Renormalization group and scale invariance in terms of asymptotic fields

The expansion of the massive renormalized field operator in terms of asymptotic fields is studied. We derive the renormalization group equation for the renormalized field operator. We obtain the renormalized scale transformations with Callan-Symanzik corrections as generated by canonical scale transformations of asymptotic fields.     

二维静态时空中Dirac场的重正化能动张量和Casimir效应

在一般渐近平直的二维静态黑洞时空中,利用重正化能动张量的一般性质, 对位于两“平行板”间满足Dirichlet条件的无质量Dirac场的重正化能动张量的真空期待值进行了分析和计算, 得到了一般表达式.利用该表达式可以给出各种具体渐近平直二维静态黑洞时空中的相应Casimir力.对于重正化能动张量及Casimir力与真空态定义(包括Boulware 真空态、Hartle-Hawking真空态和Unrum真空态三种情况)、Hawking辐射和反常迹的关系分别进行了讨论，给出了相应的表达式和计算结果. 关键词： 能动张量 Casimir 效应 黑洞 真空态     

Renormalized turbulence theory for the ion acoustic problem

Renormalized kinetic theory for the long range collective oscillations of turbulent plasmas is developed through infinite order summations of the interactions in the Vlasov-Poisson self-consistent field equations. Three levels of renormalized turbulence theory are derived, and the simply renormalized equations are solved for the problem of ion acoustic instability. The physical predictions of renormalized turbulence theory are discussed and used to interpret several experiments on ion acoustic turbulence.     

Renormalized operator form of quantum action principle

The derivatives of the renormalized field operator with respect to the parameters (coupling constants, masses) are discussed. Two ways of obtaining the finite result in terms of renormalized perturbation expansion are shown. Throughout the paper the operator language is used; in particular the operator formula for renormalized powers of the field operators (normal products) is employed. The λ?⁴ theory is considered as an illustrative example.     

Entropy of quantum field in toroidal black hole without brick wall

In this paper the entropy of a toroidal black hole due to a scalar field is investigated by using the DLM scheme. The entropy is renormalized to the standard Bekenstein-Hawking formula with a one-loop correction arising from the higher curvature terms of the gravitational action. For the scalar field, the renormalized Newton constant and two renormalized coupling constants in the toroidal black hole are the same as those in the Reissner-Nordstrom black hole except for other one.     

Unitary renormalization of the Lee model Y4

The Lee model Y₄ is renormalized by unitary transformation. A norm convergent (in each sector) sequence of unitary dressing transformations, which transform a sequence of renormalized cut-off Hamiltonians to a sequence of operators converging strongly on a dense set of states, is defined. The self-adjointness and semiboundedness (in each sector) of the renormalized Hamiltonian are proved.     

Renormalization group and Fermi liquid theory

We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ⁴ field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large.

We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.     

高频波激发低频磁场和离子声波的重整化强湍动理论

本文给出了高温等离子体中高频波激发低频磁场和离子声波强湍动过程的重整化理论,以便改善通常的弱非线性处理方法,从Vlasov-Maxwell方程组出发,在Fourier表象中得到了包含“最发散”和“次发散”效应互相耦合的高频和低频传播于重整化方程组,从而获得了高、低频振荡粒子重整化分布函数和场的耦合关系。在“最发散”重整化近似下,我们求解了高低频传播子方程组,得到了展开到v₄(高频湍动场能密度与等离子体热能密度之比)一次方的近似解和重整化介电函数等表达式。然后,在Fourier逆变换下导得了我们所要的时空表用中重整化强湍动方程组。最后,作为一个说明重整化作用的例子,在一维稳态下求解了孤立子的形式。 关键词：     

非对称Anderson模型的重整微扰展开

利用Yamada微扰论结合重整微扰方法来计算非对称Anderson模型,得到了局域电子占据数、重整化因子、重整化的局域能级以及重整化参数关于裸参数的展开式.计算了局域电子态密度和低温杂质电导,还计算了磁场对它们的影响,这些结果适用于从弱耦合到强耦合的整个耦合强度区域.由于在哈密顿量中已经将局域能级进行了初步重整,采用的重整微扰方法比Hewson的重整微扰方法更适合于研究非对称Anderson模型. 关键词： 非对称Anderson模型 重整化 磁场     

A Renormalized-Hamiltonian-Flow Approach to Eigenenergies and Eigenfunctions *

We introduce a decimation scheme of constructing renormalized Hamiltonian flows, which is useful in the study of properties of energy eigenfunctions, such as localization, as well as in approximate calculation of eigenenergies. The method is based on a generalized Brillouin-Wigner perturbation theory. Each flow is specific for a given energy and, at each step of the flow, a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step. Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows. Numerical illustration of the method is given in the Wigner-band random-matrix model.     

Renormalized waves and discrete breathers in Beta-Fermi-Pasta-Ulam chains

We demonstrate via numerical simulation that in the strongly nonlinear limit the Beta-Fermi-Pasta-Ulam (Beta-FPU) system in thermal equilibrium behaves surprisingly like weakly nonlinear waves in properly renormalized normal variables. This arises because the collective effect of strongly nonlinear interactions effectively renormalizes linear dispersion frequency and leads to effectively weak interaction among these renormalized waves. Furthermore, we show that the dynamical scenario for thermalized Beta-FPU chains is spatially highly localized discrete breathers riding chaotically on spatially extended, renormalized waves.     

Statistical behaviors for renormalization of correlated permeability field

In this article, the statistical properties for the renormalized permeability obtained from the renormalization of the correlated permeability field are investigated. In contrast to the uncorrelated porous media, the scaling of the variance of the renormalized permeability field exhibits a crossover behavior. When the correlation lengths are larger compared with the domain scale covered by the renormalization procedure, the variance of the renormalized permeability will decrease slowly and the scaling exponent will be close to zero. As the renormalization number increases, the covered domain scale will eventually become larger than the correlation lengths, and then the scaling property will transit to the uncorrelated case. The convergent values of the renormalized permeability for isotropic and anisotropic correlated media are also investigated. Both the theoretical analysis and the simulation results show that larger correlation length in one direction will lead to a larger convergent value in the corresponding direction. For the log-normal permeability field, numerical simulations show that the crossover scaling and also the convergent value for the renormalized permeability can be fitted very well by simple mathematical functions.     

Scale transformations for renormalized field operators: Discussion of the soluble model

We discuss the operator formulation of the Zachariasen-Thirring model, describing the chain approximation to the propagator (the sum of three-particle massless bubbles) in massless λ⁴ theory. Such a model is formally scale-invariant and explicitly soluble. All intermediate steps of conventional renormalization procedure, regularization, introduction of appropriate counterterms, and cut-off free limit, are explicitly performed. In every step the scaling properties are discussed and respective dilatation currents are written down. After the proper choice of scale transformations for the renormalized field operator, we obtain the nonlocal dilatation current, defining the renormalized dilatation generator D_Λ^R(t). In the cut-off free limit Λ → ∞ the ET commutator of D_Λ^R(t) with renormalized field operators reproduces the Callan-Symanzik modification of “naive” canonical scale transformations. The renormalized scale transformations coincide in the cut-off free limit with renormalized dimensional transformations and define the exact symmetry of the renormalized theory.     

Towards a Renormalized Lattice Boltzmann Equation for Fluid Turbulence

A coarse-grained Lattice Boltzmann equation is examined in which the effects of unresolved (subgrid) scales are formally incorporated within a renormalized relaxation time of the collision operator. Actual values of the renormalized relaxation time are analyzed for the practical case of high-Reynolds flows past slant bodies (airfoils).     

OCCUPATION RENORMALIZED HARTREE-FOCK APPROXIMATION IN LIPKIN MODEL

The occupation renormalized Hartree-Fock single particle potential is extended to include the 'particle' state occupation. The exac solution of the occupation renormalized Hartree-Fock approximation and that of the Hartree-Fock approximation are calculated in Lipkin Model. It turns out that the RHF solution is more close to the exact one than the HF solution. The effect of occupation probability depends on the strength of the interaction of the two body term.     

A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

Evolution of the entropy of stationary states in selforganization processes in the control parameter space

The behaviour of entropy (Shannon-information) and renormalized entropy (based on theS-theorem [3]) is investigated for systems with an exponential stationary probability distribution function (1). Analytical results for the derivatives with respect to the control parameters are derived. One class of systems (3) is separated for which the renormalized entropy is a monotonously decreasing function of the control parameters.     

Renormalization of QED with planar binary trees

The Dyson relations between renormalized and bare photon and electron propagators and are expanded over planar binary trees. This yields explicit recursive relations for the terms of the expansions. When all the trees corresponding to a given power of the electron charge are summed, recursive relations are obtained for the finite coefficients of the renormalized photon and electron propagators. These relations significantly decrease the number of integrals to carry out, as compared to the standard Feynman diagram technique. In the case of massless quantum electrodynamics (QED), the relation between renormalized and bare coefficients of the perturbative expansion is given in terms of a Hopf algebra structure. Received: 23 March 2000 / Revised version: 24 November 2000 / Published online: 6 April 2001     

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.