Renormalization Of Propagator Research Articles

Parametric Hamilton’s equations for stochastic systems

In the context of instanton method for stochastic system this paper purposes a modification of the arclength parametrization of the Hamilton’s equations allowing for an arbitrary instanton speed. The main results of the paper are: (i) it generalizes the parametrized Hamilton’s equations to any speed required. (ii) Corrects the parametric action on the occasion that the Hamiltonian is small but finite and how it adjusts to the probability density function (pdf). (iii) Improves instanton approximation to pdf by noise and propagator renormalization. As an application of the above set up we evaluate the instanton and predict the statistics of two models: Ornstein–Uhlenbeck and passive scalar gradients in a Lagrangian model for turbulence, namely the scalar gradient recent fluid deformation closure.

Effect of propagator renormalization on the band gap of insulating solids

We present momentum-resolved spectral functions and band gaps from bare and self-consistent second-order perturbation theory for insulating periodic solids. We establish that, for systems with large gap sizes, both bare and self-consistent perturbation theory yield reasonable gaps. However, smaller gap sizes require a self-consistent adjustment of the propagator. In contrast to results obtained within a quasiparticle formalism used on top of bare second-order perturbation theory, no unphysical behavior of the band gap is observed. Our implementation of a fully self-consistent, $\mathrm{\ensuremath{\Phi}}$-derivable, and thermodynamically consistent finite-temperature diagrammatic perturbation theory forms a framework on which embedding theories such as the dynamical mean-field theory and self-energy embedding theories can be implemented.

Renormalization of quark propagator, vertex functions, and twist-2 operators from twisted-mass lattice QCD atNf=4

We present a precise nonperturbative determination of the renormalization constants in the mass independent RI'-MOM scheme. The lattice implementation uses the Iwasaki gauge action and four degenerate dynamical twisted-mass fermions. The gauge configurations are provided by the ETM Collaboration. Renormalization constants for scalar, pseudoscalar, vector and axial operators, as well as the quark propagator renormalization, are computed at three different values of the lattice spacing, two volumes and several twisted-mass parameters. The method we developed allows for a precise cross-check of the running, thanks to the particular proper treatment of hypercubic artifacts. Results for the twist-2 operator ${O}_{44}$ are also presented.

THE RARITA–SCHWINGER FIELD: RENORMALIZATION AND PHENOMENOLOGY

We discuss renormalization of propagator of interacting Rarita–Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For nonleading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of Δ++(1232) in π+ p →π+p leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.

Absence of higher derivatives in the renormalization of propagators in quantum field theories with infinitely many couplings

I study some aspects of the renormalization of quantum field theories with infinitely many couplings in arbitrary spacetime dimensions. I prove that when the spacetime manifold admits a metric of constant curvature, the propagator is not affected by terms with higher derivatives. More generally, certain Lagrangian terms are not turned on by renormalization, if they are absent at the tree level. This restricts the form of the action of a non-renormalizable theory, and has applications to quantum gravity. The new action contains infinitely many couplings, but not all of the ones that might have been expected. In quantum gravity, the metric of constant curvature is an extremal, but not a minimum, of the complete action. Nonetheless, it appears to be the right perturbative vacuum, at least when the curvature is negative, suggesting that the quantum vacuum has a negative asymptotically constant curvature. The results of this paper give also a set of rules for a more economical use of effective quantum field theories and suggest that it might be possible to give mathematical sense to theories with infinitely many couplings at high energies, to search for physical predictions.

Feedback effects and the self-consistent Thouless criterion of the attractive Hubbard model

We propose a fully microscopic theory of the anomalous normal state of the attractive Hubbard model in the low-density limit that accounts for propagator renormalization. Our analytical conclusions regarding the thermodynamic instabilities contained in the self-consistent equations associated with this formulation have been verified by our comprehensive numerical study of the same equations. The resulting theory is found to contain no transitions at non-zero temperatures for all finite lattices, and we have confirmed, using our numerical studies, that this behaviour persists in the thermodynamic limit for low-dimensional systems.

Self-Consistent Calculations of Quasiparticle States in Metals and Semiconductors

We solve the Dyson equation for the one-particle Green{close_quote}s function in a periodic solid self-consistently within the shielded-interaction (or GW ) approximation. The effect of self-consistency (propagator renormalization) is found to be substantial. We illustrate this finding via calculations of quasiparticle states in K and Si. In the case of Si we show that the current standard of {ital ab initio} quasiparticle theory, the GW self-energy diagram, fails to account for the observed value of the absolute band gap{emdash}if properly, i.e., self-consistently, evaluated. {copyright} {ital 1998} {ital The American Physical Society }

Summation of free-energy diagrams of an anharmonic crystal and equation of state for a Lennard-Jones solid

We present a method of calculating the Helmholtz free energy of an anharmonic crystal. The exact expression for $F,$ obtained by summing an infinite series of contributions, from all the loops and bubbles (quartic and cubic contributions to the self-energy of the Green's function), is evaluated numerically and the equation of state results for a Lennard-Jones solid are compared with the ${\ensuremath{\lambda}}^{2}$ perturbation theory (PT) which contains only the lowest order cubic and quartic contributions. It is shown that the infinite sum results are considerably improved over the ${\ensuremath{\lambda}}^{2}$ PT results for higher temperatures. Next we have presented a powerful ansatz approach of evaluating the same sum. The numerical results from this method are shown to be identical to the exact sum except at near ${T}_{m}$ where they are very slightly different. The ansatz method is then extended to the higher order ${\ensuremath{\lambda}}^{4}$ diagrams and here too the numerical results are found to be improved over the results from the ${\ensuremath{\lambda}}^{4}$ PT. The ansatz procedure is then extended to the propagator renormalization and the numerical results obtained seem to have the best agreement with the results of classical Monte Carlo simulations.

Development of the Green function diagrammatic technique for local spins

We show using as an example of the singlet-singlet (the transverse Ising model) model how the renormalization of local propagators and population factors may be achieved in the frame of the loop expansion of the self-energy. By this the Green function diagrammatic technique for interacting local spins in the presence of the crystalline field becomes free from shortcomings induced by the practice in which only the interaction undergoes the renormalization. The low order renormalization of the propagators leads to the calculated high-temperature ( T→∞) frequency shift while the population renormalization reduces the ferromagnetic T c.

A statistical dynamical theory of strongly nonlinear internal gravity waves

Abstract A statistical dynamical closure theory describing the interaction of strongly (and weakly) nonlinear two-dimensional internal waves in the presence of viscous dissipation and thermal conduction is derived. By applying renormalization methods originally formulated for quantum and classical statistical field theory, closures similar to the Direct Interaction and eddy-damped quasi-normal procedures of turbulence are derived. These methods are applied directly to the strongly nonlinear primitive field equations in Eulerian variables, thus avoiding the small amplitude assumptions inherent in the resonant interaction formalism. Propagator renormalization techniques provide formulas for the nonlinear internal wave frequency and spectral width in terms of the energy spectrum. The commonly used multiple time and space scale analysis is replaced by an analysis of the two-point correlation functions in terms of sum and difference variables. This permits the systematic development of a Landau equation. This ...

Instanton correction to some vacuum energy densities and the bag constant

Earlier calculations of a lower bound for the MIT bag constant B are corrected for an effect due to instanton tunneling. This is done by taking into account a non-perturbative correction to the renormalization group β-function defined in the Savvidy renormalization scheme. From this β-function one can obtain the energy density in the presence of a constant magnetic field. This is then used for estimating the energy density in a vacuum ansatz state and, thereby, also a bound on the bag constant B. Formulated as a bound on the QCD scale parameter Λp in the propagator renormalization scheme and taking B 1 4 = 145 MeV , we obtain Λp ⩽ 0.27 GeV. Taking into account excitation of the Nielsen-Olesen unstable mode (in the way that we described earlier) one gets instead Λp ⩽ 0.11 GeV.

A note on the combinatorics of the renormalisation of turbulent diffusion propagators

Abstract A direct enumeration of combinatorial factors arising in propagator renormalization is used to resolve a dispute in the published literature and to locate the errors in one of the combinatorial arguments presented.

Effects of dynamical friction on the renormalization of propagator in turbulent plasmas

It is shown that there appear two stages in effects of fluctuations on particle trajectories in weakly turbulent plasmas. A new propagator including dynamical friction is obtained, which is different from the Dupree type one.

Renormalized Fokker-Planck equation for a multimode solid-state laser

A Fokker-Planck equation is derived which describes the radiation field of a multimode solid-state laser. Under the assumption of small concentration in active atoms but arbitrary coupling between the atoms and the field, the drift and diffusion coefficients of the Fokker-Planck equation are defined as the solutions of discrete integral equations (corresponding to a propagator renormalization in quantum field theory). For monomode and bimode lasers, these integral equations are explicitly solved. As an application, we give for a monomode laser closed analytical (although approximate) expressions for (i) the stationary photon statistics, (ii) the frequency shift and (iii) the linewidth of the field.

Effect of rearrangement on the single-particle field ofO16

Both the third-order and the second-order rearrangemetn corrections are included in a self-consistent calculation of the single-particle field of $^{16}\mathrm{O}$, carried out with a model $G$ matrix derived from the soft-core Sprung-de-Tourreil interaction. Saturation is improved: The charge radius increases by 7% and the central nuclear density is diminished by 10%. For the interaction chosen, the effect of the second-order (energy-dependent) corrections are larger than those of the third order. The self-consistent "single-particle" energies in the nucleus, and the single-particle wave functions, are used to calculate the removal energies of single particles, the results being in quite good agreement with experiment.NUCLEAR STRUCTURE $^{16}\mathrm{O}$; calculated radius, single-particle separation energies, total binding energy. Propagator renormalization self-consistent method.

Perturbation theory of a many-fermion system: (II). Expansions in reaction matrices

Currently, the most satisfactory version of Brueckner theory from the formal point of view is the generalized-time-ordered series of Brandow. In this formalism the Brueckner-Hartree-Fock (BHF) self-energy for normally empty (“particle”) states does not factorize, and for this reason it is not included in the single-particle potential, U. This feature of the theory leads to differences: (i) between single-particle and separation energies, and (ii) between U and the real part of the optical potential. In article I the time-dependent Green function formulation was used to achieve more extensive factorization, with the consequence that U could be defined to include the leading terms of the on-energy-shell BHF potential for “particles”. In the present paper this earlier expansion is written in terms of Brueckner reaction matrices, and the low orders of the resulting series are investigated. For this task, it has been found more convenient to employ the Fourier-transformed formalism of energy-dependent Green functions, G (ω). First, diagram rules for expansions in the bare interaction, V, and an arbitrary U are given in sufficient generality to apply to finite systems, for which U and f(ω) are not diagonal matrices. The binding energy is expressed in terms of closed, propagator-renormalized, ω-dependent, ground state diagrams including over-counting corrections. Then U is chosen, in correspondence with article I and a paper of Klein, in terms of the real part of the proper self-energy. In the framework employed here U may be defined conveniently to be hermitian. A prescription, stated with remarkable simplicity in the G(ω) formalism, is obtained for converting an expansion in V to one in a general transition or reaction matrix. Our U is the quasiparticle separation-energy potential, containing on-energy-shell self-energies of all topologies. For example, when the reaction matrix is that of Brueckner, the first-order (BHF) and secondorder (“rearrangement energy”) insertions are shown to be included in U both for “particles” and holes. Truncation schemes based on a stationary property of the propagator-renormalized series are explored. The simplest is a renormalized BHF approximation similar to that for Brandow's expansion but differing from it by (a) containing the RBHF potential for “particle” states, which implies a smaller energy gap and greater diffuseness at the Fermi surface; and (b) propagator renormalization (“line weighting”) factors which contain single-particle density matrices (“true occupation probabilities”) as in Brandow's expansion, plus “folded” terms. The present formulation allows a close connection between “virtual” and “valence” single-particle states, while staying close to the computationally successful framework of the Brueckner theory and avoiding complex energies.

Renormalization and Analysis of the Cottingham Formula and the Consistency of SU(3) and Electromagnetic Mass Shifts in Parton Models

We show that the divergent pieces of the Cottingham expression for electromagnetic mass shifts may always be identified, by means of structure-function sum rules, with the contributions (to the total mass shift) resulting from the divergent electromagnetic mass shifts and propagator renormalization of the bare partons themselves. This enables one to carry out a renormalization program, to first order in $\ensuremath{\alpha}$. The SU(3) and electromagnetic mass shifts of the baryon octet are analyzed and shown to display a substantial consistency with one another. Predictions for fixed poles in the Compton amplitudes of all baryons result once that for the proton is known. In addition we extract quark masses for a given value of the $\ensuremath{\pi}\ensuremath{-}N \ensuremath{\sigma}$ term.

Effect of Lattice Vibrations in a Multiple-Scattering Description of Low-Energy Electron Diffraction. I. Formal Perturbation Theory

A diagrammatic version of perturbation theory is developed for the description of the influence of lattice vibrations on the elastic and inelastic scattering cross sections of low-energy electrons from surfaces of single-crystal solids. The formalism describes the effects on the cross sections of a thermodynamic-equilibrium distribution of both bulk and surface phonon modes. The relationships between our general formalism and the conventional single-scattering analysis of inelastic electron-solid scattering are displayed. Multiple-scattering and virtual-phonon emission from a given ion core are included in the theory via vertex renormalizations of the electron-ion-core scattering vertices. Propagator renormalization is estimated to be small and consequently neglected. The diagrammatic contributions to the elastic scattering cross section are summed explicitly using the approximation that diagrams with internal phonon propagators are small relative to those without such propagators. In this approximation we obtain a set of coupled integral equations for appropriately renormalized scattering amplitudes describing elastic electron scattering from planar layers of ion cores.

Particle Mixing and theZ= 0 Condition

The compositeness conditions of particles in quantum field theory are investigated in the case where two particles with identical quantum numbers can appear in the intermediate states of a certain scattering process as a consequence of the particle-mixing interaction. It is shown that, if we use the generalized propagator renormalization constants to state the compositeness condition, we encounter the curious situation first suggested by Srivastava and Choudhury, but, if we rely on the generalized wave-function renormalization constants, we can verify that the compositeness criteria still hold good in the presence of particle mixing.