backgrounds. We show that the variational problem in all such cases can be made well defined by the following procedure, which is intrinsic to the system in question and does not rely on the existence of a holographically dual theory: (i) The first step is the construction of the space of the most general asymptotic solutions of the classical equati...
The Renormalization of the Electroweak Standard Model to All Orders
Kraus, E
1998-01-01
We give the renormalization of the standard model of electroweak interactions to all orders of perturbation theory by using the method of algebraic renormalization, which is based on general properties of renormalized perturbation theory and not on a specific regularization scheme. The Green functions of the standard model are uniquely constructed to all orders, if one defines the model by the Slavnov-Taylor identity, Ward-identities of rigid symmetry and a specific form of the abelian local gauge Ward-identity, which continues the Gell-Mann Nishijima relation to higher orders. Special attention is directed to the mass diagonalization of massless and massive neutral vectors and ghosts. For obtaining off-shell infrared finite expressions it is required to take into account higher order corrections into the functional symmetry operators. It is shown, that the normalization conditions of the on-shell schemes are in agreement with the most general symmetry transformations allowed by the algebraic constraints.
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.)
Renormalization Scheme Dependence in a QCD Cross Section
Chishtie, Farrukh
2015-01-01
From the perturbatively computed contributions to the $e^+e^- \\rightarrow$ hadrons cross section $R_{e^{+}e^{-}}$, we are able to determine the sum of all leading-log (LL), next-to-leading-log (NLL) etc. contributions to $R_{e^{+}e^{-}}$ up to four loop order (ie, the N$^3$LL contributions) by using the renormalization group equation. We then sum all logarithmic contributions, giving the result for $R_{e^{+}e^{-}}$ in terms of the log-independent contribution and the RG $\\beta$-function. Two renormalization schemes are then considered, both of which lead to an expression for $R_{e^{+}e^{-}}$ in terms of scheme-independent parameters. Both schemes result in expressions for $R_{e^{+}e^{-}}$ that are independent of the renormalization scale parameter $\\mu$. They are then compared with purely perturbative results and RG-summed N$^{3}$LL results.
Power Counting and Wilsonian Renormalization in Nuclear Effective Field Theory
Valderrama, Manuel Pavon
2016-01-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental ---perhaps unknown or unsolvable--- high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding ...
Renormalization Group Equation for Low Momentum Effective Nuclear Interactions
Bogner, S K; Kuo, T T S; Brown, G E
2001-01-01
We consider two nonperturbative methods originally used to derive shell model effective interactions in nuclei. These methods have been applied to the two nucleon sector to obtain an energy independent effective interaction V_{low k}, which preserves the low momentum half-on-shell T matrix and the deuteron pole, with a sharp cutoff imposed on all intermediate state momenta. We show that V_{low k} scales with the cutoff precisely as one expects from renormalization group arguments. This result is a step towards reformulating traditional model space many-body calculations in the language of effective field theories and the renormalization group. The numerical scaling properties of V_{low k} are observed to be in excellent agreement with our exact renormalization group equation.
Renormalization of position space amplitudes in a massless QFT
Todorov, Ivan
2017-03-01
Ultraviolet renormalization of position space massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree is determined by the degree of divergence while their order—the highest power of logarithm in the dilation anomaly—is given by the number of (sub)divergences. In the present paper we review these results and observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformally invariant theory internal integration is also proven to preserve the order of associate homogeneity. The renormalized 4-point amplitudes in the φ4 theory (in four space-time dimensions) are written as (non-analytic) translation invariant functions of four complex variables with calculable conformal anomaly. Our conclusion concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless φ4 theory agrees with the old result of Lowenstein and Zimmermann [23].
Renormalization group analysis of the gluon mass equation
Aguilar, A C; Papavassiliou, J
2014-01-01
In the present work we carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass. A detailed, all-order analysis of the complete kernel appearing in this particular equation reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, whose deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various p...
Renormalization group approach to scalar quantum electrodynamics on de Sitter
González, Francisco Fabián
2016-01-01
We consider the quantum loop effects in scalar electrodynamics on de Sitter space by making use of the functional renormalization group approach. We first integrate out the photon field, which can be done exactly to leading (zeroth) order in the gradients of the scalar field, thereby making this method suitable for investigating the dynamics of the infrared sector of the theory. Assuming that the scalar remains light we then apply the functional renormalization group methods to the resulting effective scalar theory and focus on investigating the effective potential, which is the leading order contribution in the gradient expansion of the effective action. We find symmetry restoration at a critical renormalization scale $\\kappa=\\kappa_{\\rm cr}$ much below the Hubble scale $H$. When compared with the results of Serreau and Guilleux [arXiv:1306.3846 [hep-th], arXiv:1506.06183 [hep-th
Systematic renormalization at all orders in the DiffRen and improved Epstein-Glaser schemes
Gracia-Bondía, José M
2015-01-01
Proceeding by way of examples, we update the combinatorics of the treatment of Feynman diagrams with subdivergences in differential renormalization from more recent viewpoints in Epstein--Glaser renormalization in $x$-space.
Dynamics and applicability of the similarity renormalization group
Energy Technology Data Exchange (ETDEWEB)
Launey, K D; Dytrych, T; Draayer, J P [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Popa, G, E-mail: kristina@baton.phys.lsu.edu [Department of Physics and Astronomy, Ohio University, Zanesville, OH 43701 (United States)
2012-01-13
The similarity renormalization group (SRG) concept (or flow equations methodology) is studied with a view toward the renormalization of nucleon-nucleon interactions for ab initio shell-model calculations. For a general flow, we give quantitative measures, in the framework of spectral distribution theory, for the strength of the SRG-induced higher order (many-body) terms of an evolved interaction. Specifically, we show that there is a hierarchy among the terms, with those of the lowest particle rank being the most important. This feature is crucial for maintaining the unitarity of SRG transformations and key to the method's applicability. (paper)
Perturbative n-Loop Renormalization by an Implicit Regularization Technique
Gobira, S R
2001-01-01
We construct a regularization independent procedure for implementing perturbative renormalization. An algebraic identity at the level of the internal lines of the diagrams is used which allows for the identification of counterterms in a purely algebraic way. Order by order in a perturbative expansion we automatically obtain in the process, finite contributions, local and nonlocal divergences. The notorious complications of overlapping divergences never enter and the corresponding counterterms arise automatically on the same footing as any other counterterm. The result of the present mathematical procedure is a considerable algebraic simplification which clarifies the connection between renormalization and counterterms in the Lagrangian.
Real-space renormalization yields finitely correlated states
Barthel, Thomas; Eisert, Jens
2010-01-01
Real-space renormalization approaches for quantum lattice systems generate certain hierarchical classes of states that are subsumed by the multi-scale entanglement renormalization ansatz (MERA). It is shown that, with the exception of one dimension, MERA states can be efficiently mapped to finitely-correlated states, also known as projected entangled pair states (PEPS), with a bond dimension independent of the system size. Hence, MERA states form an efficiently contractible class of PEPS and obey an area law for the entanglement entropy. It is shown further that there exist other efficiently contractible schemes violating the area law.
Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
Klebanov, Igor R; Pufu, Silviu S; Safdi, Benjamin R
2012-01-01
The renormalized entanglement entropy (REE) across a circle of radius R has been proposed as a c-function in Poincar\\'e invariant (2+1)-dimensional field theory. A proof has been presented of its monotonic behavior as a function of R, based on the strong subadditivity of entanglement entropy. However, this proof does not directly establish stationarity of REE at conformal fixed points of the renormalization group. In this note we study the REE for the free massive scalar field theory near the UV fixed point described by a massless scalar. Our numerical calculation indicates that the REE is not stationary at the UV fixed point.
Renormalized position space amplitudes in a massless QFT
Todorov, Ivan
2015-01-01
Ultraviolet renormalization of massless Feynman amplitudes has been shown to yield associate homogeneous distributions. Their degree coincides with the degree of divergence while their order - the highest power of the logarithm in the dilation anomaly - is given by the number of (sub)divergences. We observe that (convergent) integration over internal vertices does not alter the total degree of (superficial) ultraviolet divergence. For a conformal invariant theory internal integration is also proven to preserve the order of associate homogeneity. Our conclusions concerning the (off-shell) infrared finiteness of the ultraviolet renormalized massless $\\varphi^4$ theory agrees with the old result of Lowenstein and Zimmermann [LZ].
Four loop renormalization of the Gross-Neveu model
Gracey, J A; Schroder, Y
2016-01-01
We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.
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
1999-01-01
In this paper we apply the renormalization-group (RG) inspired resummation method to the one-loop effective potential at finite temperature evaluated in the massive scalar 04 model renormalized at zero-temperature, and study whether ourresummation procedure a la RG uccessfully resum the dominant correction terms apperaed in the perturbative caluculation in the T = 0 renormalization scheme or not.Our findings are i) that if we start from the theory renormalized at T = 0, then the condition tha...
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
Chen, Xia; Kulik, Alexey M.
2012-01-01
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
Optical force on toroidal nanostructures: toroidal dipole versus renormalized electric dipole
Zhang, Xu-Lin; Lin, Zhifang; Sun, Hong-Bo; Chan, C T
2015-01-01
We study the optical forces acting on toroidal nanostructures. A great enhancement of optical force is unambiguously identified as originating from the toroidal dipole resonance based on the source-representation, where the distribution of the induced charges and currents is characterized by the three families of electric, magnetic, and toroidal multipoles. On the other hand, the resonant optical force can also be completely attributed to an electric dipole resonance in the alternative field-representation, where the electromagnetic fields in the source-free region are expressed by two sets of electric and magnetic multipole fields based on symmetry. The confusion is resolved by conceptually introducing the irreducible electric dipole, toroidal dipole, and renormalized electric dipole. We demonstrate that the optical force is a powerful tool to identify toroidal response even when its scattering intensity is dwarfed by the conventional electric and magnetic multipoles.
Inverse Symmetry Breaking and the Exact Renormalization Group
Pietroni, M; Tetradis, N
1997-01-01
We discuss the question of inverse symmetry breaking at non-zero temperature using the exact renormalization group. We study a two-scalar theory and concentrate on the nature of the phase transition during which the symmetry is broken. We also examine the persistence of symmetry breaking at temperatures higher than the critical one.
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.
Renormalization group flows in gauge-gravity duality
Murugan, Arvind
2016-01-01
This is a copy of the 2009 Princeton University thesis which examined various aspects of gauge/gravity duality, including renormalization group flows, phase transitions of the holographic entanglement entropy, and instabilities associated with the breaking of supersymmetry. Chapter 5 contains new unpublished material on various instabilities of the weakly curved non-supersymmetric $AdS_4$ backgrounds of M-theory.
Renorms and topological linear contractions on Hilbert spaces
Institute of Scientific and Technical Information of China (English)
施茂祥; 谭炳均; 陈国强
1999-01-01
Properties of and the relationships between (topological) proper contractions, (topological) strict contractions and (topological) contractions are investigated, Explicit renorms are constructed so that all operators in a (finite or countable) family or a semigroup simultaneously become proper contractions or strict contractions. Some results are obtained for operator weighted shifts or operator weighted continuous shifts to be topological strict contractions.
Renormalization 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.
On Newton-Cartan local renormalization group and anomalies
Auzzi, Roberto; 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.
Computing the effective action with the functional renormalization group
DEFF Research Database (Denmark)
Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław
2016-01-01
The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples of such...... 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.......The “exact” or “functional” renormalization group equation describes the renormalization group flow of the effective average action Γ k. The ordinary effective action Γ 0 can be obtained by integrating the flow equation from an ultraviolet scale k= Λ down to k= 0. We give several examples...... of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization...
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.)
Lorentz space estimates for the Coulombian renormalized energy
Serfaty, Sylvia
2011-01-01
In this paper we obtain optimal estimates for the "currents" associated to point masses in the plane, in terms of the Coulombian renormalized energy of Sandier-Serfaty \\cite{ss1,ss3}. To derive the estimates, we use a technique that we introduced in \\cite{st}, which couples the "ball construction method" to estimates in the Lorentz space $L^{2,\\infty}$.
Renormalization of four-fermion operators for higher twist calculations
Capitani, S; Horsley, R; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A
1999-01-01
The evaluation of the higher twist contributions to Deep Inelastic Scattering amplitudes involves a non trivial choice of operator bases for the higher orders of the OPE expansion of the two hadronic currents. In this talk we discuss the perturbative renormalization of the four-fermion operators that appear in the above bases.
Renormings concerning exposed points and non-smoothness
Institute of Scientific and Technical Information of China (English)
GARCíA-PACHECO; Francisco; Javier
2009-01-01
Intuitively, non-smooth points might look like exposed points. However, in this paper we show that real Banach spaces having dimension greater than or equal to three can be equivalently renormed to obtain non-smooth points which are also non-exposed.
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Directory of Open Access Journals (Sweden)
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
Holographic torus entanglement and its renormalization group flow
Bueno, Pablo; Witczak-Krempa, William
2017-03-01
We study the universal contributions to the entanglement entropy (EE) of 2 +1 -dimensional and 3 +1 -dimensional holographic conformal field theories (CFTs) on topologically nontrivial manifolds, focusing on tori. The holographic bulk corresponds to anti-de Sitter-soliton geometries. We characterize the properties of these regulator-independent EE terms as a function of both the size of the cylindrical entangling region, and the shape of the torus. In 2 +1 dimensions, in the simple limit where the torus becomes a thin one-dimensional ring, the EE reduces to a shape-independent constant 2 γ . This is twice the EE obtained by bipartitioning an infinite cylinder into equal halves. We study the renormalization group flow of γ by defining a renormalized EE that (1) is applicable to general QFTs, (2) resolves the failure of the area law subtraction, and (3) is inspired by the F-theorem. We find that the renormalized γ decreases monotonically at small coupling when the holographic CFT is deformed by a relevant operator for all allowed scaling dimensions. We also discuss the question of nonuniqueness of such renormalized EEs both in 2 +1 dimensions and 3 +1 dimensions.
On the renormalization group transformation for scalar hierarchical models
Energy Technology Data Exchange (ETDEWEB)
Koch, H. (Texas Univ., Austin (USA). Dept. of Mathematics); Wittwer, P. (Geneva Univ. (Switzerland). Dept. de Physique Theorique)
1991-06-01
We give a new proof for the existence of a non-Gaussian hierarchical renormalization group fixed point, using what could be called a beta-function for this problem. We also discuss the asymptotic behavior of this fixed point, and the connection between the hierarchical models of Dyson and Gallavotti. (orig.).
Renormalization Group Flows, Cycles, and c-Theorem Folklore
Curtright, Thomas L.; Jin, Xiang; Zachos, Cosmas K.
2012-03-01
Monotonic renormalization group flows of the “c” and “a” functions are often cited as reasons why cyclic or chaotic coupling trajectories cannot occur. It is argued here, based on simple examples, that this is not necessarily true. Simultaneous monotonic and cyclic flows can be compatible if the flow function is multivalued in the couplings.
Schmitt, Sebastian; Anders, Frithjof B.
2010-04-01
The quantum transport through nanoscale junctions is governed by the charging energy U of the device. We employ the recently developed scattering-states numerical renormalization-group approach to open quantum systems to study nonequilibrium Green’s functions and current-voltage characteristics of such junctions for small and intermediate values of U . We establish the accuracy of the approach by a comparison with diagrammatic Kadanoff-Baym-Keldysh results which become exact in the weak-coupling limit U→0 . We demonstrate the limits of the diagrammatic expansions at intermediate values of the charging energy. While the numerical renormalization-group approach correctly predicts only one single, universal low-energy scale at zero bias voltage, some diagrammatic expansions yield two different low-energy scales for the magnetic and the charge fluctuations. At large voltages, however, the self-consistent second Born as well as the GW approximation reproduce the scattering-states renormalization-group spectral functions for symmetric junctions while for asymmetric junctions the voltage-dependent redistribution of spectral weight differs significantly in the different approaches. The second-order perturbation theory does not capture the correct single-particle dynamics at large bias and violates current conservation for asymmetric junctions.
Dimensional regularization in position space and a Forest Formula for Epstein-Glaser renormalization
Dütsch, Michael; Fredenhagen, Klaus; Keller, Kai Johannes; Rejzner, Katarzyna
2014-12-01
We reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time-ordered products as solutions to the induction scheme of Epstein-Glaser. This closed expression, which we call the Epstein-Glaser Forest Formula, is analogous to Zimmermann's Forest Formula for BPH renormalization. For scalar fields, the resulting renormalization method is always applicable, we compute several examples. We also analyze the Hopf algebraic aspects of the combinatorics. Our starting point is the Main Theorem of Renormalization of Stora and Popineau and the arising renormalization group as originally defined by Stückelberg and Petermann.
Renormalization aspects of N=1 Super Yang-Mills theory in the Wess-Zumino gauge
Capri, M A L; Guimaraes, M S; Justo, I F; Mihaila, L; Sorella, S P; Vercauteren, D
2014-01-01
The renormalization of N=1 Super Yang-Mills theory is analysed in the Wess-Zumino gauge, employing the Landau condition. An all orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field and gluino renormalization. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino, as explicitly shown through a three loop calculation.
Holographic Renormalization of Asymptotically Flat Gravity
Park, Miok
2012-01-01
We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \\rightarrow \\infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.
Topologically twisted renormalization group flow and its holographic dual
Nakayama, Yu
2017-03-01
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (also known as topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a nontrivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS /CFT . We argue that the nontrivial fixed points require fine-tuning of the bulk theory, in general, but remarkably we find that the O (3 ) Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean anti-de Sitter metric.
Ghost wavefunction renormalization in asymptotically safe quantum gravity
Energy Technology Data Exchange (ETDEWEB)
Groh, Kai; Saueressig, Frank, E-mail: kgroh@thep.physik.uni-mainz.d, E-mail: saueressig@thep.physik.uni-mainz.d [Institute of Physics, University of Mainz, Staudingerweg 7, D-55099 Mainz (Germany)
2010-09-10
Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein-Hilbert truncation supplemented by the wavefunction renormalization of the ghost fields. The latter induces non-trivial corrections to the {beta}-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point, in agreement with the asymptotic safety conjecture which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is {eta}*{sub c} = -1.8, supporting spacetime being effectively two dimensional at short distances.
On the renormalization of non-commutative field theories
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
Keldysh functional renormalization group for electronic properties of graphene
Fräßdorf, Christian; Mosig, Johannes E. M.
2017-03-01
We construct a nonperturbative nonequilibrium theory for graphene electrons interacting via the instantaneous Coulomb interaction by combining the functional renormalization group method with the nonequilibrium Keldysh formalism. The Coulomb interaction is partially bosonized in the forward scattering channel resulting in a coupled Fermi-Bose theory. Quantum kinetic equations for the Dirac fermions and the Hubbard-Stratonovich boson are derived in Keldysh basis, together with the exact flow equation for the effective action and the hierarchy of one-particle irreducible vertex functions, taking into account a possible nonzero expectation value of the bosonic field. Eventually, the system of equations is solved approximately under thermal equilibrium conditions at finite temperature, providing results for the renormalized Fermi velocity and the static dielectric function, which extends the zero-temperature results of Bauer et al., Phys. Rev. B 92, 121409 (2015), 10.1103/PhysRevB.92.121409.
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
Topologically twisted renormalization group flow and its holographic dual
Nakayama, Yu
2016-01-01
Euclidean field theories admit more general deformations than usually discussed in quantum field theories because of mixing between rotational symmetry and internal symmetry (a.k.a topological twist). Such deformations may be relevant, and if the subsequent renormalization group flow leads to a non-trivial fixed point, it generically gives rise to a scale invariant Euclidean field theory without conformal invariance. Motivated by an ansatz studied in cosmological models some time ago, we develop a holographic dual description of such renormalization group flows in the context of AdS/CFT. We argue that the non-trivial fixed points require fine-tuning of the bulk theory in general, but remarkably we find that the $O(3)$ Yang-Mills theory coupled with the four-dimensional Einstein gravity in the minimal manner supports such a background with the Euclidean AdS metric.
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.)
Signal inference with unknown response: calibration uncertainty renormalized estimator
Dorn, Sebastian; Greiner, Maksim; Selig, Marco; Böhm, Vanessa
2014-01-01
The calibration of a measurement device is crucial for every scientific experiment, where a signal has to be inferred from data. We present CURE, the calibration uncertainty renormalized estimator, to reconstruct a signal and simultaneously the instrument's calibration from the same data without knowing the exact calibration, but its covariance structure. The idea of CURE is starting with an assumed calibration to successively include more and more portions of calibration uncertainty into the signal inference equations and to absorb the resulting corrections into renormalized signal (and calibration) solutions. Thereby, the signal inference and calibration problem turns into solving a single system of ordinary differential equations and can be identified with common resummation techniques used in field theories. We verify CURE by applying it to a simplistic toy example and compare it against existent self-calibration schemes, Wiener filter solutions, and Markov Chain Monte Carlo sampling. We conclude that the...
Renormalization group study of damping in nonequilibrium field theory
Zanella, J
2006-01-01
In this paper we shall study whether dissipation in a $\\lambda\\phi^{4}$ may be described, in the long wavelength, low frequency limit, with a simple Ohmic term $\\kappa\\dot{\\phi}$, as it is usually done, for example, in studies of defect formation in nonequilibrium phase transitions. We shall obtain an effective theory for the long wavelength modes through the coarse graining of shorter wavelengths. We shall implement this coarse graining by iterating a Wilsonian renormalization group transformation, where infinitesimal momentum shells are coarse-grained one at a time, on the influence action describing the dissipative dynamics of the long wavelength modes. To the best of our knowledge, this is the first application of the nonequilibrium renormalization group to the calculation of a damping coefficient in quantum field theory.
One Loop Mass Renormalization of Unstable Particles in Superstring Theory
Sen, Ashoke
2016-01-01
Most of the massive states in superstring theory are expected to undergo mass renormalization at one loop order. Typically these corrections should contain imaginary parts, indicating that the states are unstable against decay into lighter particles. However in such cases, direct computation of the renormalized mass using superstring perturbation theory yields divergent result. Previous approaches to this problem involve various analytic continuation techniques, or deforming the integral over the moduli space of the torus with two punctures into the complexified moduli space near the boundary. In this paper we use insights from string field theory to describe a different approach that gives manifestly finite result for the mass shift satisfying unitarity relations. The procedure is applicable to all states of (compactified) type II and heterotic string theories. We illustrate this by computing the one loop correction to the mass of the first massive state on the leading Regge trajectory in SO(32) heterotic st...
Rapidity renormalized TMD soft and beam functions at two loops
Energy Technology Data Exchange (ETDEWEB)
Luebbert, Thomas [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Oredsson, Joel [DESY, Hamburg (Germany). Theory Group; Lund Univ. (Sweden). Dept. of Astronomy and Theoretical Physics; Stahlhofen, Maximilian [DESY, Hamburg (Germany). Theory Group; Mainz Univ. (Germany). PRISMA Cluster of Excellence
2016-03-15
We compute the transverse momentum dependent (TMD) soft function for the production of a color-neutral final state at the LHC within the rapidity renormalization group (RRG) framework to next-to-next-to-leading order (NNLO). We use this result to extract the universal renormalized TMD beam functions (aka TMDPDFs) in the same scheme and at the same order from known results in another scheme. We derive recurrence relations for the logarithmic structure of the soft and beam functions, which we use to cross check our calculation. We also explicitly confirm the non-Abelian exponentiation of the TMD soft function in the RRG framework at two loops. Our results provide the ingredients for resummed predictions of p {sub perpendicular} {sub to} -differential cross sections at NNLL' in the RRG formalism. The RRG provides a systematic framework to resum large (rapidity) logarithms through (R)RG evolution and assess the associated perturbative uncertainties.
Simple approach to renormalize the Cabibbo-Kabayashi-Maskawa matrix
Energy Technology Data Exchange (ETDEWEB)
Kniehl, B.A.; Sirlin, A. [Max-Planck-Institut fuer Physik, Muenchen (Germany)
2006-08-15
We present an explicit on-shell framework to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix at the one-loop level. After explaining how to separate the external-leg mixing corrections into gauge-independent self-mass (sm) and gauge-dependent wave-function renormalization contributions, the mass counterterms are chosen to cancel all divergent sm contributions, and also their finite parts subject to hermiticity constraints. The proof of gauge independence and finiteness of the remaining one-loop corrections to W{yields} q{sub i}+ anti q{sub j} reduces to the single-generation case. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which is gauge independent and preserves unitarity. (orig.)
Dimensional Reduction, Hard Thermal Loops and the Renormalization Group
Stephens, C R; Hess, P O; Astorga, F; Weber, Axel; Hess, Peter O.; Astorga, Francisco
2004-01-01
We study the realization of dimensional reduction and the validity of the hard thermal loop expansion for lambda phi^4 theory at finite temperature, using an environmentally friendly finite-temperature renormalization group with a fiducial temperature as flow parameter. The one-loop renormalization group allows for a consistent description of the system at low and high temperatures, and in particular of the phase transition. The main results are that dimensional reduction applies, apart from a range of temperatures around the phase transition, at high temperatures (compared to the zero temperature mass) only for sufficiently small coupling constants, while the HTL expansion is valid below (and rather far from) the phase transition, and, again, at high temperatures only in the case of sufficiently small coupling constants. We emphasize that close to the critical temperature, physics is completely dominated by thermal fluctuations that are not resummed in the hard thermal loop approach and where universal quant...
A Novel Formulation of Cabibbo-Kobayashi-Maskawa Matrix Renormalization
Kniehl, Bernd A
2009-01-01
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.
Background independent exact renormalization group for conformally reduced gravity
2015-01-01
Within the conformally reduced gravity model, where the metric is parametrised by a function f ( ϕ ) of the conformal factor ϕ , we keep dependence on both the background and fluctuation fields, to local potential approximation and O ∂ 2 $$ \\mathcal{O}\\left({\\partial}^2\\right) $$ respectively, making no other approximation. Explicit appearances of the background metric are then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) ...
Subtractive Renormalization Group Invariance: Pionless EFT at NLO
Timóteo, Varese S.; Szpigel, Sérgio; Durães, Francisco O.
2010-11-01
We show some results concerning the renormalization group (RG) invariance of the nucleon-nucleon (NN) interaction in pionless effective field theory at next-to-leading order (NLO), using a non-relativistic Callan-Symanzik equation (NRCS) for the driving term of the Lippmann-Schwinger (LS) equation with three recursive subtractions. The phase-shifts obtained for the RG evolved potential are same as those for the original potential, apart from relative differences of order 10-15.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
Renormalized Thermodynamic Entropy of Black Holes in Higher Dimensions
Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
1996-01-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstr\\"{o}m 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 dimens...
Scalar meson mass from renormalized One Boson Exchange Potential
Cordon, A Calle
2008-01-01
We determine the mass and strength of the scalar meson from NN scattering data by renormalizing the One Boson Exchange Potential. This procedure provides a great insensitivity to the unknown short distance interaction making the vector mesons marginally important and allowing for SU(3) couplings in the 1S0 channel. The scalar meson parameters are tightly constrained by low energy np. We discuss whether this scalar should be compared to the recent findings based on the Roy equations analysis of pipi scattering.
Renormalization of 3d quantum gravity from matrix models
Ambjørn, Jan; Loll, R
2004-01-01
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
Renormalization and Induced Gauge Action on a Noncommutative Space
Grosse, Harald
2007-01-01
Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to $\\phi^3$ models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\\theta$-deformed space and derive noncommutative gauge actions.
The proton-proton scattering without Coulomb force renormalization
Directory of Open Access Journals (Sweden)
Glöckle W.
2010-04-01
Full Text Available We demonstrate numerically that proton-proton (pp scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS equation for an exponentially screened Coulomb potential. For the limit of large screening radii we conﬁrm analytically predicted properties for oﬀ-shell, half-shell and on-shell elements of the Coulomb t-matrix.
The Renormalization Effects in the Microstrip-SQUID Amplifier
Berman, G P; Tsifrinovich, V I
2011-01-01
The peculiarities of the microstrip-DC SQUID amplifier caused by the resonant structure of the input circuit are analyzed. It is shown that the mutual inductance, that couples the input circuit and the SQUID loop, depends on the frequency of electromagnetic field. The renormalization of the SQUID parameters due to the screening effect of the input circuit vanishes when the Josephson frequency is much greater than the signal frequency.
Massive renormalization scheme and perturbation theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Blaizot, Jean-Paul, E-mail: jean-paul.blaizot@cea.fr [Institut de Physique Théorique, CNRS/URA2306, CEA-Saclay, 91191 Gif-sur-Yvette (France); Wschebor, Nicolás [Instituto de Fìsica, Faculdad de Ingeniería, Universidade de la República, 11000 Montevideo (Uruguay)
2015-02-04
We argue that the choice of an appropriate, massive, renormalization scheme can greatly improve the apparent convergence of perturbation theory at finite temperature. This is illustrated by the calculation of the pressure of a scalar field theory with quartic interactions, at 2-loop order. The result, almost identical to that obtained with more sophisticated resummation techniques, shows a remarkable stability as the coupling constant grows, in sharp contrast with standard perturbation theory.
Renormalization-group calculation of excitation properties for impurity models
Yoshida, M.; Whitaker, M. A.; Oliveira, L. N.
1990-05-01
The renormalization-group method developed by Wilson to calculate thermodynamical properties of dilute magnetic alloys is generalized to allow the calculation of dynamical properties of many-body impurity Hamiltonians. As a simple illustration, the impurity spectral density for the resonant-level model (i.e., the U=0 Anderson model) is computed. As a second illustration, for the same model, the longitudinal relaxation rate for a nuclear spin coupled to the impurity is calculated as a function of temperature.
Lattice renormalization of the static quark derivative operator
Blossier, B; Morénas, V; Pène, O
2006-01-01
We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $\\tau_{1/2}(1)$ and $\\tau_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.
Renormalization group analysis of the gluon mass equation
Aguilar, A. C.; Binosi, D.; Papavassiliou, J.
2014-04-01
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansätze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called "power-law" running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned.
Renormalization Group Analysis of Weakly Rotating Turbulent Flows
Institute of Scientific and Technical Information of China (English)
王晓宏; 周全
2011-01-01
Dynamic renormalization group (RNG) analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence. For turbulent How subject to weak rotation, the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part. Then, with a low-order approximation, the coarsening procedure of RNG transformation is performed. After implementing the coarsening and rescaling procedures, the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k) ∝ k11/5 for weakly rotating turbulence. It is also shown that the Coriolis force will disturb the stability of the Kolmogorov -5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.%Dynamic renormalization group(RNG)analysis is applied to the investigation of the behavior of the infrared limits of weakly rotating turbulence.For turbulent flow subject to weak rotation,the anisotropic part in the renormalized propagation is considered to be a perturbation of the isotropic part.Then,with a low-order approximation,the coarsening procedure of RNG transformation is performed.After implementing the coarsening and rescaling procedures,the RNG analysis suggests that the spherically averaged energy spectrum has the scaling behavior E(k)∝ k-11/5 for weakly rotating turbulence.It is also shown that the Coriolis force will disturb the stability of the Kolmogorov-5/3 energy spectrum and will change the scaling behavior even in the case of weak rotation.
Renormalization of the Spin-dependent WIMP scattering off nuclei
Divari, P C
2013-01-01
We study the amplitude for the spin-dependent WIMP scattering off nuclei by including the leading long-range two-body currents in the most important isovector contribution. We show that such effects are essentially independent of the target nucleus and, as a result, they can be treated as a mere renormalization of the effective nucleon cross section or, equivalently, of the corresponding effective coupling with values around 25%.
Renormalization-group flows and fixed points in Yukawa theories
DEFF Research Database (Denmark)
Mølgaard, Esben; Shrock, R.
2014-01-01
We study renormalization-group flows in Yukawa theories with massless fermions, including determination of fixed points and curves that separate regions of different flow behavior. We assess the reliability of perturbative calculations for various values of Yukawa coupling y and quartic scalar....... In the regime of weak couplings where the perturbative calculations are most reliable, we find that the theories have no nontrivial fixed points, and the flow is toward a free theory in the infrared....
Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model
Wang, Zhituo
2012-01-01
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
Power counting and Wilsonian renormalization in nuclear effective field theory
Valderrama, Manuel Pavón
2016-05-01
Effective field theories are the most general tool for the description of low energy phenomena. They are universal and systematic: they can be formulated for any low energy systems we can think of and offer a clear guide on how to calculate predictions with reliable error estimates, a feature that is called power counting. These properties can be easily understood in Wilsonian renormalization, in which effective field theories are the low energy renormalization group evolution of a more fundamental — perhaps unknown or unsolvable — high energy theory. In nuclear physics they provide the possibility of a theoretically sound derivation of nuclear forces without having to solve quantum chromodynamics explicitly. However there is the problem of how to organize calculations within nuclear effective field theory: the traditional knowledge about power counting is perturbative but nuclear physics is not. Yet power counting can be derived in Wilsonian renormalization and there is already a fairly good understanding of how to apply these ideas to non-perturbative phenomena and in particular to nuclear physics. Here we review a few of these ideas, explain power counting in two-nucleon scattering and reactions with external probes and hint at how to extend the present analysis beyond the two-body problem.
Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets
Indian Academy of Sciences (India)
N Nimai Singh; S Biramani Singh
2000-02-01
Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefﬁcients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD–QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the uniﬁcation of top-- Yukawa couplings at the scale =0.59× 108GeV for a ﬁxed value of tan =58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of =0.59× 1011GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.
Renormalization group study of excitonic and superconducting order in doped honeycomb bilayer
Murray, James; Vafek, Oskar
2014-03-01
We explore the competition between spin-charge order and unconventional superconductivity in the context of the AB stacked bilayer honeycomb lattice, realized experimentally as bilayer graphene, which features approximately parabolically touching electron bands. Using a weak-coupling renormalization group theory, we show that unconventional superconductivity arises generically for repulsively interacting fermions as excitonic order is suppressed by adding charge carriers to the system. We investigate the effects of finite temperature and further-neighbor hopping, the latter of which leads to so-called ``trigonal warping'' and destroys the perfect circular symmetry of the Fermi surfaces. We show that superconductivity survives for a finite range of trigonal warping, and that the nature of the superconducting phase may change as a function of further neighbor hopping. Depending on the range of interactions and the degree of trigonal warping, we find that the most likely superconducting instabilities are to f-wave, chiral d-wave, and pair density wave phases. It is shown that unconventional superconductivity is significantly enhanced by fluctuations in particle-hole channels, with the critical temperature reaching a maximum near the excitonic phase. Supported by the NSF CAREER award under Grant No. DMR-0955561, NSF Cooperative Agreement No. DMR-0654118, and the State of Florida, as well as by ICAM-I2CAM (NSF grant DMR-0844115) and by DoE, Office of Basic Energy Sciences (Award DE-FG02-08ER46544).
Energy Technology Data Exchange (ETDEWEB)
Song, Mi-Young; Yoon, Jung-Sik [Plasma Technology Research Center, National Fusion Research Institute, 814-2 Osikdo-Dong, Gunsan-City, Jeollabuk-Do 573-540 (Korea, Republic of); Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr [Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590 (United States); Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of)
2015-04-15
The renormalization shielding effects on the electron-impact ionization of hydrogen atom are investigated in dense partially ionized plasmas. The effective projectile-target interaction Hamiltonian and the semiclassical trajectory method are employed to obtain the transition amplitude as well as the ionization probability as functions of the impact parameter, the collision energy, and the renormalization parameter. It is found that the renormalization shielding effect suppresses the transition amplitude for the electron-impact ionization process in dense partially ionized plasmas. It is also found that the renormalization effect suppresses the differential ionization cross section in the peak impact parameter region. In addition, it is found that the influence of renormalization shielding on the ionization cross section decreases with an increase of the relative collision energy. The variations of the renormalization shielding effects on the electron-impact ionization cross section are also discussed.
Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
Skouroupathis, A.; Panagopoulos, H.
2007-11-01
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators ψ¯Γψ, where Γ denotes the scalar and pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, Zm. As a prerequisite for the above, we also compute the quark field renormalization, Zψ, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in cSW, in terms of both the renormalized and bare coupling constants, in the renormalized Feynman gauge. We also confirm the one-loop renormalization functions, for generic gauge. Finally, we present our results in the MS¯ scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, are included in the Appendix.
Two-loop renormalization of scalar and pseudoscalar fermion bilinears on the lattice
Skouroupathis, A
2007-01-01
We compute the two-loop renormalization functions, in the RI $^\\prime$ scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma$ denotes the Scalar and Pseudoscalar Dirac matrices, in the lattice formulation of QCD. We consider both the flavor non-singlet and singlet operators; the latter, in the scalar case, leads directly to the two-loop fermion mass renormalization, $Z_m$. As a prerequisite for the above, we also compute the quark field renormalization, $Z_{\\psi}$, up to two loops. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. We also confirm the 1-loop renormalization functions, for generic gauge. Finally, we present our results in the $\\bar{MS}$ scheme, for easier comparison with calculations in the continuum.
Duka, P; Zralek, M
2000-01-01
Quantization and renormalization of the left-right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev-Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on mass shell renormalization is performed and, as a test of consistency, the renormalization of the ZNiNj vertex is analyzed.
Gómez-Rocha, María
2016-01-01
The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling with the renormalization-group scale and summarize the basic elements needed in the formulation of the bound-state problem.
One-loop renormalization of fermionic currents with the overlap-Dirac operator
Alexandrou, C; Panagopoulos, H; Vicari, E
2000-01-01
We compute the one-loop lattice renormalization of the two-quark operators$\\bar{\\psi} \\Gamma \\psi$, where $\\Gamma$ denotes the generic Dirac matrix, forthe lattice formulation of QCD using the overlap-Dirac operator. We also study the renormalization of quark bilinears which are more extendedand have better chiral properties. Finally, we present improved estimates of these renormalization constants,coming from cactus resummation and from mean field perturbation theory.
Prykarpatski, A. K.; Bogolubov, N. N.
2017-01-01
A quantum fermionic massless charged particle self-intercating with its own self-generated bosonic electromagnetic field is reanalyzed in the framework of the Fock many-temporal and Feynman proper time approaches. The self-interaction phenomenon structure is discussed within the renormalized quantum Fock space. The quantum electromagnetic charged particle mass origin is suggested.
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.
Setting the renormalization scale in QCD: The principle of maximum conformality
DEFF Research Database (Denmark)
Brodsky, S. J.; Di Giustino, L.
2012-01-01
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...
Connection between the renormalization groups of Stueckelberg-Petermann and Wilson
Energy Technology Data Exchange (ETDEWEB)
Duetsch, Michael [Courant Research Centre in Mathematics, Universitaet Goettingen (Germany); Brunetti, Romeo [Dipartimento di Matematica, Universita di Trento (Italy); Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2010-07-01
The Stueckelberg-Petermann renormalization group (RG) relies on the non-uniqueness of the S-matrix in causal perturbation theory (i.e. Epstein-Glaser renormalization); it is the family of all finite renormalizations. The RG in the sense of Wilson refers to the dependence of the theory on a cutoff. A new formalism for perturbative algebraic quantum field theory allows to clarify the relation between these different notions of RG. In particular we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method.
Non-renormalization theorems and N=2 supersymmetric backgrounds
Butter, Daniel; 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.
Non-renormalization theorems andN=2 supersymmetric backgrounds
Energy Technology Data Exchange (ETDEWEB)
Butter, Daniel [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Wit, Bernard de [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Institute for Theoretical Physics, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Lodato, Ivano [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands)
2014-03-28
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Renormalization group and scaling within the microcanonical fermionic average approach
Azcoiti, V; Di Carlo, G; Galante, A; Grillo, A F; Azcoiti, V; Laliena, V; Di Carlo, G; Galante, A; Grillo, A F
1994-01-01
The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the \\beta, m plane for the study of chiral condensate in QED) without the need of computing the fermionic determinant at each point. We exploit this possibility for extracting both the renormalization group trajectories ("constant physics lines") and the scaling function, and we test it in the Schwinger Model. We discuss the applicability of this method to realistic theories.
Renormalization of Wilson Operators in the Light-Cone Gauge
Andrasi, A
2001-01-01
We test the renormalization of Wilson operators and the Mandelstam- Leibbrandt gauge in the case when the sides of the loop are parallel to the n, n* vectors used in the M-L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M-L gauge show double divergences and single divergences with non-local si and ci functions. In Appendix C we briefly discuss the problems of the M-L gauge for loops containing spacelike lines.
Density matrix renormalization group numerical study of the kagome antiferromagnet.
Jiang, H C; Weng, Z Y; Sheng, D N
2008-09-12
We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.
Renormalized thermodynamic entropy of black holes in higher dimensions
Kim, Sang Pyo; Kim, Sung Ku; Soh, Kwang-Sup; Yee, Jae Hyung
1997-02-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordström 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.
Renormalized thermodynamic entropy of black holes in higher dimensions
Energy Technology Data Exchange (ETDEWEB)
Kim, S.P. [Department of Physics, Kunsan National University, Kunsan 573-701 (Korea); Kim, S.K. [Department of Physics, Ewha Womans University, Seoul 120-750 (Korea); Soh, K. [Department of Physics Education, Seoul National University, Seoul 151-742 (Korea); Yee, J.H. [Department of Physics and Institute for Mathematical Sciences, Yonsei University, Seoul 120-749 (Korea)
1997-02-01
We study the ultraviolet divergent structures of the matter (scalar) field in a higher D-dimensional Reissner-Nordstr{umlt o}m 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} {ital 1997} {ital The American Physical Society}
Renormalization and applications of baryon distribution amplitudes QCD
Energy Technology Data Exchange (ETDEWEB)
Rohrwild, Juergen Holger
2009-07-17
Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N{sup *} distribution amplitudes. (orig.)
Renormalization and applications of baryon distribution amplitudes in QCD
Energy Technology Data Exchange (ETDEWEB)
Rohrwild, Juergen Holger
2009-07-17
Higher-twist effects are relevant for precision calculations of hard exclusive reactions. Furthermore, they reveal fine details of the hadron structure. In this work we construct an operator basis for arbitrary twist respecting the conformal symmetry of QCD (which is realized on 1-loop level). Using this basis the 1-loop renormalization kernels of twist 4 are constructed for baryon operators. The full spectrum of anomalous dimensions and the multiplicatively renormalizable operators is obtained. As an application of these results the radiative N{sup *}(1535) decay is discussed. Employing light-cone sum rule, the transition form factors can be directly related to the N* distribution amplitudes. (orig.)
Renormalization-group running cosmologies and the generalized second law
Horvat, R
2007-01-01
We explore some thermodynamical consequences of accelerated universes driven by a running cosmological constant (CC) from the renormalization group (RG). Application of the generalized second law (GSL) of gravitational thermodynamics to a framework where the running of the CC goes at the expense of energy transfer between vacuum and matter, strongly restricts the mass spectrum of a (hypothetical) theory controlling the CC running. We find that quantum effects driving the running of the CC should be dominated by a trans-planckian mass field, in marked contrast with the GUT-scale upper mass bo obtained by analyzing density perturbations for the running CC. The model shows compliance with the holographic principle.
Singlet vs Nonsinglet Perturbative Renormalization of Fermion Bilinears
Constantinou, M; Panagopoulos, H; Spanoudes, G
2016-01-01
In this paper we present the perturbative evaluation of the difference between the renormalization functions of flavor singlet and nonsinglet bilinear quark operators on the lattice. The computation is performed to two loops and to lowest order in the lattice spacing, for a class of improved lattice actions, including Wilson, tree-level (TL) Symanzik and Iwasaki gluons, twisted mass and SLiNC Wilson fermions, as well as staggered fermions with twice stout-smeared links. In the staggered formalism, the stout smearing procedure is also applied to the definition of bilinear operators.
Fine-grained entanglement loss along renormalization group flows
Latorre, J I; Rico, E; Vidal, G
2004-01-01
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 RG trajectories from the properties of the vacuum only, without need to study the whole hamiltonian.
Dynamical gap generation in graphene with frequency dependent renormalization effects
Carrington, M E; von Smekal, L; Thoma, M H
2016-01-01
We study the frequency dependencies in the renormalization of the fermion Greens function for the $\\pi$-band electrons in graphene and their influence on the dynamical gap generation at sufficiently strong interaction. Adopting the effective QED-like description for the low-energy excitations within the Dirac-cone region we self consistently solve the fermion Dyson-Schwinger equation in various approximations for the photon propagator and the vertex function with special emphasis on frequency dependent Lindhard screening and retardation effects.
On background-independent renormalization of spin foam models
Bahr, Benjamin
2014-01-01
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical consistency of path integral measures gives a natural analogue of Wilson's RG flow equations for background-independent systems. We discuss the conditions for the continuum measures to be diffeomorphism-invariant, and consider both exact and approximate examples.
A novel formulation of Cabibbo-Kobayashi-Maskawa matrix renormalization
Energy Technology Data Exchange (ETDEWEB)
Kniehl, Bernd A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Sirlin, Alberto [New York Univ., NY (United States). Dept. of Physics
2008-12-15
We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy. (orig.)
Anomalous Contagion and Renormalization in Dynamical Networks with Nodal Mobility
Manrique, Pedro D; Zheng, Minzhang; Xu, Chen; Hui, Pak Ming; Johnson, Neil F
2015-01-01
The common real-world feature of individuals migrating through a network -- either in real space or online -- significantly complicates understanding of network processes. Here we show that even though a network may appear static on average, underlying nodal mobility can dramatically distort outbreak profiles. Highly nonlinear dynamical regimes emerge in which increasing mobility either amplifies or suppresses outbreak severity. Predicted profiles mimic recent outbreaks of real-space contagion (social unrest) and online contagion (pro-ISIS support). We show that this nodal mobility can be renormalized in a precise way for a particular class of dynamical networks.
Truncation Effects in Monte Carlo Renormalization Group Improved Lattice Actions
Takaishi, T; Forcrand, Ph. de
1998-01-01
We study truncation effects in the SU(3) gauge actions obtained by the Monte Carlo renormalization group method. By measuring the heavy quark potential we find that the truncation effects in the actions coarsen the lattice by 40-50 % from the original blocked lattice. On the other hand, we find that rotational symmetry of the heavy quark potentials is well recovered on such coarse lattices, which may indicate that rotational symmetry breaking terms are easily cancelled out by adding a short distance operator. We also discuss the possibility of reducing truncation effects.
Renormalized entanglement entropy flow in mass-deformed ABJM theory
Kim, Kyung Kiu; Kwon, O.-Kab; Park, Chanyong; Shin, Hyeonjoon
2014-08-01
We investigate a mass deformation effect on the renormalized entanglement entropy (REE) near the UV fixed point in (2+1)-dimensional field theory. In the context of the gauge/gravity duality, we use the Lin-Lunin-Maldacena geometries corresponding to the vacua of the mass-deformed ABJM theory. We analytically compute the small mass effect for various droplet configurations and show in holographic point of view that the REE is monotonically decreasing, positive, and stationary at the UV fixed point. These properties of the REE in (2+1)-dimensions are consistent with the Zamolodchikov c-function proposed in (1+1)-dimensional conformal field theory.
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.
Tensor renormalization group analysis of CP(N-1) model
Kawauchi, Hikaru
2016-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.
Tensor renormalization group analysis of CP (N -1 ) model
Kawauchi, Hikaru; Takeda, Shinji
2016-06-01
We apply the higher-order tensor renormalization group to the lattice CP (N -1 ) model in two dimensions. A tensor network representation of the CP (N -1 ) model in the presence of the θ term is derived. We confirm that the numerical results of the CP(1) model without the θ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region β ≫1 and that obtained by the Monte Carlo simulation in a wider range of β . The numerical computation including the θ term is left for future challenges.
Renormalized Polyakov loops in various representations in finite temperature SU(2) gauge theory
Huebner, K
2008-01-01
We present results for the renormalized Polyakov loop in the three lowest irreducible representations of SU(2) gauge theory at finite temperature. We will discuss their scaling behavior near $T_c$ and test Casimir scaling in the deconfined phase. Moreover, we will compare these results to calculations for the renormalized Polyakov loops in several representations in the SU(3) gauge theory.
Non-perturbative renormalization of the static quark theory in a large volume
Korcyl, Piotr; Ishikawa, Tomomi
2015-01-01
We report on progress to renormalize non-pertubatively the static heavy quark theory on the lattice. In particular, we present first results for position-space renormalization scheme for heavy-light bilinears. We test our approach on RBC's 16^3 x 32 lattice ensemble with m_pi = 420 MeV, Iwasaki gauge action and domain wall light fermions.
Energy Technology Data Exchange (ETDEWEB)
Camblong, Horacio E. [Department of Physics, University of San Francisco, San Francisco, CA 94117-1080 (United States)]. E-mail: camblong@usfca.edu; Epele, Luis N. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Fanchiotti, Huner [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Garcia Canal, Carlos A. [Laboratorio de Fisica Teorica, Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67-1900 La Plata (Argentina); Ordonez, Carlos R. [Department of Physics, University of Houston, Houston, TX 77204-5506 (United States); World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, TX 77204-5506 (United States)
2007-05-14
A unified S-matrix framework of quantum singular interactions is presented for the comparison of self-adjoint extensions and physical renormalization. For the long-range conformal interaction the two methods are not equivalent, with renormalization acting as selector of a preferred extension and regulator of the unbounded Hamiltonian.
Kalagov, G. A.; Kompaniets, M. V.; Nalimov, M. Yu.
2014-11-01
We use quantum-field renormalization group methods to study the phase transition in an equilibrium system of nonrelativistic Fermi particles with the "density-density" interaction in the formalism of temperature Green's functions. We especially attend to the case of particles with spins greater than 1/2 or fermionic fields with additional indices for some reason. In the vicinity of the phase transition point, we reduce this model to a ϕ 4 -type theory with a matrix complex skew-symmetric field. We define a family of instantons of this model and investigate the asymptotic behavior of quantum field expansions in this model. We calculate the β-functions of the renormalization group equation through the third order in the ( 4 ∈)-scheme. In the physical space dimensions D = 2, 3, we resum solutions of the renormalization group equation on trajectories of invariant charges. Our results confirm the previously proposed suggestion that in the system under consideration, there is a first-order phase transition into a superconducting state that occurs at a higher temperature than the classical theory predicts.
Tadpole renormalization and relativistic corrections in lattice NRQCD
Shakespeare, N H; Shakespeare, Norman H.; Trottier, Howard D.
1998-01-01
We make a comparison of two tadpole renormalization schemes in the context of the quarkonium hyperfine splittings in lattice NRQCD. Improved gauge-field and NRQCD actions are analyzed using the mean-link $u_{0,L}$ in Landau gauge, and using the fourth root of the average plaquette $u_{0,P}$. Simulations are done for $c\\bar c$, $b\\bar c$, and $b\\bar b$ systems. The hyperfine splittings are computed both at leading and at next-to-leading order in the relativistic expansion. Results are obtained at lattice spacings in the range of about 0.14~fm to 0.38~fm. A number of features emerge, all of which favor tadpole renormalization using $u_{0,L}$. This includes much better scaling behavior of the hyperfine splittings in the three quarkonium systems when $u_{0,L}$ is used. We also find that relativistic corrections to the spin splittings are smaller when $u_{0,L}$ is used, particularly for the $c\\bar c$ and $b\\bar c$ systems. We also see signs of a breakdown in the NRQCD expansion when the bare quark mass falls below...
Superfluid phase transition with activated velocity fluctuations: Renormalization group approach.
Dančo, Michal; Hnatič, Michal; Komarova, Marina V; Lučivjanský, Tomáš; Nalimov, Mikhail Yu
2016-01-01
A quantum field model that incorporates Bose-condensed systems near their phase transition into a superfluid phase and velocity fluctuations is proposed. The stochastic Navier-Stokes equation is used for a generation of the velocity fluctuations. As such this model generalizes model F of critical dynamics. The field-theoretic action is derived using the Martin-Siggia-Rose formalism and path integral approach. The regime of equilibrium fluctuations is analyzed within the perturbative renormalization group method. The double (ε,δ)-expansion scheme is employed, where ε is a deviation from space dimension 4 and δ describes scaling of velocity fluctuations. The renormalization procedure is performed to the leading order. The main corollary gained from the analysis of the thermal equilibrium regime suggests that one-loop calculations of the presented models are not sufficient to make a definite conclusion about the stability of fixed points. We also show that critical exponents are drastically changed as a result of the turbulent background and critical fluctuations are in fact destroyed by the developed turbulence fluctuations. The scaling exponent of effective viscosity is calculated and agrees with expected value 4/3.
Electroweak renormalization group corrections in high energy processes
Melles, M
2001-01-01
At energies ($\\sqrt{s}$) much higher than the electroweak gauge boson masses ($M$) large logarithmic corrections of the scale ratio $\\sqrt{s}/M$ occur. While the electroweak Sudakov type double (DL) and universal single (SL) logarithms have recently been resummed, at higher orders the electroweak renormalization group (RG) corrections are folded with the DL Sudakov contributions and must be included for a consistent subleading treatment to all orders. In this paper we derive first all relevant formulae for massless as well as massive gauge theories including all such terms up to order ${\\cal O} (\\alpha^n \\beta_0 \\log^{2n-1} \\frac{s}{M^2})$ by integrating over the corresponding running couplings. The results for broken gauge theories in the high energy regime are then given in the framework of the infrared evolution equation (IREE) method. The analogous QED-corrections below the weak scale $M$ are included by appropriately matching the low energy solution to the renormalization group improved high energy resul...
Algebraic renormalization and Feynman integrals in configuration spaces
Ceyhan, Ozgur
2013-01-01
This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory. We consider a variant of the wonderful compactification of configuration spaces that works simultaneously for all graphs with a given number of vertices and that also accounts for the external structure of Feynman graph. As in our previous work, we consider two version of the Feynman amplitude in configuration space, which we refer to as the real and complex versions. In the real version, we show that we can extend to the massive case a method of evaluating Feynman integrals, based on expansion in Gegenbauer polynomials, that we investigated previously in the massless case. In the complex setting, we show that we can use algebro-geometric methods to renormalize the Feynman amplitudes, so that the renormalized values of the Feynman integrals are given by periods of a mixed ...
Unitary Networks from the Exact Renormalization of Wave Functionals
Fliss, Jackson R; Parrikar, Onkar
2016-01-01
The exact renormalization group (ERG) for $O(N)$ vector models (at large $N$) on flat Euclidean space can be interpreted as the bulk dynamics corresponding to a holographically dual higher spin gauge theory on $AdS_{d+1}$. This was established in the sense that at large $N$ the generating functional of correlation functions of single trace operators is reproduced by the on-shell action of the bulk higher spin theory, which is most simply presented in a first-order (phase space) formalism. In this paper, we extend the ERG formalism to the wave functionals of arbitrary states of the $O(N)$ vector model at the free fixed point. We find that the ERG flow of the ground state and a specific class of excited states is implemented by the action of unitary operators which can be chosen to be local. Consequently, the ERG equations provide a continuum notion of a tensor network. We compare this tensor network with the entanglement renormalization networks, MERA, and its continuum version, cMERA, which have appeared rece...
Exploration of Similarity Renormalization Group Generators in 1-Dimensional Potentials
Heinz, Matthias
2016-09-01
The Similarity Renormalization Group (SRG) is used in nuclear theory to decouple high- and low-momentum components of potentials to improve convergence and thus reduce the computational requirements of many-body calculations. The SRG is a series of unitary transformations defined by a differential equation for the Hamiltonian. The user input into the SRG evolution is a matrix called the generator, which determines to what form the Hamiltonian is transformed. As it is currently used, the SRG evolves Hamiltonian into a band diagonal form. However, due to many-body forces induced by the evolution, the SRG introduces errors when used to renormalize many-body potentials. This makes it unfit for calculations with nuclei larger than a certain size. A recent paper suggests that alternate generators may induce smaller many-body forces. Smaller many-body force induction would allow SRG use to be extended to larger nuclei. I use 1-dimensional systems of two, three, and four bosons to further study the SRG evolution and how alternate generators affect many-body forces induced.
A Note on Holographic Renormalization of Probe D-Branes
Benincasa, Paolo
2009-01-01
A great deal of progress has been recently made in the study of holography for non-conformal branes. Considering the near-horizon limit of backgrounds generated by such branes, we discuss the holographic renormalization of probe D-branes in these geometries. More specifically, we discuss in some detail systems with a codimension-one defect. For this class of systems, the mode which describes the probe branes wrapping a maximal 2-sphere in the transverse space behaves like a free massive scalar propagating in a higher-dimensional (asymptotically) AdS_{q+1}-space. The counterterms needed are then the ones of a free massive scalar in asymptotically AdS_{q+1}. The original problem can be recovered by compactifying the AdS-space on a torus and finally performing the analytic continuation of q to the value of interest, which can be fractional. We compute the one-point correlator for the operator dual to the embedding function. We finally comment on holographic renormalization in the more general cases of codimensio...
Brodsky, Stanley J
2012-01-01
The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal $\\{\\beta_i\\}$-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC renormalization scale $\\mu^{\\rm PMC}_R$ and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial ren...
Renormalization Constants of Quark Operators for the Non-Perturbatively Improved Wilson Action
Becirevic, D; Lubicz, V; Martinelli, G; Papinutto, Mauro; Reyes, J
2004-01-01
We present the results of an extensive lattice calculation of the renormalization constants of bilinear and four-quark operators for the non-perturbatively O(a)-improved Wilson action. The results are obtained in the quenched approximation at four values of the lattice coupling by using the non-perturbative RI/MOM renormalization method. Several sources of systematic uncertainties, including discretization errors and final volume effects, are examined. The contribution of the Goldstone pole, which in some cases may affect the extrapolation of the renormalization constants to the chiral limit, is non-perturbatively subtracted. The scale independent renormalization constants of bilinear quark operators have been also computed by using the lattice chiral Ward identities approach and compared with those obtained with the RI-MOM method. For those renormalization constants the non-perturbative estimates of which have been already presented in the literature we find an agreement which is typically at the level of 1%...
Renormalization aspects of N = 1 Super Yang-Mills theory in the Wess-Zumino gauge
Energy Technology Data Exchange (ETDEWEB)
Capri, M.A.L.; Granado, D.R.; Guimaraes, M.S.; Justo, I.F.; Sorella, S.P.; Vercauteren, D. [UERJ-Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Instituto de Fisica, Maracana, Rio de Janeiro (Brazil); Mihaila, L. [Karlsruhe Institute of Technology (KIT), Institut fuer Theoretische Teilchenphysik, Karlsruhe (Germany)
2014-04-15
The renormalization of N = 1 Super Yang-Mills theory is analyzed in the Wess-Zumino gauge, employing the Landau condition. An all-orders proof of the renormalizability of the theory is given by means of the Algebraic Renormalization procedure. Only three renormalization constants are needed, which can be identified with the coupling constant, gauge field, and gluino renormalization. The nonrenormalization theorem of the gluon-ghost-antighost vertex in the Landau gauge is shown to remain valid in N = 1 Super Yang-Mills. Moreover, due to the non-linear realization of the supersymmetry in the Wess-Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino. These features are explicitly checked through a three-loop calculation. (orig.)
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.)
Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi
2016-03-01
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
Photon splitting in a strongly magnetized, charge-asymmetric plasma
Directory of Open Access Journals (Sweden)
Chistyakov M.V.
2016-01-01
Full Text Available The process of the photon splitting, γ → γγ, is investigated in the presence of strongly magnetized charge-asymmetric cold plasma. The dispersion properties of photons and the new polarization selection rules are obtained in such plasma. The absorption rate of the leading photon splitting channel are calculated with taking account of the photon dispersion and wave function renormalization. In addition, a comparison of the photon splitting and the Compton scattering processes is performed.
Thompson's renormalization group method applied to QCD at high energy scale
Nassif, Claudio; Silva, P R
2007-01-01
We use a renormalization group method to treat QCD-vacuum behavior specially closer to the regime of asymptotic freedom. QCD-vacuum behaves effectively like a "paramagnetic system" of a classical theory in the sense that virtual color charges (gluons) emerges in it as a spin effect of a paramagnetic material when a magnetic field aligns their microscopic magnetic dipoles. Due to that strong classical analogy with the paramagnetism of Landau's theory,we will be able to use a certain Landau effective action without temperature and phase transition for just representing QCD-vacuum behavior at higher energies as being magnetization of a paramagnetic material in the presence of a magnetic field $H$. This reasoning will allow us to apply Thompson's approach to such an action in order to extract an "effective susceptibility" ($\\chi>0$) of QCD-vacuum. It depends on logarithmic of energy scale $u$ to investigate hadronic matter. Consequently we are able to get an ``effective magnetic permeability" ($\\mu>1$) of such a ...
Hewson, Alex C; Bauer, Johannes
2010-03-24
We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density ρ(x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to the infinite dimensional Holstein-Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.
Energy Technology Data Exchange (ETDEWEB)
Carvalho, Vanuildo S. de [Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, GO (Brazil); Freire, Hermann, E-mail: hfreire@mit.edu [Instituto de Física, Universidade Federal de Goiás, 74.001-970 Goiânia, GO (Brazil); Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2013-10-21
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi{sub 2}Sr{sub 2}CaCu{sub 2}O{sub 8+} {sub δ} by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.
Universality and scaling in a charge two-channel Kondo device
Mitchell, Andrew K.; Landau, L. A.; Fritz, L.; Sela, E.
2016-01-01
We study a charge two-channel Kondo model, demonstrating that recent experiments [Iftikhar et al, Nature 526, 233 (2015)] realize an essentially perfect quantum simulation -- not just of its universal physics, but also nonuniversal effects away from the scaling limit. Numerical renormalization group
Local Scale Transformations on the Lattice with Tensor Network Renormalization
Evenbly, G.; Vidal, G.
2016-01-01
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
Renormalized stress-energy tensor for stationary black holes
Levi, Adam
2017-01-01
We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the t -splitting variant of the method, which was first presented for ⟨ϕ2⟩ren , to compute the RSET in a stationary, asymptotically flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.
Strong parameter renormalization from optimum lattice model orbitals
Brosco, Valentina; Ying, Zu-Jian; Lorenzana, José
2017-01-01
Which is the best single-particle basis to express a Hubbard-like lattice model? A rigorous variational answer to this question leads to equations the solution of which depends in a self-consistent manner on the lattice ground state. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the noninteracting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model Hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density-matrix functional theory, thus establishing an unsuspected correspondence between continuum and lattice approaches.
Renormalized stress-energy tensor for stationary black holes
Levi, Adam
2016-01-01
We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized stress-energy tensor (RSET). We show in detail how to employ the $t$-splitting variant of the method, which was first presented for $\\left\\langle\\phi^{2}\\right\\rangle_{ren}$, to compute the RSET in a stationary, asymptotically-flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally-coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.
Renormalization group and critical behaviour in gravitational collapse
Hara, T; Adachi, S; Hara, Takashi; Koike, Tatsuhiko; Adachi, Satoshi
1996-01-01
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various types of universality and scaling observed in numerical studies. In particular, universality in initial data space and universality for different models are understood in a unified way. (2) It enables us to perform a detailed analysis of time evolution beyond linear perturbation, by providing rigorous controls on nonlinear terms. Under physically reasonable assumptions we prove: (1) Uniqueness of the relevant mode around a fixed point implies universality in initial data space. (2) The critical exponent \\beta_{\\rm BH} and the unique positive eigenvalue \\kappa of the relevant mode is exactly related by \\beta_{\\rm BH} = \\beta /\\kappa, where \\beta is a scaling exponent. (3) The above (1) and (2) hold also for discretely self-similar case (replacing ``fixed point'' with ``limi...
Emergent Space-Time via a Geometric Renormalization Method
Rastgoo, Saeed
2016-01-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully, may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of spacetime can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the...
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.
Renormalization of a Lorentz invariant doubled worldsheet theory
Nibbelink, Stefan Groot; Patalong, Peter
2013-01-01
Manifestly T-duality covariant worldsheet string models can be constructed by doubling the coordinate fields. We describe the underlying gauge symmetry of a recently proposed Lorentz invariant doubled worldsheet theory that makes half of the worldsheet degrees of freedom redundant. By shifting the Lagrange multiplier, that enforces the gauge fixing condition, the worldsheet action can be cast into various guises. We investigate the renormalization of this theory using a non-linear background/quantum split by employing a normal coordinate expansion adapted to the gauge-fixed theory. The propagator of the doubled coordinates contains a projection operator encoding that half of them do not propagate. We determine the doubled target space equations of motion by requiring one-loop Weyl invariance. Some of them are generalizations of the conventional sigma model beta-functions, while others seem to be novel to the doubled theory: In particular, a dilaton equation seems related to the strong constraint of double fie...
Magnus expansion and in-medium similarity renormalization group
Morris, T. D.; Parzuchowski, N. M.; Bogner, S. K.
2015-09-01
We present an improved variant of the in-medium similarity renormalization group (IM-SRG) based on the Magnus expansion. In the new formulation, one solves flow equations for the anti-Hermitian operator that, upon exponentiation, yields the unitary transformation of the IM-SRG. The resulting flow equations can be solved using a first-order Euler method without any loss of accuracy, resulting in substantial memory savings and modest computational speedups. Since one obtains the unitary transformation directly, the transformation of additional operators beyond the Hamiltonian can be accomplished with little additional cost, in sharp contrast to the standard formulation of the IM-SRG. Ground state calculations of the homogeneous electron gas (HEG) and 16O nucleus are used as test beds to illustrate the efficacy of the Magnus expansion.
Symmetry-Preserving Loop Regularization and Renormalization of QFTs
Wu, Yue-Liang
A new symmetry-preserving loop regularization method proposed in Ref. 1 is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the Lagrangian formalism or the spacetime dimension of original theory. The appearance of characteristic energy scale Mc and sliding energy scale μs offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.
One-loop non-renormalization results in EFTs
Directory of Open Access Journals (Sweden)
J. Elias-Miró
2015-07-01
Full Text Available In Effective Field Theories (EFTs with higher-dimensional operators many anomalous dimensions vanish at the one-loop level. With the use of supersymmetry, and a classification of the operators according to their embedding in super-operators, we are able to understand why many of these anomalous dimensions are zero. The key observation is that one-loop contributions from superpartners trivially vanish in many cases under consideration, making the superfield formalism a powerful tool even for non-supersymmetric models. We show this in detail in a simple U(1 model with a scalar and fermions, and explain how to extend this to SM EFTs and the QCD Chiral Lagrangian. This provides an understanding of why most “current–current” operators do not renormalize “loop” operators at the one-loop level, and allows to find the few exceptions to this ubiquitous rule.
Local covariance, renormalization ambiguity, and local thermal equilibrium in cosmology
Verch, Rainer
2011-01-01
This article reviews some aspects of local covariance and of the ambiguities and anomalies involved in the definition of the stress energy tensor of quantum field theory in curved spacetime. Then, a summary is given of the approach proposed by Buchholz et al. to define local thermal equilibrium states in quantum field theory, i.e., non-equilibrium states to which, locally, one can assign thermal parameters, such as temperature or thermal stress-energy. The extension of that concept to curved spacetime is discussed and some related results are presented. Finally, the recent approach to cosmology by Dappiaggi, Fredenhagen and Pinamonti, based on a distinguished fixing of the stress-energy renormalization ambiguity in the setting of the semiclassical Einstein equations, is briefly described. The concept of local thermal equilibrium states is then applied, to yield the result that the temperature behaviour of a quantized, massless, conformally coupled linear scalar field at early cosmological times is more singul...
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal
2016-01-01
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal; Andersen, Jens O.
2017-02-01
In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in 1 +1 dimensions in the large-Nc limit and in the 3 +1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Resummation and renormalization in effective theories of particle physics
Jakovac, Antal
2015-01-01
Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to vario...
Improved quasi parton distribution through Wilson line renormalization
Chen, Jiunn-Wei; Zhang, Jian-Hui
2016-01-01
Recent developments showed that hadron light-cone parton distributions could be directly extracted from spacelike correlators, known as quasi parton distributions, in the large hadron momentum limit. Unlike the normal light-cone parton distribution, a quasi parton distribution contains ultraviolet (UV) power divergence associated with the Wilson line self energy. We show that to all orders in the coupling expansion, the power divergence can be removed by a "mass" counterterm in the auxiliary $z$-field formalism, in the same way as the renormalization of power divergence for an open Wilson line. After adding this counterterm, the quasi quark distribution is improved such that it contains at most logarithmic divergences. Based on a simple version of discretized gauge action, we present the one-loop matching kernel between the improved non-singlet quasi quark distribution with a lattice regulator and the corresponding quark distribution in dimensional regularization.
Renormalization of the Yang-Mills spectral action
van Suijlekom, Walter D
2011-01-01
We prove renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, a power-counting argument shows that it is superrenormalizable. We determine the counterterms at one-loop using zeta function regularization in a background field gauge and establish their gauge invariance. Consequently, the spectral action can be renormalized by a simple shift of the coefficients appearing in the asymptotic expansion of the spectral action. This manuscript provides more details than the shorter companion paper, where we have used a (formal) quantum action principle to arrive at gauge invariance of the counterterms. Here, we give in addition an explicit expression for the gauge propagator.
Extracting Supersymmetry-Breaking Effects from Wave-Function Renormalization
Giudice, Gian Francesco
1998-01-01
We show that in theories in which supersymmetry breaking is communicated by renormalizable perturbative interactions, it is possible to extract the soft terms for the observable fields from wave-function renormalization. Therefore all the information about soft terms can be obtained from anomalous dimensions and beta functions, with no need to further compute any Feynman diagram. This method greatly simplifies calculations which are rather involved if performed in terms of component fields. For illustrative purposes we reproduce known results of theories with gauge-mediated supersymmetry breaking. We then use our method to obtain new results of phenomenological importance. We calculate the next-to-leading correction to the Higgs mass parameters, the two-loop soft terms induced by messenger-matter superpotential couplings, and the soft terms generated by messengers belonging to vector supermultiplets.
Chiral potential renormalized in harmonic-oscillator space
Yang, C -J
2016-01-01
We renormalize the chiral effective field theory (EFT) potential in harmonic-oscillator (HO) model space. The low energy constants (LECs) are utilized to absorb not just the ultra-violet part of the physics due to the cutoff, but also the infrared part due to the truncation of model space. We use the inverse J-matrix method to reproduce the nucleon-nucleon (NN) scattering phase shifts in the given model space. We demonstrate that by including the NLO correction, the nucleon-nucleon scattering in the continuum could be well reproduced in the truncated HO trap space up to laboratory energy $T_{lab}=100$ MeV with number of HO basis $n_{max}$ as small as 10. A perturbative power counting starts at subleading order is adopted in this work, and how to extract the perturbative contribution is demonstrated. Our work serves as the input to perform ab-initio calculations.
The Polarizable Embedding Density Matrix Renormalization Group Method
Hedegård, Erik D
2016-01-01
The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures ...
Advanced density matrix renormalization group method for nuclear structure calculations
Legeza, Ö; Poves, A; Dukelsky, J
2015-01-01
We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous $400$ KeV discrepancy in the ground state energy of $^{56}$Ni. We then report the first DMRG results in the $pf+g9/2$ shell model space for the ground $0^+$ and first $2^+$ states of $^{64}$Ge which are benchmarked with reference data obtained from Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of the two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.
Advanced density matrix renormalization group method for nuclear structure calculations
Legeza, Ã.-.; Veis, L.; Poves, A.; Dukelsky, J.
2015-11-01
We present an efficient implementation of the Density Matrix Renormalization Group (DMRG) algorithm that includes an optimal ordering of the proton and neutron orbitals and an efficient expansion of the active space utilizing various concepts of quantum information theory. We first show how this new DMRG methodology could solve a previous 400 keV discrepancy in the ground state energy of 56Ni. We then report the first DMRG results in the p f +g 9 /2 shell model space for the ground 0+ and first 2+ states of 64Ge which are benchmarked with reference data obtained from a Monte Carlo shell model. The corresponding correlation structure among the proton and neutron orbitals is determined in terms of two-orbital mutual information. Based on such correlation graphs we propose several further algorithmic improvement possibilities that can be utilized in a new generation of tensor network based algorithms.
Holographic Renormalization of general dilaton-axion gravity
Papadimitriou, Ioannis
2011-01-01
We consider a very general dilaton-axion system coupled to Einstein-Hilbert gravity in arbitrary dimension and we carry out holographic renormalization for any dimension up to and including five dimensions. This is achieved by developing a new systematic algorithm for iteratively solving the radial Hamilton-Jacobi equation in a derivative expansion. The boundary term derived is valid not only for asymptotically AdS backgrounds, but also for more general asymptotics, including non-conformal branes and Improved Holographic QCD. In the second half of the paper, we apply the general result to Improved Holographic QCD with arbitrary dilaton potential. In particular, we derive the generalized Fefferman-Graham asymptotic expansions and provide a proof of the holographic Ward identities.
The density matrix renormalization group for ab initio quantum chemistry
Wouters, Sebastian
2014-01-01
During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational co...
Functional renormalization group studies of nuclear and neutron matter
Drews, Matthias
2016-01-01
Functional renormalization group (FRG) methods applied to calculations of isospin-symmetric and asymmetric nuclear matter as well as neutron matter are reviewed. The approach is based on a chiral Lagrangian expressed in terms of nucleon and meson degrees of freedom as appropriate for the hadronic phase of QCD with spontaneously broken chiral symmetry. Fluctuations beyond mean-field approximation are treated solving Wetterich's FRG flow equations. Nuclear thermodynamics and the nuclear liquid-gas phase transition are investigated in detail, both in symmetric matter and as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of symmetric nuclear matter and pure neutron matter are found to be in good agreement with advanced ab-initio many-body computations. Contacts with perturbative many-body approaches (in-medium chiral perturbation theory) are discussed. As an interesting test case, the density dependence of the pion mass in the medium is investigated. The questio...
On the Standard Approach to Renormalization Group Improvement
Chishtie, F A; Mann, R B; McKeon, D G C; Steele, T G
2006-01-01
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing N^{n}LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless $\\lambda \\phi^{4}$ model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.
Aperiodic quantum XXZ chains: Renormalization-group results
Vieira, André P.
2005-04-01
We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.
Inheritance principle and Non-renormalization theorems at finite temperature
Brigante, M; Liu, H; Brigante, Mauro; Festuccia, Guido; Liu, Hong
2006-01-01
We show that in the large $N$ limit, a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$) satisfies an ``inheritance principle'' in the low temperature phase. Finite temperature correlation functions of gauge invariant single-trace operators are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. This implies that the corresponding finite temperature string theory dual can be formulated as a sigma model with Euclidean time direction periodically compactified. As a consequence, various non-renormalization theorems of $\\NN=4$ Super-Yang-Mills theory survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.
Renormalization Group Optimized Perturbation Theory at Finite Temperatures
Kneur, J -L
2015-01-01
A recently developed variant of the so-called optimized perturbation theory (OPT), making it perturbatively consistent with renormalization group (RG) properties, RGOPT, was shown to drastically improve its convergence for zero temperature theories. Here the RGOPT adapted to finite temperature is illustrated with a detailed evaluation of the two-loop pressure for the thermal scalar $ \\lambda\\phi^4$ field theory. We show that already at the simple one-loop level this quantity is exactly scale-invariant by construction and turns out to qualitatively reproduce, with a rather simple procedure, results from more sophisticated resummation methods at two-loop order, such as the two-particle irreducible approach typically. This lowest order also reproduces the exact large-$N$ results of the $O(N)$ model. Although very close in spirit, our RGOPT method and corresponding results differ drastically from similar variational approaches, such as the screened perturbation theory or its QCD-version, the (resummed) hard therm...
Local Scale Transformations on the Lattice with Tensor Network Renormalization.
Evenbly, G; Vidal, G
2016-01-29
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
Percolation, renormalization, and quantum computing with nondeterministic gates.
Kieling, K; Rudolph, T; Eisert, J
2007-09-28
We apply a notion of static renormalization to the preparation of entangled states for quantum computing, exploiting ideas from percolation theory. Such a strategy yields a novel way to cope with the randomness of nondeterministic quantum gates. This is most relevant in the context of optical architectures, where probabilistic gates are common, and cold atoms in optical lattices, where hole defects occur. We demonstrate how to efficiently construct cluster states without the need for rerouting, thereby avoiding a massive amount of conditional dynamics; we furthermore show that except for a single layer of gates during the preparation, all subsequent operations can be shifted to the final adapted single-qubit measurements. Remarkably, cluster state preparation is achieved using essentially the same scaling in resources as if deterministic gates were available.
Emergent space-time via a geometric renormalization method
Rastgoo, Saeed; Requardt, Manfred
2016-12-01
We present a purely geometric renormalization scheme for metric spaces (including uncolored graphs), which consists of a coarse graining and a rescaling operation on such spaces. The coarse graining is based on the concept of quasi-isometry, which yields a sequence of discrete coarse grained spaces each having a continuum limit under the rescaling operation. We provide criteria under which such sequences do converge within a superspace of metric spaces, or may constitute the basin of attraction of a common continuum limit, which hopefully may represent our space-time continuum. We discuss some of the properties of these coarse grained spaces as well as their continuum limits, such as scale invariance and metric similarity, and show that different layers of space-time can carry different distance functions while being homeomorphic. Important tools in this analysis are the Gromov-Hausdorff distance functional for general metric spaces and the growth degree of graphs or networks. The whole construction is in the spirit of the Wilsonian renormalization group (RG). Furthermore, we introduce a physically relevant notion of dimension on the spaces of interest in our analysis, which, e.g., for regular lattices reduces to the ordinary lattice dimension. We show that this dimension is stable under the proposed coarse graining procedure as long as the latter is sufficiently local, i.e., quasi-isometric, and discuss the conditions under which this dimension is an integer. We comment on the possibility that the limit space may turn out to be fractal in case the dimension is noninteger. At the end of the paper we briefly mention the possibility that our network carries a translocal far order that leads to the concept of wormhole spaces and a scale dependent dimension if the coarse graining procedure is no longer local.
A renormalization in group study of supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Heilmann, Marianne
2015-05-13
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
Indian Academy of Sciences (India)
Mosumi Das; S Ramasesha
2006-01-01
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the $1^{1} B_{u}^{-}$ exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.
Energy Technology Data Exchange (ETDEWEB)
Parker, Shane M.; Shiozaki, Toru [Department of Chemistry, Northwestern University, 2145 Sheridan Rd., Evanston, Illinois 60208 (United States)
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
Lahoche, Vincent; Rivasseau, Vincent
2015-01-01
We study a just renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which allows a precise characterization of the leading order Feynman graphs. We define the renormalization of the model, compute its (perturbative) renormalization group flow and write its expansion in terms of effective couplings. We then establish closed equations for the two point and four point functions at leading (melonic) order. Using the effective expansion and its uniform exponential bounds we prove that these equations admit a unique solution at small renormalized coupling.
Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
Avohou, Remi Cocou; Tanasa, Adrian
2015-01-01
This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop beta function, confirming the asymptotic freedom of the model. We then define the Connes-Kreimer-like Hopf algebra describing the combinatorics of the renormalization of this model and we analyze in detail, at one- and two-loop levels, the Hochschild cohomology allowing to write the combinatorial Dyson-Schwinger equations. Feynman tensor graph Hopf subalgebras are also exhibited.
A Systematic All-Orders Method to Eliminate Renormalization-Scale and Scheme Ambiguities in PQCD
Mojaza, Matin; Wu, Xing-Gang
2012-01-01
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {\\beta_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatized. The new method satisfies all of the principles of the renormalization group and eliminates an unnecessary source of systematic error.
Kullback-Leibler and Renormalized Entropy Applications to EEGs of Epilepsy Patients
Quiroga, R Q; Lehnertz, K; Grassberger, Peter
1999-01-01
Recently, renormalized entropy was proposed as a novel measure of relative entropy (P. Saparin et al., Chaos, Solitons & Fractals 4, 1907 (1994)) and applied to several physiological time sequences, including EEGs of patients with epilepsy. We show here that this measure is just a modified Kullback-Leibler (K-L) relative entropy, and it gives similar numerical results to the standard K-L entropy. The latter better distinguishes frequency contents of e.g. seizure and background EEGs than renormalized entropy. We thus propose that renormalized entropy might not be as useful as claimed by its proponents. In passing we also make some critical remarks about the implementation of these methods.
Active space decomposition with multiple sites: Density matrix renormalization group algorithm
Parker, Shane M
2014-01-01
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few {\\mu}Eh or less) with M = 128 in both cases, which is in contrast to conventional ab initio density matrix renormalization group.
Renormalization of Anisotropy and Glueball Masses on Tadpole Improved Lattice Gauge Action
Loan, M; Hamer, C; Loan, Mushtaq; Byrnes, Tim; Hamer, Chris
2003-01-01
The Numerical calculations for tadpole-improved U(1) lattice gauge theory in three-dimensions on anisotropic lattices have been performed using standard path integral Monte Carlo techniques. Using average plaquette tadpole renormalization scheme, simulations were done with temporal lattice spacings much smaller than the spatial ones and results were obtained for the string tension, the renormalized anisotropy and scalar glueball masses. We find, by comparing the `regular' and `sideways' potentials, that tadpole improvement results in very little renormalization of the bare anisotropy and reduces the discretization errors in the static quark potential and in the glueball masses.
Renormalization of the momentum density on the lattice using shifted boundary conditions
Robaina, Daniel
2013-01-01
In order to extract transport quantities from energy-momentum-tensor (EMT) correlators in Lattice QCD there is a strong need for a non-perturbative renormalization of these operators. This is due to the fact that the lattice regularization explicitly breaks translational invariance, invalidating the non-renormalization-theorem. Here we present a non-perturbative calculation of the renormalization constant of the off-diagonal components of the EMT in SU(3) pure gauge theory using lattices with shifted boundary conditions. This allows us to induce a non-zero momentum in the system controlled by the shift parameter and to determine the normalization of the momentum density operator.
Revisiting on-shell renormalization conditions in theories with flavour mixing
Grimus, W
2016-01-01
In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are non-singular in $\\varepsilon = p^2 - m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.
Revisiting on-shell renormalization conditions in theories with flavor mixing
Grimus, W.; Löschner, M.
2016-08-01
In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are nonsingular in 𝜀 = p2 - m n2, where p is the external four-momentum and mn is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.
Kopitzki, K.; Warnke, P. C.; Timmer, J.
1998-10-01
Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatiotemporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.
Kopitzki, K; Timmer, J
1998-01-01
Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatio-temporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.
Nikolov, Nikolay M.
2016-11-01
We propose a new renormalization procedure to all orders in perturbation theory, which is formulated on an extended position space. This allows us to apply methods from massless Quantum Field Theory to models of massive fields. These include the technique of homogeneous and associate homogeneous distributions for the extension problem contained in the renormalization theory on position space. This also makes it possible to generalize the notion of residues of Feynman amplitudes, which characterize the presence of additional scales due to renormalization, to the massive case.
Renormalization procedure for random tensor networks and the canonical tensor model
Sasakura, Naoki
2015-01-01
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.
Gómez-Rocha, María
2017-03-01
The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling constant with the renormalization-group scale and we summarize the basic elements needed in the formulation of the bound-state problem.
Charge-carrier screening in single-layer graphene.
Siegel, David A; Regan, William; Fedorov, Alexei V; Zettl, A; Lanzara, Alessandra
2013-04-05
The effect of charge-carrier screening on the transport properties of a neutral graphene sheet is studied by directly probing its electronic structure. We find that the Fermi velocity, Dirac point velocity, and overall distortion of the Dirac cone are renormalized due to the screening of the electron-electron interaction in an unusual way. We also observe an increase of the electron mean free path due to the screening of charged impurities. These observations help us to understand the basis for the transport properties of graphene, as well as the fundamental physics of these interesting electron-electron interactions at the Dirac point crossing.
Discrete solvent effects on the effective interaction between charged colloids
Allahyarov, E
2000-01-01
Using computer simulations of two charged colloidal spheres with their counterions in a hard sphere solvent, we show that the granular nature of the solvent significantly influences the effective colloidal interaction. For divalent counterions, the total effective force can become attractive generated by counterion hydration, while for monovalent counterions the forces are repulsive and well-described by a solvent-induced colloidal charge renormalization. Both effects are not contained in the traditional "primitive" approaches but can be accounted for in a solvent-averaged primitive model.
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.)
Energy Technology Data Exchange (ETDEWEB)
Kim, Sung Soo [Department of Applied Mathematics, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Jung, Young-Dae [Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791 (Korea, Republic of); Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590 (United States)
2013-12-15
The renormalization plasma screening effects on the electron-ion collision are investigated in dense partially ionized hydrogen plasmas. The Hamilton-Jacobi and eikonal methods with the effective interaction potential are employed to obtain the eikonal scattering phase shift and eikonal cross section for the electron-ion collision. It is found that the influence of renormalization screening strongly suppresses the eikonal scattering phase shift as well as the eikonal cross section, especially, for small impact parameter regions. In addition, the renormalization screening effect reduces the total eikonal cross section in all energy domains. The variation of the renormalization effects on the electron-ion collision in dense partially ionized hydrogen plasmas is also discussed.
A geometrical formulation of the renormalization group method for global analysis
Kunihiro, T
1995-01-01
On the basis of the classical theory of envelope,we formulate the renormalization group (RG) method for global analysis, recently proposed by Goldenfeld et al. It is clarified why the RG equation improves things.
Renormalization group flows for the second Z{sub 5} parafermionic field theory
Energy Technology Data Exchange (ETDEWEB)
Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail: dotsenko@lpthe.jussieu.fr; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589. Universite Pierre et Marie Curie, Paris VI (France) and CNRS, Universite Denis Diderot, Paris VII, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail: estienne@lpthe.jussieu.fr
2006-12-28
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub 5}. New fixed points are found and classified.
Two-loop renormalization of fermion bilinear operators on the lattice
Skouroupathis, A
2010-01-01
We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma= 1, \\gamma_5, \\gamma_\\mu, \\gamma_5\\gamma_\\mu, \\gamma_5\\sigma_{\\mu\
Chan, Garnet Kin-Lic; Nakatani, Naoki; Li, Zhendong; White, Steven R
2016-01-01
Current descriptions of the ab initio 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 par...
Generalization of the tensor renormalization group approach to 3-D or higher dimensions
Teng, Peiyuan
2017-04-01
In this paper, a way of generalizing the tensor renormalization group (TRG) is proposed. Mathematically, the connection between patterns of tensor renormalization group and the concept of truncation sequence in polytope geometry is discovered. A theoretical contraction framework is therefore proposed. Furthermore, the canonical polyadic decomposition is introduced to tensor network theory. A numerical verification of this method on the 3-D Ising model is carried out.
Nacir, Diana López
2009-01-01
We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to $2s$ powers of the spatial momentum, the subtraction necessary to renormalize $$ and $$ depends on $s$. We first describe our previous analysis for spatially flat Friedman-Robertson-Walker and Bianchi type I metrics. Then we present a new power counting analysis for general background metrics in the weak field approximation.
A renormalization-group approach to finite-temperature mass corrections
Marini, A; Marini, A; Burgess, C P
1994-01-01
We illustrate how the reorganization of perturbation theory at finite temperature can be economically cast in terms of the Wilson-Polchinski renormalization methods. We take as an example the old saw of the induced thermal mass of a hot scalar field with a quartic coupling, which we compute to second order in the coupling constant. We show that the form of the result can be largely determined by renormalization-group arguments without the explicit evaluation of Feynman graphs.
Prospects and status of quark mass renormalization in three-flavour QCD
Campos, I; Pena, C; Preti, D; Ramos, A; Vladikas, A
2015-01-01
We present the current status of a revised strategy to compute the running of renormalized quark masses in QCD with three flavours of massless O(a) improved Wilson quarks. The strategy employed uses the standard finite-size scaling method in the Schr\\"odinger functional and accommodates for the non-perturbative scheme-switch which becomes necessary at intermediate renormalized couplings as discussed in [arXiv:1411.7648].
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
Ueda, K.; Otani, R.; Nishio, Y; Gendiar, A.; Nishino, T
2004-01-01
We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by ea...
SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY
Institute of Scientific and Technical Information of China (English)
Kou Yanlei; Ding Shijin
2007-01-01
In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.
Energy Technology Data Exchange (ETDEWEB)
Brito, L.C.T. [Federal University of Minas Gerais, Physics Department, ICEx, PO Box 702, 30.161-970 Belo Horizonte, MG (Brazil)], E-mail: lctbrito@fisica.ufmg.br; Fargnoli, H.G. [Federal University of Minas Gerais, Physics Department, ICEx, PO Box 702, 30.161-970 Belo Horizonte, MG (Brazil)], E-mail: helvecio@fisica.ufmg.br; Baeta Scarpelli, A.P. [Centro Federal de Educacao Tecnologica, MG, Avenida Amazonas, 7675, 30510-000 Nova Gameleira, Belo Horizonte, MG (Brazil)], E-mail: scarp@fisica.ufmg.br; Sampaio, Marcos [Federal University of Minas Gerais, Physics Department, ICEx, PO Box 702, 30.161-970 Belo Horizonte, MG (Brazil)], E-mail: msampaio@fisica.ufmg.br; Nemes, M.C. [Federal University of Minas Gerais, Physics Department, ICEx, PO Box 702, 30.161-970 Belo Horizonte, MG (Brazil)], E-mail: carolina@fisica.ufmg.br
2009-03-23
We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals I{sub log}{sup (i)}({lambda}{sup 2}), i=1,2,...,n, {lambda} being the renormalization group scale, which need not be evaluated. Only the coefficients of the basic divergent integrals are show to determine renormalization group functions. Relations between these coefficients of different loop orders are derived.
Renormalization of the hydrogen sulfide properties due to the strong electron-phonon interaction
Kudryashov, N. A.; Kutukov, A. A.; Mazur, E. A.
2017-01-01
The normal state of a metal is described by generalized Eliashberg theory which takes into account the finite width of an electron band, strong electron-phonon coupling and electron-hole nonequivalence. Reconstructed parameters of the conduction band of the metallic hydrogen sulfide for both the real and imaginary parts of the mass renormalization of the electron Green’s function and the real and imaginary parts of the renormalization of the chemical potential have been found.
Directory of Open Access Journals (Sweden)
Prasad Chitra
2006-09-01
Full Text Available Abstract CHARGE syndrome was initially defined as a non-random association of anomalies (Coloboma, Heart defect, Atresia choanae, Retarded growth and development, Genital hypoplasia, Ear anomalies/deafness. In 1998, an expert group defined the major (the classical 4C's: Choanal atresia, Coloboma, Characteristic ears and Cranial nerve anomalies and minor criteria of CHARGE syndrome. Individuals with all four major characteristics or three major and three minor characteristics are highly likely to have CHARGE syndrome. However, there have been individuals genetically identified with CHARGE syndrome without the classical choanal atresia and coloboma. The reported incidence of CHARGE syndrome ranges from 0.1–1.2/10,000 and depends on professional recognition. Coloboma mainly affects the retina. Major and minor congenital heart defects (the commonest cyanotic heart defect is tetralogy of Fallot occur in 75–80% of patients. Choanal atresia may be membranous or bony; bilateral or unilateral. Mental retardation is variable with intelligence quotients (IQ ranging from normal to profound retardation. Under-development of the external genitalia is a common finding in males but it is less apparent in females. Ear abnormalities include a classical finding of unusually shaped ears and hearing loss (conductive and/or nerve deafness that ranges from mild to severe deafness. Multiple cranial nerve dysfunctions are common. A behavioral phenotype for CHARGE syndrome is emerging. Mutations in the CHD7 gene (member of the chromodomain helicase DNA protein family are detected in over 75% of patients with CHARGE syndrome. Children with CHARGE syndrome require intensive medical management as well as numerous surgical interventions. They also need multidisciplinary follow up. Some of the hidden issues of CHARGE syndrome are often forgotten, one being the feeding adaptation of these children, which needs an early aggressive approach from a feeding team. As the child
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.
Holography as a highly efficient renormalization group flow. I. Rephrasing gravity
Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan
2016-07-01
We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.
Albrecht, J; Babu, K; Bernstein, R H; Blum, T; Brown, D N; Casey, B C K; Cheng, C -h; Cirigliano, V; Cohen, A; Deshpande, A; Dukes, E C; Echenard, B; Gaponenko, A; Glenzinski, D; Gonzalez-Alonso, M; Grancagnolo, F; Grossman, Y; Harnik, R; Hitlin, D G; Kiburg, B; Knoepfe, K; Kumar, K; Lim, G; Lu, Z -T; McKeen, D; Miller, J P; Ramsey-Musolf, M; Ray, R; Roberts, B L; Rominsky, M; Semertzidis, Y; Stoeckinger, D; Talman, R; Van De Water, R; Winter, P
2013-01-01
This is the report of the Intensity Frontier Charged Lepton Working Group of the 2013 Community Summer Study "Snowmass on the Mississippi", summarizing the current status and future experimental opportunities in muon and tau lepton studies and their sensitivity to new physics. These include searches for charged lepton flavor violation, measurements of magnetic and electric dipole moments, and precision measurements of the decay spectrum and parity-violating asymmetries.
Spectral functions and transport coefficients from the functional renormalization group
Energy Technology Data Exchange (ETDEWEB)
Tripolt, Ralf-Arno
2015-06-03
In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.
Alternative similarity renormalization group generators in nuclear structure calculations
Dicaire, Nuiok M; Navratil, Petr
2014-01-01
The similarity renormalization group (SRG) has been successfully applied to soften interactions for ab initio nuclear calculations. In almost all practical applications in nuclear physics, an SRG generator with the kinetic energy operator is used. With this choice, a fast convergence of many-body calculations can be achieved, but at the same time substantial three-body interactions are induced even if one starts from a purely two-nucleon (NN) Hamiltonian. Three-nucleon (3N) interactions can be handled by modern many-body methods. However, it has been observed that when including initial chiral 3N forces in the Hamiltonian, the SRG transformations induce a non-negligible four-nucleon interaction that cannot be currently included in the calculations for technical reasons. Consequently, it is essential to investigate alternative SRG generators that might suppress the induction of many-body forces while at the same time might preserve the good convergence. In this work we test two alternative generators with oper...
Functional renormalization group studies of nuclear and neutron matter
Drews, Matthias; Weise, Wolfram
2017-03-01
Functional renormalization group (FRG) methods applied to calculations of isospin-symmetric and asymmetric nuclear matter as well as neutron matter are reviewed. The approach is based on a chiral Lagrangian expressed in terms of nucleon and meson degrees of freedom as appropriate for the hadronic phase of QCD with spontaneously broken chiral symmetry. Fluctuations beyond mean-field approximation are treated solving Wetterich's FRG flow equations. Nuclear thermodynamics and the nuclear liquid-gas phase transition are investigated in detail, both in symmetric matter and as a function of the proton fraction in asymmetric matter. The equations of state at zero temperature of symmetric nuclear matter and pure neutron matter are found to be in good agreement with advanced ab-initio many-body computations. Contacts with perturbative many-body approaches (in-medium chiral perturbation theory) are discussed. As an interesting test case, the density dependence of the pion mass in the medium is investigated. The question of chiral symmetry restoration in nuclear and neutron matter is addressed. A stabilization of the phase with spontaneously broken chiral symmetry is found to persist up to high baryon densities once fluctuations beyond mean-field are included. Neutron star matter including beta equilibrium is discussed under the aspect of the constraints imposed by the existence of two-solar-mass neutron stars.
Ultrasoft renormalization of the potentials in vNRQCD
Energy Technology Data Exchange (ETDEWEB)
Stahlhofen, Maximilian Horst
2009-02-18
The effective field theory vNRQCD allows to describe among others the production of top-antitop pairs in electron-positron collisions at threshold, i.e. with very small relative velocity {upsilon} << 1 of the quarks. Potentially large logarithms {proportional_to} ln {upsilon} are systematically summed up and lead to a scale dependence of the Wilson coefficients of the theory. The missing contributions to the cross section {sigma}(e{sup +}e{sup -} {yields} t anti t) in the resonance region at NNLL level are the so-called mixing contributions to the NNLL anomalous dimension of the S-wave production/annihilation current of the topquark pair. To calculate these one has to know the NLL renormalization group running of so-called potentials (4-quark operators). The dominant contributions to the anomalous dimension of these potentials come from vNRQCD diagrams with ultrasoft gluon loops. The aim of this thesis is to derive the complete ultrasoft NLL running of the relevant potentials. For that purpose the UV divergent parts of about 10{sup 4} two-loop diagrams are determined. Technical and conceptional issues are discussed. Some open questions related to the calculation of the non-Abelian two-loop diagrams arise. Preliminary results are analysed with regard to the consequences for the mentioned cross section and its theoretical uncertainty. (orig.)
High-performance functional Renormalization Group calculations for interacting fermions
Lichtenstein, J.; Sánchez de la Peña, D.; Rohe, D.; Di Napoli, E.; Honerkamp, C.; Maier, S. A.
2017-04-01
We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations even in the case of complex multiband systems. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the t ,t‧ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.
Renormalization of the unitary evolution equation for coined quantum walks
Boettcher, Stefan; Li, Shanshan; Portugal, Renato
2017-03-01
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential for attaining the Grover limit for quantum search algorithms in physically realizable, low-dimensional geometries. In particular, we analyze the exact real-space renormalization group (RG) procedure recently introduced to study the scaling of quantum walks on fractal networks. While this procedure, when implemented numerically, was able to provide some deep insights into the relation between classical and quantum walks, its analytic basis has remained obscure. Our discussion here is laying the groundwork for a rigorous implementation of the RG for this important class of transport and algorithmic problems, although some instances remain unresolved. Specifically, we find that the RG fixed-point analysis of the classical walk, which typically focuses on the dominant Jacobian eigenvalue {λ1} , with walk dimension dw\\text{RW}={{log}2}{λ1} , needs to be extended to include the subdominant eigenvalue {λ2} , such that the dimension of the quantum walk obtains dw\\text{QW}={{log}2}\\sqrt{{λ1}{λ2}} . With that extension, we obtain analytically previously conjectured results for dw\\text{QW} of Grover walks on all but one of the fractal networks that have been considered.
The impact of renormalization group theory on magnetism
Köbler, U.; Hoser, A.
2007-11-01
The basic issues of renormalization group (RG) theory, i.e. universality, crossover phenomena, relevant interactions etc. are verified experimentally on magnetic materials. Universality is demonstrated on account of the saturation of the magnetic order parameter for T ↦ 0. Universal means that the deviations with respect to saturation at T = 0 can perfectly be described by a power function of absolute temperature with an exponent ɛ that is independent of spin structure and lattice symmetry. Normally the Tɛ function holds up to ~0.85Tc where crossover to the critical power function occurs. Universality for T ↦ 0 cannot be explained on the basis of the material specific magnon dispersions that are due to atomistic symmetry. Instead, continuous dynamic symmetry has to be assumed. The quasi particles of the continuous symmetry can be described by plane waves and have linear dispersion in all solids. This then explains universality. However, those quasi particles cannot be observed using inelastic neutron scattering. The principle of relevance is demonstrated using the competition between crystal field interaction and exchange interaction as an example. If the ratio of crystal field interaction to exchange interaction is below some threshold value the local crystal field is not relevant under the continuous symmetry of the ordered state and the saturation moment of the free ion is observed for T ↦ 0. Crossover phenomena either between different exponents or between discrete changes of the pre-factor of the Tɛ function are demonstrated for the spontaneous magnetization and for the heat capacity.
Holographic Renormalization Group Structure in Higher-Derivative Gravity
Fukuma, M; Fukuma, Masafumi; Matsuura, So
2002-01-01
Classical higher-derivative gravity is investigated in the context of the holographic renormalization group (RG). We parametrize the Euclidean time such that one step of time evolution in (d+1)-dimensional bulk gravity can be directly interpreted as that of block spin transformation of the d-dimensional boundary field theory. This parametrization simplifies the analysis of the holographic RG structure in gravity systems, and conformal fixed points are always described by AdS geometry. We find that higher-derivative gravity generically induces extra degrees of freedom which acquire huge mass around stable fixed points and thus are coupled to highly irrelevant operators at the boundary. In the particular case of pure R^2-gravity, we show that some region of the coefficients of curvature-squared terms allows us to have two fixed points (one is multicritical) which are connected by a kink solution. We further extend our analysis to Minkowskian time to investigate a model of expanding universe described by the act...
Improved renormalization group theory for critical asymmetry of fluids.
Wang, Long; Zhao, Wei; Wu, Liang; Li, Liyan; Cai, Jun
2013-09-28
We develop an improved renormalization group (RG) approach incorporating the critical vapor-liquid equilibrium asymmetry. In order to treat the critical asymmetry of vapor-liquid equilibrium, the integral measure is introduced in the Landau-Ginzbug partition function to achieve a crossover between the local order parameter in Ising model and the density of fluid systems. In the implementation of the improved RG approach, we relate the integral measure with the inhomogeneous density distribution of a fluid system and combine the developed method with SAFT-VR (statistical associating fluid theory of variable range) equation of state. The method is applied to various fluid systems including square-well fluid, square-well dimer fluid and real fluids such as methane (CH4), ethane (C2H6), trifluorotrichloroethane (C2F3Cl3), and sulfur hexafluoride (SF6). The descriptions of vapor-liquid equilibria provided by the developed method are in excellent agreement with simulation and experimental data. Furthermore, the improved method predicts accurate and qualitatively correct behavior of coexistence diameter near the critical point and produces the non-classical 3D Ising criticality.
Critical asymmetry in renormalization group theory for fluids.
Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun
2013-06-21
The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.
Does Multiplicity Replace Renormalization and Link Genetics too?
Goradia, Shantilal
2007-04-01
The substitution of sixty orders of magnitude, the age of the universe in Planck times, for W in entropy equation S = ln W, yields 138, close to the reciprocal of fine-structure constant (137) consistent with (1) Einstein's 1919 retraction of cosmological constant, (2) non-decreasing nature of entropy (3) Gamow's view. I link cosmology and Boltzmann statistics in terms of encryption in sequences of the OPEN and CLOSED states (or their superposition) pictorially shown in fig 1 [1]. I take an algorithmic approach to explain the expression of genetic information in cloning in terms of black hole information theory via Planck scale and flexible Einstein Rosen bridges linking physical particles of genetic tape with spacetime. Einstein's retraction of cosmological constant, long before Hubble's finding, surprised me, possibly you and Mike Turner too, during my last encounter with Mike at NDU. In 1919, Einstein addressed multiplicity, not GR. Unlike later papers on MOND without dark matter, I use no renormalization tricks in v2 of [1]. [1] physics/0210040 v3 (Jan 2007). To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.NES07.C1.7
Applications of the Similarity Renormalization Group to the Nuclear Interaction
Jurgenson, E D
2009-01-01
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations that leads to computational benefits is the decoupling of low-energy nuclear physics from high-energy details of the inter-nucleon interaction. We examine decoupling quantitatively for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small. To explore the SRG evolution of many-body forces, we use as a laboratory a one-dimensional system of bosons with short-range repulsion and mid-range attraction, which emulates realistic nuclear forces. The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. ...
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Friederich, Simon
2010-12-08
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
Controlling sign problems in spin models using tensor renormalization
Energy Technology Data Exchange (ETDEWEB)
Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.
2014-01-09
We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
Band renormalization and spin polarization of MoS{sub 2} in graphene/MoS{sub 2} heterostructures
Energy Technology Data Exchange (ETDEWEB)
Coy-Diaz, Horacio; Batzill, Matthias [Department of Physics, University of South Florida, Tampa, FL (United States); Bertran, Francois; Chen, Chaoyu; Avila, Jose; Rault, Julien; Le Fevre, Patrick; Asensio, Maria C. [Synchrotron SOLEIL, L' Orme des Merisiers, Gif sur Yvette (France)
2015-12-15
Transition metal dichalcogenides exhibit spin-orbit split bands at the K-point that become spin polarized for broken crystal inversion symmetry. This enables simultaneous manipulation of valley and spin degrees of freedom. While the inversion symmetry is broken for monolayers, we show here that spin polarization of the MoS{sub 2} surface may also be obtained by interfacing it with graphene, which induces a space charge region in the surface of MoS{sub 2}. Polarization induced symmetry breaking in the potential gradient of the space charge is considered to be responsible for the observed spin polarization. In addition to spin polarization we also observe a renormalization of the valence band maximum (VBM) upon interfacing of MoS{sub 2} with graphene. The energy difference between the VBM at the Γ-point and K-point shifts by ∝150 meV between the clean and graphene covered surface. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Kukushkin, V. I.; Kirpichev, V. E.; Kukushkin, I. V.
2016-07-01
The properties of plasma and magnetoplasma excitations in free-hanging graphene have been studied for the first time by Raman scattering. In addition to single-particle excitations associated with transitions between empty Landau levels of electrons and holes, collective plasma and magnetoplasma excitations in the system of electrons (and holes) of various densities have been discovered for the first time. Hybridization of plasma and cyclotron modes corresponding to the Kohn law has been shown to occur in the limit of high filling factors, which allows measuring directly the plasma and cyclotron energies. The dependence of the electron and hole velocities on their density has been investigated via the magnetic-field dependence of the cyclotron energy in free-hanging graphene. The effect of strong renormalization of the electron and hole dispersion relations seen as an increase in the velocity (by 40-50%) with a decrease in the charge-carrier density to 1011 cm-2 has been discovered. The charge-carrier density dependences of the widths of magnetoplasma resonances in free-hanging graphene and graphene lying on a silicon dioxide surface have been measured and shown to be at least 3.5 and 14.8 meV, respectively.
Suijlekom, W.D. van
2008-01-01
We study the structure of renormalization Hopf algebras of gauge theories. We identify certain Hopf subalgebras in them, whose character groups are semidirect products of invertible formal power series with formal diffeomorphisms. This can be understood physically as wave function renormalization and renormalization of the coupling constants, respectively. After taking into account the Slavnov-Taylor identities for the couplings as generators of a Hopf ideal, we find Hopf subalgebras in the c...
Energy Technology Data Exchange (ETDEWEB)
Connes, A.; Kreimer, D. [Institut des Hautes Etudes Sci., Bures sur Yvette (France)
2001-01-01
We showed in Part I that the Hopf algebra H of Feynman graphs in a given QFT is the algebra of coordinates on a complex infinite dimensional Lie group G and that the renormalized theory is obtained from the unrenormalized one by evaluating at {epsilon}=0 the holomorphic part {gamma}{sub +}({epsilon}) of the Riemann-Hilbert decomposition {gamma}{sub -}({epsilon}){sup -1}{gamma}{sub +}({epsilon}) of the loop {gamma}({epsilon}) element of G provided by dimensional regularization. We show in this paper that the group G acts naturally on the complex space X of dimensionless coupling constants of the theory. More precisely, the formula g {sub 0}=gZ{sub 1}Z{sub 3}{sup -3/2} for the effective coupling constant, when viewed as a formal power series, does define a Hopf algebra homomorphism between the Hopf algebra of coordinates on the group of formal diffeomorphisms to the Hopf algebra H. This allows first of all to read off directly, without using the group G, the bare coupling constant and the renormalized one from the Riemann-Hilbert decomposition of the unrenormalized effective coupling constant viewed as a loop of formal diffeomorphisms. This shows that renormalization is intimately related with the theory of non-linear complex bundles on the Riemann sphere of the dimensional regularization parameter {epsilon}. It also allows to lift both the renormalization group and the {beta}-function as the asymptotic scaling in the group G. This exploits the full power of the Riemann-Hilbert decomposition together with the invariance of {gamma}{sub -}({epsilon}) under a change of unit of mass. This not only gives a conceptual proof of the existence of the renormalization group but also delivers a scattering formula in the group G for the full higher pole structure of minimal subtracted counterterms in terms of the residue. (orig.)
Tensor renormalization group methods for spin and gauge models
Zou, Haiyuan
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Radiation Reaction, Renormalization and Poincaré Symmetry
Directory of Open Access Journals (Sweden)
Yurij Yaremko
2005-11-01
Full Text Available We consider the self-action problem in classical electrodynamics of a massive point-like charge, as well as of a massless one. A consistent regularization procedure is proposed, which exploits the symmetry properties of the theory. The radiation reaction forces in both 4D and 6D are derived. It is demonstrated that the Poincaré-invariant six-dimensional electrodynamics of the massive charge is renormalizable theory. Unlike the massive case, the rates of radiated energy-momentum tend to infinity whenever the source is accelerated. The external electromagnetic fields, which do not change the velocity of the particle, admit only its presence within the interaction area. The effective equation of motion is the equation for eigenvalues and eigenvectors of the electromagnetic tensor. The interference part of energy-momentum radiated by two massive point charges arbitrarily moving in flat spacetime is evaluated. It is shown that the sum of work done by Lorentz forces of charges acting on one another exhausts the effect of combination of outgoing electromagnetic waves generated by the charges.
Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
de Rham, Claudia; Heisenberg, Lavinia; Pirtskhalava, David
2012-01-01
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear action, and (b) global field-space Galilean transformations of the scalar field. The Lagrangian contains a set of non-topological interaction terms of the above-mentioned dimensionality, which we show are not renormalized at any order in perturbation theory. We also discuss the renormalization of other operators, that may be generated by loops and/or receive loop-corrections, and identify the regime in which they are sub-leading with respect to the operators that do not get renormalized. Interestingly, such scalar-tensor theories emerge in a certain high-energy limit of the ghost-free theory of massive gravity. One can use the non-renormalization properties of the high-energy limit to estimate the magnitude of quantum corrections in the full theory. We show that the quantum co...
Gauge-independent $\\overline{MS}$ renormalization in the 2HDM
Denner, Ansgar; Lang, Jean-Nicolas; Sturm, Christian
2016-01-01
We present a consistent renormalization scheme for the CP-conserving Two-Higgs-Doublet Model based on $\\overline{MS}$ renormalization of the mixing angles and the soft-$Z_2$-symmetry-breaking scale $M_{sb}$ in the Higgs sector. This scheme requires to treat tadpoles fully consistently in all steps of the calculation in order to provide gauge-independent $S$-matrix elements. We show how bare physical parameters have to be defined and verify the gauge independence of physical quantities by explicit calculations in a general $R_{\\xi}$-gauge. The procedure is straightforward and applicable to other models with extended Higgs sectors. In contrast to the proposed scheme, the $\\overline{MS}$ renormalization of the mixing angles combined with popular on-shell renormalization schemes gives rise to gauge-dependent results already at the one-loop level. We present explicit results for electroweak NLO corrections to selected processes in the appropriately renormalized Two-Higgs-Doublet Model and in particular discuss the...
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.
Renormalization of local quark-bilinear operators for Nf=3 flavors of SLiNC fermions
Constantinou, M; Panagopoulos, H; Perlt, H; Rakow, P E L; Schierholz, G; Schiller, A; Zanotti, J M
2014-01-01
The renormalization factors of local quark-bilinear operators are computed non-perturbatively for $N_f=3$ flavors of SLiNC fermions, with emphasis on the various procedures for the chiral and continuum extrapolations. The simulations are performed at a lattice spacing $a=0.074$ fm, and for five values of the pion mass in the range of 290-465 MeV, allowing a safe and stable chiral extrapolation. Emphasis is given in the subtraction of the well-known pion pole which affects the renormalization factor of the pseudoscalar current. We also compute the inverse propagator and the Green's functions of the local bilinears to one loop in perturbation theory. We investigate lattice artifacts by computing them perturbatively to second order as well as to all orders in the lattice spacing. The renormalization conditions are defined in the RI$'$-MOM scheme, for both the perturbative and non-perturbative results. The renormalization factors, obtained at different values of the renormalization scale, are translated to the ${...
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.
Nonlocal Coulomb Correlations in Metals Close to a Charge Order Insulator Transition
Merino, Jaime
2007-07-01
The charge ordering transition induced by the nearest-neighbor Coulomb repulsion V in the 1/4-filled extended Hubbard model is investigated using cellular dynamical mean-field theory. We find a transition to a strongly renormalized charge ordered Fermi liquid at VCO and a metal-to-insulator transition at VMI>VCO. Short range antiferromagnetism occurs concomitantly with the CO transition. Approaching the charge ordered insulator, V≲VMI, the Fermi surface deforms and the scattering rate of electrons develops momentum dependence on the Fermi surface.
Renormalization of Optical Excitations in Molecules near a Metal Surface
DEFF Research Database (Denmark)
García Lastra, Juan Maria; Thygesen, Kristian Sommer
2011-01-01
The lowest electronic excitations of benzene and a set of donor-acceptor molecular complexes are calculated for the gas phase and on the Al(111) surface using the many-body Bethe-Salpeter equation. The energy of the charge-transfer excitations obtained for the gas phase complexes are found to be ...
Large-N expansion, conformal field theory and renormalization-group flows in three dimensions
Anselmi, D
2000-01-01
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.
Electroweak theory. Framework of on-shell renormalization and study of higher-order effects
Energy Technology Data Exchange (ETDEWEB)
Aoki, Ken-ichi; Hioki, Zenro; Kawabe, Rokuo; Konuma, Michiji; Muta, Taizo
1983-03-01
The electroweak theory (the Weinberg-Salam theory) is reviewed emphasizing its aspect of a renormalizable gauge field theory with spontaneous symmetry breaking. The on-shell renormalization procedure is developed where all the renormalization constants are fixed on the mass shell of gauge bosons, fermions and Higgs bosons. It is applied to the calculation of radiative corrections to leptonic processes ..nu.. sub(..mu..)e ..-->.. ..nu.. sub(..mu..)e, ..nu..-bar sub(..mu..)e ..-->.. ..nu..-bar sub(..mu..)e, ..nu.. sub(..mu..)e ..-->.. ..mu nu..sub(e) and ..mu.. ..-->.. e..nu..-barsub(e)..nu.. sub (..mu..). The experimental significance of the radiative corrections and the effect of the corrections to the values of physical masses of W/sup + -/ and Z are discussed. The relation among different renormalization procedures is clarified.
Protecting the conformal symmetry via bulk renormalization on Anti deSitter space
Duetsch, Michael
2010-01-01
The problem of perturbative breakdown of conformal symmetry can be avoided, if a conformally covariant quantum field phi on d-dimensional Minkowski spacetime is viewed as the boundary limit of a quantum field Phi on d+1-dimensional anti-deSitter spacetime (AdS). We study the boundary limit in renormalized perturbation theory with polynomial interactions in AdS, and point out the differences as compared to renormalization directly on the boundary. In particular, provided the limit exists, there is no conformal anomaly. We compute explicitly the "fish diagram" on AdS_4 by differential renormalization, and calculate the anomalous dimension of the composite boundary field phi^2 with bulk interaction Phi^4.
Renormalization-group symmetries for solutions of nonlinear boundary value problems
Kovalev, V F
2008-01-01
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov renormalization group treated as a Lie group of continuous transformations. Overwhelmingly dominating practical quantum field theory calculations, the renormalization-group method formed the basis for the discovery of the asymptotic freedom of strong nuclear interactions and underlies the Grand Unification scenario. This paper describes the logical framework of a new algorithm based on the modern theory of transformation groups and presents the most interesting results of application of the method to differential and/or integral equation problems and to problems that involve linear functionals of solutions. Examples from nonlinear optics, kinetic theory, and plasma dynamics are given, where new analytical solutions obtained with this algorithm have allowed describing the singular...
Two-loop renormalization of vector, axial-vector and tensor fermion bilinears on the lattice
Skouroupathis, A
2008-01-01
We compute the two-loop renormalization functions, in the RI' scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma$ corresponds to the Vector, Axial-Vector and Tensor Dirac operators, in the lattice formulation of QCD. We consider both the flavor nonsinglet and singlet operators. We use the clover action for fermions and the Wilson action for gluons. Our results are given as a polynomial in $c_{SW}$, in terms of both the renormalized and bare coupling constant, in the renormalized Feynman gauge. Finally, we present our results in the MSbar scheme, for easier comparison with calculations in the continuum. The corresponding results, for fermions in an arbitrary representation, together with some special features of superficially divergent integrals, are included in the Appendices.
Sector-dependent versus standard renormalization of Pauli-Villars-regulated light-front QED
Chabysheva, S S
2009-01-01
We consider quantum electrodynamics quantized on the light front in Feynman gauge and regulated in the ultraviolet by the inclusion of massive, negative-metric Pauli--Villars (PV) particles in the Lagrangian. The eigenstate of the electron is approximated by a Fock-state expansion truncated to include one photon. The Fock-state wave functions are computed from the fundamental Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic moment. Two methods of renormalization are considered: a sector-dependent renormalization, where the bare parameters of the Lagrangian are allowed to depend on the Fock sectors between which the particular Hamiltonian term acts, and a standard renormalization, where the bare parameters are the same for all sectors. Both methods are shown to require some care with respect to ultraviolet divergences; neither method can allow all PV masses to be taken to infinity. In addition, the sector-dependent approach suffers from an infrared divergence that requires a nonzero ...
Renormalization constants for $N_{\\rm f}=2+1+1$ twisted mass QCD
Blossier, Benoit; Guichon, Pierre; Morénas, Vincent; Pène, Olivier; Rodríguez-Quintero, Jose; Zafeiropoulos, Savvas
2014-01-01
We summarize recent non-perturbative results obtained for the renormalization constants computed in the RI'-MOM scheme for $N_{\\rm f}=2+1+1$ twisted mass QCD. Our implementation employs the Iwasaki gauge action and four dynamical degenerate twisted mass fermions. Renormalization constants for scalar, pseudo-scalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two different volumes and several values of the twisted mass. Our method allows for a precise cross-check of the running, because of the particular proper treatment of the hypercubic artifacts. Preliminary results for twist-2 operators are also presented.
A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators
Directory of Open Access Journals (Sweden)
A.J. Chambers
2015-01-01
Full Text Available A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. The method is based on the Feynman–Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current Aμ and the scalar density S for both nonsinglet and singlet operators for Nf=3 flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.
Güven, Can; Hinczewski, Michael; Berker, A Nihat
2010-11-01
The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched randomness, is extended in this study to systems with quenched randomness. Local magnetizations and correlation functions as a function of spin separation are calculated as tensor products subject to renormalization-group transformation. Phase diagrams are extracted from the long-distance behavior of the correlation functions. The approach is illustrated with the quenched bond-diluted Ising model on the triangular lattice. An accurate phase diagram is obtained in temperature and bond-dilution probability for the entire temperature range down to the percolation threshold at zero temperature.
A novel approach to nonperturbative renormalization of singlet and nonsinglet lattice operators
Energy Technology Data Exchange (ETDEWEB)
Chambers, A.J. [CSSM, Department of Physics, University of Adelaide, Adelaide, SA 5005 (Australia); Horsley, R. [School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ (United Kingdom); Nakamura, Y. [RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 650-0047 (Japan); Perlt, H., E-mail: perlt@itp.uni-leipzig.de [Institut für Theoretische Physik, Universität Leipzig, 04103 Leipzig (Germany); Rakow, P.E.L. [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool L69 3BX (United Kingdom); Schierholz, G. [Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg (Germany); Schiller, A. [Institut für Theoretische Physik, Universität Leipzig, 04103 Leipzig (Germany); Zanotti, J.M. [CSSM, Department of Physics, University of Adelaide, Adelaide, SA 5005 (Australia)
2015-01-05
A novel method for nonperturbative renormalization of lattice operators is introduced, which lends itself to the calculation of renormalization factors for nonsinglet as well as singlet operators. The method is based on the Feynman–Hellmann relation, and involves computing two-point correlators in the presence of generalized background fields arising from introducing additional operators into the action. As a first application, and test of the method, we compute the renormalization factors of the axial vector current A{sub μ} and the scalar density S for both nonsinglet and singlet operators for N{sub f}=3 flavors of SLiNC fermions. For nonsinglet operators, where a meaningful comparison is possible, perfect agreement with recent calculations using standard three-point function techniques is found.
Competition between superconductivity and charge density waves
Kim, Ki-Seok
2007-02-01
We derive an effective field theory for the competition between superconductivity (SC) and charge density waves (CDWs) by employing the SO(3) pseudospin representation of the SC and CDW order parameters. One important feature in the effective nonlinear σ model is the emergence of a Berry phase even at half filling, originating from the competition between SC and CDWs, i.e., the pseudospin symmetry. A-well known conflict between the previous studies of Oshikawa [Phys. Rev. Lett. 84, 1535 (2000)] and Lee and Shankar [Phys. Rev. Lett. 65, 1490 (1990)] is resolved by the appearance of the Berry phase. The Berry phase contribution allows a deconfined quantum critical point of fractionalized charge excitations with e instead of 2e in the SC-CDW quantum transition at half filling. Furthermore, we investigate the stability of the deconfined quantum criticality against quenched randomness by performing a renormalization group analysis of an effective vortex action. We argue that, although randomness results in a weak disorder fixed point differing from the original deconfined quantum critical point, deconfinement of the fractionalized charge excitations still survives at the disorder fixed point owing to a nonzero fixed point value of the vortex charge.
Duality, Gauge Symmetries, Renormalization Groups and the BKT Transition
José, Jorge V.
2013-06-01
In this chapter, I will briefly review, from my own perspective, the situation within theoretical physics at the beginning of the 1970s, and the advances that played an important role in providing a solid theoretical and experimental foundation for the Berezinskii-Kosterlitz-Thouless theory (BKT). Over this period, it became clear that the Abelian gauge symmetry of the 2D-XY model had to be preserved to get the right phase structure of the model. In previous analyses, this symmetry was broken when using low order calculational approximations. Duality transformations at that time for two-dimensional models with compact gauge symmetries were introduced by José, Kadanoff, Nelson and Kirkpatrick (JKKN). Their goal was to analyze the phase structure and excitations of XY and related models, including symmetry breaking fields which are experimentally important. In a separate context, Migdal had earlier developed an approximate Renormalization Group (RG) algorithm to implement Wilson's RG for lattice gauge theories. Although Migdal's RG approach, later extended by Kadanoff, did not produce a true phase transition for the XY model, it almost did asymptotically in terms of a non-perturbative expansion in the coupling constant with an essential singularity. Using these advances, including work done on instantons (vortices), JKKN analyzed the behavior of the spin-spin correlation functions of the 2D XY-model in terms of an expansion in temperature and vortex-pair fugacity. Their analysis led to a perturbative derivation of RG equations for the XY model which are the same as those first derived by Kosterlitz for the two-dimensional Coulomb gas. JKKN's results gave a theoretical formulation foundation and justification for BKT's sound physical assumptions and for the validity of their calculational approximations that were, in principle, strictly valid only at very low temperatures, away from the critical TBKT temperature. The theoretical predictions were soon tested
Setting the Renormalization Scale in QCD: The Principle of Maximum Conformality
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC /Southern Denmark U., CP3-Origins; Di Giustino, Leonardo; /SLAC
2011-08-19
A key problem in making precise perturbative QCD predictions is the uncertainty in determining the renormalization scale {mu} of the running coupling {alpha}{sub s}({mu}{sup 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 non-conformal {beta} {ne} 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. The PMC is also the theoretical principle underlying the BLM procedure, commensurate scale relations between observables, and the scale-setting method used in lattice gauge theory. The number of active flavors nf in the QCD {beta} function is also correctly determined. We discuss several methods for determining the PMC/BLM scale for QCD processes. We show that a single global PMC scale, valid at leading order, can be derived from basic properties of the perturbative QCD cross section. The elimination of the renormalization scheme ambiguity using the PMC will not only increase the precision of QCD tests, but it will also increase the sensitivity of collider experiments to new physics beyond the Standard Model.
Stefanov, Stefan Z
2011-01-01
The realization of Daily Artificial Dispatcher as a quantum/relativistic computation consists of perturbative renormalization of the Electrical Power System (EPS), generating the flowcharts of computation, verification, validation, description and help. Perturbative renormalization of EPS energy and time has been carried out in this paper for a day ahead via virtual thermalization of the EPS for a day ahead.
Allès, B; Di Giacomo, Adriano; Pica, C
2005-01-01
We present a study of the systematic effects in the nonperturbative evaluation of the renormalization constants which appear in the field-theoretical determination of the topological susceptibility in pure Yang-Mills theory. The study is performed by computing the renormalization constants on configurations that have been calibrated by use of the Ginsparg-Wilson formalism and by cooling.
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
Brizola, A; Sampaio, M D; Nemes, M C; Sampaio, Marcos
2002-01-01
We describe in detail how a sliding scale is introduced in the renormalization of a QFT according to integer-dimensional implicit regularization scheme. We show that since no regulator needs to be specified at intermediate steps of the calculation, the introduction of a mass scale is a direct consequence of a set of renormalization conditions. As an illustration the one loop beta-function for QED and lambda*phi^4 theories are derived. They are given in terms of derivatives of appropriately systematized functions (related to definited parts of the amplitudes) with respect to a mass scale mu. Our formal scheme can be easily generalized to higher loop calculations.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; Wu, Xing-Gang; /Chongqing U.
2012-04-02
The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal {l_brace}{beta}{sub i}{r_brace}-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC renormalization scale {mu}{sub R}{sup PMC} and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale {mu}{sub R}{sup init}, consistent with renormalization group invariance. Moreover, after PMC scale-setting, the n!-growth of the pQCD expansion is eliminated. Even the residual scale-dependence at fixed order due to unknown higher-order {l_brace}{beta}{sub i}{r_brace}-terms is substantially suppressed. As an application, we apply the PMC procedure to obtain NNLO predictions for the t{bar t}-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for {sigma}{sub t{bar t}} is larger in magnitude in comparison with the conventional scale-setting method, and it agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the
Three- and four-body systems with the Functional Renormalization Group
Raziel, Benjamín; Ávila, Jaramillo
2016-10-01
The Efimov effect arises in three-body systems near the unitary limit. Some of its features are universal, while others are not. This article uses a Functional-Renormalization- Group approach to discuss the Efimov effect and four-body systems. In this context, the Efimov effect appears as a consequence of the Renormalization-Group flow of couplings. On the four- body system, we find three tetramers below each Efimov trimer, and no evidence of four- body universality breaking. Two of these tetramers are in agreement with quantum-mechanical calculations and experimental results.
Gauge invariant composite operators of QED in the exact renormalization group formalism
Sonoda, Hidenori
2013-01-01
Using the exact renormalization group (ERG) formalism, we study the gauge invariant composite operators in QED. Gauge invariant composite operators are introduced as infinitesimal changes of the gauge invariant Wilson action. We examine the dependence on the gauge fixing parameter of both the Wilson action and gauge invariant composite operators. After defining ``gauge fixing parameter independence,'' we show that any gauge independent composite operators can be made ``gauge fixing parameter independent'' by appropriate normalization. As an application, we give a concise but careful proof of the Adler-Bardeen non-renormalization theorem for the axial anomaly in an arbitrary covariant gauge by extending the original proof by A. Zee.
Energy Technology Data Exchange (ETDEWEB)
Almasy, Andrea A. [Liverpool Univ. (United Kingdom). Dept. of Mathematical Sciences; Kniehl, Bernd A. [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Sirlin, Alberto [New York Univ., NY (United States). Dept. of Physics
2011-01-15
We study the numerical effects of several renormalization schemes of the Cabibbo-Kobayashi- Maskawa (CKM) quark mixing matrix on the top-quark decay widths. We then employ these results to infer the relative shifts in the CKM parameters vertical stroke V{sub tq} vertical stroke {sup 2} due to the quark mixing renormalization corrections, assuming that they are determined directly from the top-quark partial decay widths, without imposing unitarity constraints. We also discuss the implications of these effects on the ratio R = {gamma}(t {yields} Wb){gamma}{sub t} and the determination of vertical stroke V{sub tb} vertical stroke {sup 2}. (orig.)
Renormalization of domain-wall bilinear operators with short-distance current correlators
Tomii, M; Fahy, B; Fukaya, H; Hashimoto, S; Kaneko, T; Noaki, J
2016-01-01
We determine the renormalization constants for flavor non-singlet fermion bilinear operators of M\\"obius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to $O(\\alpha_s^4)$. We employ $2+1$-flavor lattice ensembles at three lattice spacings in the range 0.044--0.080~fm.
Renormalization and Computation II: Time Cut-off and the Halting Problem
Manin, Yuri I
2009-01-01
This is the second installment to the project initiated in [Ma3]. In the first Part, I argued that both philosophy and technique of the perturbative renormalization in quantum field theory could be meaningfully transplanted to the theory of computation, and sketched several contexts supporting this view. In this second part, I address some of the issues raised in [Ma3] and provide their development in three contexts: a categorification of the algorithmic computations; time cut--off and Anytime Algorithms; and finally, a Hopf algebra renormalization of the Halting Problem.
Vieru, Andrei
2016-01-01
The renormalization of MZV was until now carried out by algebraic means. In this paper, we show that renormalization in general, and in particular of the multiple zeta functions, is more than just a pure algebraic convention. We give a simple analytic method of computing the regularized values of multiple zeta functions in any dimension for arguments of the form (1,...,1), where the series do not converge. These values happen to be the coefficients of the asymptotic expansion of the inverse G...
Renormalization constants for Wilson fermion lattice QCD with four dynamical flavours
Dimopoulos, P; Herdoiza, G; Jansen, K; Lubicz, V; Palao, D; Rossi, G C
2010-01-01
We report on an ongoing non-perturbative computation of RI-MOM scheme renormalization constants for the lattice action with four dynamical flavours currently in use by ETMC. For this goal dedicated simulations with four degenerate sea quark flavours are performed at several values of the standard and twisted quark mass parameters. We discuss a method for removing possible O(a) artifacts at all momenta and extrapolating renormalization constant estimators to the chiral limit. We give preliminary results at one lattice spacing.
Why one needs a functional renormalization group to survive in a disordered world
Indian Academy of Sciences (India)
Kay Jörg Wiese
2005-05-01
In this paper, we discuss why functional renormalization is an essential tool to treat strongly disordered systems. More specifically, we treat elastic manifolds in a disordered environment. These are governed by a disorder distribution, which after a finite renormalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss how a renormalizable field theory can be constructed even beyond 2-loop order. We then consider an elastic manifold embedded in dimensions, and give the exact solution for → ∞. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. Finally, the effective action at order 1/ is reported.
Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
Ghosh, A; Talukdar, B; Ghosh, Angsula; Adhikari, Sadhan K.
1998-01-01
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.
Dimensional versus cut-off renormalization and the nucleon-nucleon interaction
Ghosh, Angsula; Adhikari, Sadhan K.; Talukdar, B.
1998-10-01
The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.
Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory
Krajewski, Thomas; Tanasa, Adrian
2012-01-01
We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we define assigned graphs, that are graphs with appropriate decorations for the multi-scale framework. We then define Hopf algebras on these assigned graphs and on the Gallavotti-Nicol\\`o trees, particular class of trees encoding the supplementary informations of the assigned graphs. Several morphisms between these combinatorial Hopf algebras and the Connes-Kreimer algebra are given. Finally, scale dependent couplings are analyzed via this combinatorial algebraic setting.
Additional considerations in the definition and renormalization of non-covariant gauges
Joglekar, S D
2003-01-01
In this work, we pursue further consequences of a general formalism for non-covariant gauges developed in an earlier work (hep-th/0205042). We carry out further analysis of the additional restrictions on renormalizations noted in that work. We use the example of the axial gauge A_3 =0. We find that if multiplicative renormalization together with ghost-decoupling is to hold, the "prescription-term" (that defines a prescription) cannot be chosen arbitrarily but has to satisfy certain non-trivial conditions (over and above those implied by the validity of power counting) arising from the WT identitites associated with the residual gauge invariance.
Radiation reaction for a massless charged particle
Kazinski, P. O.; Sharapov, A. A.
2003-07-01
We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field with regard to the radiation back reaction. It is shown that unlike the massive case, not all the divergences resulting from the self-action of the particle are Lagrangian, i.e., can be cancelled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of a homogeneous external field, the first radiative correction to the Lorentz equation is explicitly derived via the reduction of order procedure.
Radiation reaction for a massless charged particle
Energy Technology Data Exchange (ETDEWEB)
Kazinski, P O; Sharapov, A A [Physics Faculty, Tomsk State University, Tomsk, 634050 (Russian Federation)
2003-07-07
We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field with regard to the radiation back reaction. It is shown that unlike the massive case, not all the divergences resulting from the self-action of the particle are Lagrangian, i.e., can be cancelled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of a homogeneous external field, the first radiative correction to the Lorentz equation is explicitly derived via the reduction of order procedure.
Radiation reaction for a massless charged particle
Kazinski, P O
2003-01-01
We derive effective equations of motion for a massless charged particle coupled to the dynamical electromagnetic field having regard to the radiation back reaction. It is shown that unlike the massive case not all the divergences resulting from the self-action of the particle are Lagrangian, i.e. can be canceled out by adding appropriate counterterms to the original action. Besides, the order of renormalized differential equations governing the effective dynamics turns out to be greater than the order of the corresponding Lorentz-Dirac equation for a massive particle. For the case of homogeneous external field the first radiative correction to the Lorentz equation is explicitly derived via the reduction of order procedure.
Charged Magnetic Brane Correlators and Twisted Virasoro Algebras
D'Hoker, Eric
2011-01-01
Prior work using gauge/gravity duality has established the existence of a quantum critical point in the phase diagram of 3+1-dimensional gauge theories at finite charge density and background magnetic field. The critical theory, obtained by tuning the dimensionless charge density to magnetic field ratio, exhibits nontrivial scaling in its thermodynamic properties, and an associated nontrivial dynamical critical exponent. In the present work, we analytically compute low energy correlation functions in the background of the charged magnetic brane solution to 4+1-dimensional Einstein-Maxwell-Chern-Simons theory, which represents the bulk description of the critical point. Results are obtained for neutral scalar operators, the stress tensor, and the U(1)-current. The theory is found to exhibit a twisted Virasoro algebra, constructed from a linear combination of the original stress tensor and chiral U(1)-current. The effective speed of light in the IR is renormalized downward for one chirality, but not the other, ...
Holographic Renormalization of Einstein-Maxwell-Dilaton Theories
Kim, Bom Soo
2016-01-01
We generalize the boundary value problem with a mixed boundary condition that involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton theories. In particular, the expectation value of the dual scalar operator can be a function of the expectation value of the current operator. The properties are prevalent in a fixed charge ensemble because the conserved charge is shared by both fields through the dilaton coupling, which is also responsible for non-Fermi liquid properties. We study the on-shell action and the stress energy tensor to note practical importances of the boundary value problem. In the presence of the scalar fields, physical quantities are not fully fixed due to the finite boundary terms that manifest in the massless scalar or the scalar with mass saturating the Breitenlohner-Freedman bound.
Neutralino Decays in the Complex MSSM at One-Loop: a Comparison of On-Shell Renormalization Schemes
Bharucha, A; von der Pahlen, F; Schappacher, C
2012-01-01
We evaluate two-body decay modes of neutralinos in the Minimal Supersymmetric Standard Model with complex parameters (cMSSM). Assuming heavy scalar quarks we take into account all two-body decay channels involving charginos, neutralinos, (scalar) leptons, Higgs bosons and Standard Model gauge bosons. The evaluation of the decay widths is based on a full one-loop calculation including hard and soft QED radiation. Of particular phenomenological interest are decays involving the Lightest Supersymmetric Particle (LSP), i.e. the lightest neutralino, or a neutral or charged Higgs boson. For the chargino/neutralino sector we employ two different renormalization schemes, which differ in the treatment of the complex phases. In the numerical analysis we concentrate on the decay of the heaviest neutralino and show the results in the two different schemes. The higher-order corrections of the heaviest neutralino decay widths involving the LSP can easily reach a level of about 10-15%, while the corrections to the decays to...
A huge renormalization of transport effective mass in the magnetic-polaronic state of EuB{sub 6}
Energy Technology Data Exchange (ETDEWEB)
Glushkov, V. [A.M. Prokhorov General Physics Institute of RAS, 38 Vavilov Street, Moscow 119991 (Russian Federation)], E-mail: glushkov@lt.gpi.ru; Bogach, A.; Demishev, S.; Gon' kov, K.; Ignatov, M.; Khayrullin, Eu.; Samarin, N.; Shubin, A. [A.M. Prokhorov General Physics Institute of RAS, 38 Vavilov Street, Moscow 119991 (Russian Federation); Shitsevalova, N. [Institute for Problems of Materials Science NAS, 3 Krzhizhanovsky Street, 03680 Kiev (Ukraine); Flachbart, K. [Centre of Low Temperature Physics, IEP SAS and IPS FS UPJS, SK-04001 Kosice (Slovakia); Sluchanko, N. [A.M. Prokhorov General Physics Institute of RAS, 38 Vavilov Street, Moscow 119991 (Russian Federation)
2008-04-01
The comprehensive study of galvanomagnetic, thermoelectric and magnetic properties was carried out on the single crystals of low carrier density ferromagnetic metal EuB{sub 6} (T{sub C}{approx}13.9 K, T{sub m}=15.8 K) in a wide range of temperatures (1.8-300 K) and magnetic fields (up to 80 kOe). The analysis of the microscopic characteristics estimated from the data revealed a giant renormalization of the charge carriers' effective mass m{sub eff}, which is observed in the paramagnetic state of this compound with strong electron correlations. The gradual decrease of m{sub eff} from the maximum of m{sub eff}{approx}30m{sub eff} detected at T*{approx}80 K to the low temperature values of m{sub eff} (T{<=}T{sub C}){approx}0.2-1m{sub 0} is discussed in terms of the phase separation with the formation of low resistive ferromagnetic nano-sized regions (ferrons) in the dielectric magnetic polaronic state (T>T{sub m}). The observed unusual behavior of m{sub eff} favors recent explanation of the genesis of the metal-insulator transition scenario proposed for La-doped EuB{sub 6} systems [U. Yu, B.I. Min, Phys. Rev. Lett. 94 (2005) 117202.].
A huge renormalization of transport effective mass in the magnetic-polaronic state of EuB 6
Glushkov, V.; Bogach, A.; Demishev, S.; Gon'kov, K.; Ignatov, M.; Khayrullin, Eu.; Samarin, N.; Shubin, A.; Shitsevalova, N.; Flachbart, K.; Sluchanko, N.
2008-04-01
The comprehensive study of galvanomagnetic, thermoelectric and magnetic properties was carried out on the single crystals of low carrier density ferromagnetic metal EuB 6 ( TC≈13.9 K, Tm=15.8 K) in a wide range of temperatures (1.8-300 K) and magnetic fields (up to 80 kOe). The analysis of the microscopic characteristics estimated from the data revealed a giant renormalization of the charge carriers’ effective mass meff, which is observed in the paramagnetic state of this compound with strong electron correlations. The gradual decrease of meff from the maximum of meff∼30 meff detected at T*≈80 K to the low temperature values of meff ( T⩽ TC)∼0.2-1 m0 is discussed in terms of the phase separation with the formation of low resistive ferromagnetic nano-sized regions (ferrons) in the dielectric magnetic polaronic state ( T> Tm). The observed unusual behavior of meff favors recent explanation of the genesis of the metal-insulator transition scenario proposed for La-doped EuB 6 systems [U. Yu, B.I. Min, Phys. Rev. Lett. 94 (2005) 117202.].
Connectivity of the Mandelbrot set for the family of renormalization transformations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We show that the Mandelbrot set for the family of renormalization transformations of 2-dimensional diamond-like hierachical Potts models in statistical mechanics is connected. We also give an upper bound for the Hausdorff dimension of Julia set when it is a quasi-circle.
Energy Technology Data Exchange (ETDEWEB)
Hedegård, Erik Donovan, E-mail: erik.hedegard@phys.chem.ethz.ch; Knecht, Stefan; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch [Laboratorium für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich (Switzerland); Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard, E-mail: hjj@sdu.dk [Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, Odense (Denmark)
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
Renormalization Group, Non-Gibbsian states, their relationship and further developments.
Enter, Aernout C.D. van
2006-01-01
We review what we have learned about the “Renormalization Group peculiarities” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the
Improved Epstein-Glaser renormalization in coordinate space; 1, Euclidean framework
Gracía-Bondía, José 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.
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
Barut, A. O.
1990-04-01
By exact explicit solution it is shown that the Lorentz-Dirac equation with radiation reaction and proper initial conditions does not violate causality, even if the force is nonanalytic. We also show that if the equation is correctly renormalized there are no runaway solutions.
Hedegård, Erik Donovan; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard; Reiher, Markus
2015-01-01
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
DEFF Research Database (Denmark)
Hedegård, Erik D.; Knecht, Stefan; Kielberg, Jesper Skau
2015-01-01
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electroncorrelation...
Complex-mass shell renormalization of the higher-derivative electrodynamics
Energy Technology Data Exchange (ETDEWEB)
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.)
PyR@TE: Renormalization Group Equations for General Gauge Theories
Lyonnet, Florian; Staub, Florian; Wingerter, Akin
2014-01-01
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 ...
Renormalization group flows for the second $Z_{N}$ parafermionic field theory for N odd
Dotsenko, V S; Dotsenko, Vladimir S.; Estienne, Benoit
2007-01-01
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry $Z_{N}$, for N odd. New fixed points are found and classified.
Renormalization group flows for the second Z{sub N} parafermionic field theory for N odd
Energy Technology Data Exchange (ETDEWEB)
Dotsenko, Vladimir S. [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail: dotsenko@lpthe.jussieu.fr; Estienne, Benoit [Laboratoire de Physique Theorique et Hautes Energies, Unite Mixte de Recherche UMR 7589, Universite Pierre et Marie Curie, Paris-6 (France) and CNRS, Universite Denis Diderot, Paris-7, Boite 126, Tour 25, 5eme etage, 4 place Jussieu, F-75252 Paris Cedex 05 (France)]. E-mail: estienne@lpthe.jussieu.fr
2007-07-23
Using the renormalization group approach, the Coulomb gas and the coset techniques, the effect of slightly relevant perturbations is studied for the second parafermionic field theory with the symmetry Z{sub N}, for N odd. New fixed points are found and classified.
Full counting statistics of renormalized dynamics in open quantum transport system
Energy Technology Data Exchange (ETDEWEB)
Luo, JunYan, E-mail: jyluo@zust.edu.cn [School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023 (China); Shen, Yu; He, Xiao-Ling [School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023 (China); Li, Xin-Qi [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR (China); State Key Laboratory for Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083 (China); Department of Physics, Beijing Normal University, Beijing 100875 (China); Yan, YiJing [Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong SAR (China)
2011-11-28
The internal dynamics of a double quantum dot system is renormalized due to coupling respectively with transport electrodes and a dissipative heat bath. Their essential differences are identified unambiguously in the context of full counting statistics. The electrode coupling caused level detuning renormalization gives rise to a fast-to-slow transport mechanism, which is not resolved at all in the average current, but revealed uniquely by pronounced super-Poissonian shot noise and skewness. The heat bath coupling introduces an interdot coupling renormalization, which results in asymmetric Fano factor and an intriguing change of line shape in the skewness. -- Highlights: ► We study full counting statistics of electron transport through double quantum dots. ► Essential differences due to coupling to the electrodes and heat bath are identified. ► Level detuning induced by electrodes results in strongly enhanced shot noise and skewness. ► Interdot coupling renormalization due to heat bath leads to asymmetric noise and intriguing skewness.
Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization
Cassol-Seewald, N. C.; Farias, R. L. S.; Fraga, E. S.; Krein, G.; Ramos, Rudnei O.
2012-08-01
We consider the Langevin lattice dynamics for a spontaneously broken λϕ4 scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg-Landau-Langevin and the subtleties related to the multiplicative noise are investigated.
Complex-mass renormalization in hadronic EFT: applicability at two-loop order
Djukanovic, D; Gegelia, J; Krebs, H; Meißner, U -G
2015-01-01
We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting.
Complex-mass renormalization in hadronic EFT: Applicability at two-loop order
Energy Technology Data Exchange (ETDEWEB)
Djukanovic, D. [University of Mainz, Helmholtz Institute Mainz, Mainz (Germany); Epelbaum, E.; Krebs, H. [Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik II, Bochum (Germany); Gegelia, J. [Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany); Tbilisi State University, Tbilisi (Georgia); Meissner, U.G. [Universitaet Bonn, Helmholtz Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Forschungszentrum Juelich, Institute for Advanced Simulation, Institut fuer Kernphysik and Juelich Center for Hadron Physics, Juelich (Germany)
2015-08-15
We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting. (orig.)
New method of the functional renormalization group approach for Yang-Mills fields
Lavrov, P. M.; Shapiro, I. L.
2014-12-01
We propose a new formulation of the functional renormalization group (FRG) approach, based on the use of regulator functions as composite operators. In this case one can provide (in contrast with standard approach) on-shell gauge-invariance for the effective average action.
Loop expansion of the average effective action in the functional renormalization group approach
Lavrov, Peter M.; Merzlikin, Boris S.
2015-10-01
We formulate a perturbation expansion for the effective action in a new approach to the functional renormalization group method based on the concept of composite fields for regulator functions being their most essential ingredients. We demonstrate explicitly the principal difference between the properties of effective actions in these two approaches existing already on the one-loop level in a simple gauge model.
Loop expansion of average effective action in functional renormalization group approach
Lavrov, Peter M
2015-01-01
We formulate a perturbation expansion for the effective action in new approach to the functional renormalization group (FRG) method based on concept of composite fields for regulator functions being therein most essential ingredients. We demonstrate explicitly the principal difference between properties of effective actions in these two approaches existing already on the one-loop level in a simple gauge model.
Hadamard renormalized scalar field theory on anti-de Sitter space-time
Kent, Carl
2014-01-01
We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.
Complex-mass shell renormalization of the higher-derivative electrodynamics
Turcati, Rodrigo; Neves, Mario Junior
2016-08-01
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.
Moritz, Gerrit; Hess, Bernd Artur; Reiher, Markus
2005-01-08
The density-matrix renormalization group algorithm has emerged as a promising new method in ab initio quantum chemistry. However, many problems still need to be solved before this method can be applied routinely. At the start of such a calculation, the orbitals originating from a preceding quantum chemical calculation must be placed in a specific order on a one-dimensional lattice. This ordering affects the convergence of the density-matrix renormalization group iterations significantly. In this paper, we present two approaches to obtain optimized orderings of the orbitals. First, we use a genetic algorithm to optimize the ordering with respect to a low total electronic energy obtained at a predefined stage of the density-matrix renormalization group algorithm with a given number of total states kept. In addition to that, we derive orderings from the one- and two-electron integrals of our test system. This test molecule is the chromium dimer, which is known to possess a complicated electronic structure. For this molecule, we have carried out calculations for the various orbital orderings obtained. The convergence behavior of the density-matrix renormalization group iterations is discussed in detail.
Spontaneous R-symmetry breaking from the renormalization group flow
Amariti, Antonio
2012-01-01
We propose a mechanism of R-symmetry breaking in four-dimensional DSB models based on the RG properties of the coupling constants. By constraining the UV sector, we generate new hierarchies amongst the couplings that allow a spontaneously broken R-symmetry in models with pure chiral fields of R-charges R = 0 and R = 2 only. The result is obtained by a combination of one- and two-loop effects, both at the origin of field space and in the region dominated by leading log potentials.
Weak nonlinear surface-charging effects in electrolytic films.
Dean, D S; Horgan, R R
2003-11-01
A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full nonlinear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the renormalization of the theory and apply it to a triple-layer model for a thin film with Stern layer of thickness h. For this model we give expressions for the surface charge sigma(L) and the disjoining pressure P(d)(L) and show their dependence on the parameters. The influence of image charges naturally arises in the formalism, and we show that predictions depend strongly on h because of their effects. In particular, we show that the surface charge vanishes as the film thickness L-->0. The fluctuation terms in this class of theories contribute a Casimir-like attraction across the film. Although this attraction is well known to be negligible compared with the mean-field component for model electrolytic films with no surface-charge regulation, in the model studied here these fluctuations also affect the surface-charge regulation leading to a fluctuation component in the disjoining pressure which has the same behavior as the mean-field component even for large film thickness.
Renormalization of the Higgs sector in the triplet model
Aoki, Mayumi; Kikuchi, Mariko; Yagyu, Kei
2012-01-01
We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y=1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., $m_{H^{++}}^2-m_{H^+}^2\\simeq m_{H^+}^2-m_A^2$ and $m_A^2\\simeq m_H^2$, where the CP-even ($H$), the CP-odd ($A$) and the doubly-charged ($H^{\\pm\\pm}$) as well as the singly-charged ($H^\\pm$) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The $hhh$ coupling for the standard model-like Higgs boson ($h$) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.
Renormalization of the Higgs sector in the triplet model
Energy Technology Data Exchange (ETDEWEB)
Aoki, Mayumi [Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192 (Japan); Kanemura, Shinya; Kikuchi, Mariko [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Yagyu, Kei, E-mail: keiyagyu@jodo.sci.u-toyama.ac.jp [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); National Central University, Physics and Center for Mathematics and Theoretical Physics, No. 300, Jhongda Rd., Jhongli, Taiwan (China)
2012-08-14
We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y=1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., m{sub H{sup +}{sup +2}}-m{sub H{sup +2}} Asymptotically-Equal-To m{sub H{sup +2}}-m{sub A}{sup 2} and m{sub A}{sup 2} Asymptotically-Equal-To m{sub H}{sup 2}, where the CP-even (H), the CP-odd (A) and the doubly-charged (H{sup {+-}{+-}}) as well as the singly-charged (H{sup {+-}}) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The hhh coupling for the standard model-like Higgs boson (h) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.
Das, Mousumi
2010-05-21
We studied the nature of the ground and low-lying excited states of poly-fused thiophene oligomers within long-range Pariser-Parr-Pople (PPP) model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. Our results show that the lowest dipole-allowed state lies below the lowest dipole forbidden two-photon state, indicating that poly-fused thiophenes are strongly fluorescent. The lowest triplet state lies below the two-photon state, which is in agreement with the general trend in conjugated polymers. The charge density and bond order calculations of three low-lying excited states, along with the ground state of fused thiophene oligomers, show a significant transfer of charge from sulfur to adjacent carbon atom in the middle of the largest system size and these excitations are localized. The charge density and bond order calculations on singly and doubly doped states show that bipolarons are not stable entity in these systems. The calculations of low-lying excitations on radical cation and anion of fused thiophene oligomers show a new energy band in the low energy region, which is strongly coupled to its hole and electron conductivity. This implies that poly-fused thiophenes posses novel field-effect transistor properties.
QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization
Institute of Scientific and Technical Information of China (English)
SU Jun-Chen; SHAN Lian-You; CAO Ying-Hui
2001-01-01
The QCD one-loop renormalization is restudied in a mass-dependent subtraction scheme in which the quark mass is not set to vanish and the renormalization point is chosen to be an arbitrary time-like momentum. The correctness of the subtraction is ensured by the Ward identities which are respected in all the processes of subtraction.By considering the mass effect, the effective coupling constant and the effective quark masses derived by solving the renormalization group equations are given in improved expressions which are different from the previous results.PACS numbers: 11.10.Gh, 11.10.Hi, 12.38.-t, 12.38.Bx
Livshits, Gideon I
2014-01-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either th...
Directory of Open Access Journals (Sweden)
Semanti Chakraborty
2012-01-01
Full Text Available We present here a case of 17-year-old boy from Kolkata presenting with obesity, bilateral gynecomastia, mental retardation, and hypogonadotrophic hypogonadism. The patient weighed 70 kg and was of 153 cm height. Facial asymmetry (unilateral facial palsy, gynecomastia, decreased pubic and axillary hair, small penis, decreased right testicular volume, non-palpable left testis, and right-sided congenital inguinal hernia was present. The patient also had disc coloboma, convergent squint, microcornea, microphthalmia, pseudohypertelorism, low set ears, short neck, and choanalatresia. He had h/o VSD repaired with patch. Laboratory examination revealed haemoglobin 9.9 mg/dl, urea 24 mg/dl, creatinine 0.68 mg/dl. IGF1 77.80 ng/ml (decreased for age, GH <0.05 ng/ml, testosterone 0.25 ng/ml, FSH-0.95 ΅IU/ml, LH 0.60 ΅IU/ml. ACTH, 8:00 A.M cortisol, FT3, FT4, TSH, estradiol, DHEA-S, lipid profile, and LFT was within normal limits. Prolactin was elevated at 38.50 ng/ml. The patient′s karyotype was 46XY. Echocardiography revealed ventricularseptal defect closed with patch, grade 1 aortic regurgitation, and ejection fraction 67%. Ultrasound testis showed small right testis within scrotal sac and undescended left testis within left inguinal canal. CT scan paranasal sinuses revealed choanalatresia and deviation of nasal septum to the right. Sonomammography revealed bilateral proliferation of fibroglandular elements predominantly in subareoalar region of breasts. MRI of brain and pituitary region revealed markedly atrophic pituitary gland parenchyma with preserved infundibulum and hypothalamus and widened suprasellar cistern. The CHARGE association is an increasingly recognized non-random pattern of congenital anomalies comprising of coloboma, heart defect, choanal atresia, retarded growth and development, genital hypoplasia, ear abnormalities, and/or deafness. [1] These anomalies have a higher probability of occurring together. In this report, we have
Renormalization (and power counting) of effective field theories for the nuclear force
Energy Technology Data Exchange (ETDEWEB)
Timoteo, Varese S. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Fac. de Tecnologia; Szpigel, Sergio; Duraes, Francisco O. [Universidade Presbiteriana Mackenzie, Sao Paulo, SP (Brazil). Centro de Ciencias e Humanidades
2011-07-01
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
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
Tokuyama, Michio
2017-01-01
The renormalized simplified model is proposed to investigate indirectly how the static structure factor plays an important role in renormalizing a quadratic nonlinear term in the ideal mode-coupling memory function near the glass transition. The renormalized simplified recursion equation is then derived based on the time-convolutionless mode-coupling theory (TMCT) proposed recently by the present author. This phenomenological approach is successfully applied to check from a unified point of view how strong liquids are different from fragile liquids. The simulation results for those two types of liquids are analyzed consistently by the numerical solutions of the recursion equation. Then, the control parameter dependence of the renormalized nonlinear exponent in both types of liquids is fully investigated. Thus, it is shown that there exists a novel difference between the universal behavior in strong liquids and that in fragile liquids not only for their transport coefficients but also for their dynamics.
Institute of Scientific and Technical Information of China (English)
何春山; 李志兵
2003-01-01
The correlation function of a two-dimensionalIsing model is calculated by the corner transfer matrix renormalization group method.We obtain the critical exponent η= 0.2496 with few computer resources.
Brida, Mattia Dalla; Vilaseca, Pol
2016-01-01
The chirally rotated Schr\\"odinger functional ($\\chi$SF) renders the mechanism of automatic $O(a)$ improvement compatible with Schr\\"odinger functional (SF) renormalization schemes. Here we define a family of renormalization schemes based on the $\\chi$SF for a complete basis of $\\Delta F = 2$ parity-odd four-fermion operators. We compute the corresponding scale-dependent renormalization constants to one-loop order in perturbation theory and obtain their NLO anomalous dimensions by matching to the $\\overline{\\textrm{MS}}$ scheme. Due to automatic $O(a)$ improvement, once the $\\chi$SF is renormalized and improved at the boundaries, the step scaling functions (SSF) of these operators approach their continuum limit with $O(a^{2})$ corrections without the need of operator improvement.
Renormalized Polyakov loop in the deconfined phase of SU(N) gauge theory and gauge-string duality.
Andreev, Oleg
2009-05-29
We use gauge-string duality to analytically evaluate the renormalized Polyakov loop in pure Yang-Mills theories. For SU(3), the result is in quite good agreement with lattice simulations for a broad temperature range.
The neutrino charge radius is a physical observable
Bernabeu, J; Vidal, J
2004-01-01
We present a method which allows, at least in principle, the direct extraction of the gauge-invariant and process-independent neutrino charge radius (NCR) from experiments. Under special kinematic conditions, the judicious combination of neutrino and anti-neutrino forward differential cross-sections allows the exclusion of all target-dependent contributions, such as gauge-independent box-graphs, not related to the NCR. We show that the remaining contributions contain universal, renormalization group invariant combinations, such as the electroweak effective charge and the running mixing angle, which must be also separated out. By considering the appropriate number of independent experiments we show that one may systematically eliminate these universal terms, and finally express the NCR entirely in terms of physical cross-sections. Even though the kinematic conditions and the required precision may render the proposed experiments unfeasible, at the conceptual level the analysis presented here allows for the pro...
2005-01-01
We calculate the Coulomb interaction induced density, temperature and magnetization dependent many-body band-gap renormalization in a typical diluted magnetic semiconductor GaMnAs in the optimally-doped metallic regime as a function of carrier density and temperature. We find a large (about 0.1 eV) band gap renormalization which is enhanced by the ferromagnetic transition. We also calculate the impurity scattering effect on the gap narrowing. We suggest that the temperature, magnetization, an...
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.
Real Space Renormalization Group Study of the S=1/2 XXZ Chains with Fibonacci Exchange Modulation
Hida, Kazuo
2004-08-01
Ground state properties of the S=1/2 antiferromagnetic XXZ chain with Fibonacci exchange modulation are studied using the real space renormalization group method for strong modulation. The quantum dynamical critical behavior with a new universality class is predicted in the isotropic case. Combining our results with the weak coupling renormalization group results by Vidal et al., the ground state phase diagram is obtained.
A Practical Approach to the Hamilton-Jacobi Formulation of Holographic Renormalization
Elvang, Henriette
2016-01-01
We revisit the subject of holographic renormalization for asymptotically AdS spacetimes. For many applications of holography, one has to handle the divergences associated with the on-shell gravitational action. The brute force approach uses the Fefferman-Graham (FG) expansion near the AdS boundary to identify the divergences, but subsequent reversal of the expansion is needed to construct the infinite counterterms. While in principle straightforward, the method is cumbersome and application/reversal of FG is formally unsatisfactory. Various authors have proposed an alternative method based on the Hamilton-Jacobi equation. However, this approach may appear to be abstract, difficult to implement, and in some cases limited in applicability. In this paper, we clarify the Hamilton-Jacobi formulation of holographic renormalization and present a simple algorithm for its implementation to extract cleanly the infinite counterterms. While the derivation of the method relies on the Hamiltonian formulation of general rel...
Renormalization Group and Decoupling in Curved Space II. The Standard Model and Beyond
Gorbar, E V; Gorbar, Eduard V.; Shapiro, Ilya L.
2003-01-01
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The QCD sector at low-energies is described in terms of the composite effective fields. For fermions and scalars the massless limit shows perfect correspondence with the conformal anomaly, but similar limit in a massive vector case requires an extra compensating scalar. In all three cases the decoupling goes smoothly and monotonic. A particularly interesting case is the renormalization group flow in the theory with broken supersymmetry, where the sign of one of the beta-functions changes on the way from the UV to IR.