Renormalization and renormalization group behaviour of the O(N) non-linear sigma-model in stochastic quantization

The renormalization and renormalization group behaviour of the two-dimensional O(N) non-linear sigma-model has been discussed in the framework of stochastic quantization. For this purpose the path integral representation of the generating functional of the extended stochastic correlation function for constrained systems has been given. The renormalization is formulated by use of the stochastic effective action which can be defined from this generating functional. The renormalization group behavior of the correlation function with different fictitious time arguments has also been investigated. It reduces to the normal one if all external fictitious times are taken to be equal.     

Renormalization of an abelian gauge theory in stochastic quantization

The renormalization of an abelian gauge field coupled to a complex scalar field is disccused in the stochastic quantization method. The supper space formulation of the stochastic quantization method is used to derived the Ward Takahashi identities assocoated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahshi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constant in temrs of scaling of the fields and of the parameters appearing in the stochastic theory.     

Stability of hierarchical interfaces in a random field model

We study a hierarchical model for interfaces in a random-field ferromagnet. We prove that in dimensionD>3, at low temperatures and for weak disorder, such interfaces are rigid. Our proof uses renormalization group transformations for stochastic sequences.     

Stochastic quantization and the renormalization (to first order) of the n-field model

This article is concerned with a recently developed new approach to quantum field theory, the method of stochastic quantization. This method is based on the use of the Langevin equation, which describes the non-equilibrium dynamics of a system, for the quantization of a theory [1], In this paper it is shown how the renormalization of the coupling constant for the n-field model arises in stochastic quantization. It is also shown that the renormalization does not depend on the parametrization of the n-field (to first order in the coupling constant). The Gell-Mann-Low function is obtained to first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–6, January, 1985.In conclusion the author is grateful to A. A. Migdal for supervising this work and to M. A. Bershadskii for useful discussions.     

Stochastic treatment of the quantum-mechanical harmonic oscillator: Mass renormalization and lamb shift

By studying an oscillator coupled to the fluctuating radiation field, we obtain convergent results for the Lamb shift and for the mass renormalization even before introducing any cut-off. Once in stochastic equilibrium with the field, the oscillator obeys Schrödinger's equation.     

Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator

A method is put forward to improve the ε expansion in the theory of developed d-dimensional turbulence on the basis of the renormalization of random forcing in the stochastic Navier-Stokes equation. This renormalization takes into account additional divergences, which appear as d →2. In the nth order of the perturbation theory with the extended renormalization the first n terms of the usual ε expansion are correctly reproduced as well as the first n terms of the Laurent expansion in the parameter d-2 of the terms of the rest of the usual ε expansion. The Kolmogorov constant and skewness factor calculated in the one-loop approximation of the improved perturbation theory are in reasonable agreement with their recommended experimental values.     

Background field method for nonlinear σ-model in stochastic quantization

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model.     

Renormalization of Yang-Mills superfields in noncovariant supergauges

As a sequel to previous work of the authors in which general homogeneous non-supersymmetric choices ofN=1 supergauges were considered, we now proceed to the renormalization programme, remaining consistently within the superfield formalism. The possibility of a renormalization of the supersymmetric BRS-transformation is discussed.     

A renormalization approach to the band structure of superlattices

A k-space renormalization technique for evaluating the band structure of superlattices is examined. The large number of degrees of freedom of a superlattice tight-binding Hamiltonian is first reduced by exploiting the translational symmetry properties in layers perpendicular and parallel to the superlattice axis. The remaining degrees of freedom of the unit supercell are then systematically eliminated by renormalization techniques. Our combination of projective techniques on the one hand and full exploitation of symmetry properties on the other result in a very flexible and efficient algorithm. Some results for a simplified single-site model superlattice are presented as an example of our novel procedure.     

Sine-Gordon Model: Renormalization Group Solution and Applications

The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the g-ology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach.     

RI′/SMOM scheme amplitudes for quark currents at two loops

We determine the two loop corrections to the Green’s function of a quark current inserted in a quark 2-point function at the symmetric subtraction point. The amplitudes for the scalar, vector and tensor currents are presented in both the [`(MS)]\overline {\mathrm {MS}} and RI′/SMOM renormalization schemes. The RI′/SMOM scheme two loop renormalization for the scalar and tensor cases agree with previous work. The vector current renormalization requires special treatment as it must be consistent with the Slavnov–Taylor identity which we demonstrate. We also discuss the possibility of an alternative definition of the RI′/SMOM scheme in the case of the tensor current.     

Quantum field-theory models on fractal spacetime

Continuing the analysis of a previous paper, the present work applies rigorous renormalization group methods to the hierarchical models to establish the existence of field theories with non-Gaussian ultraviolet renormalization group fixed points in 4- dimensions.     

Static Approach to Renormalization Group Analysis of Stochastic Models with Spatially Quenched Noise

Journal of Statistical Physics - A new “static” renormalization group approach to stochastic models of fluctuating surfaces with spatially quenched noise is proposed in which only...     

无碰撞等离子体的相干重整化理论

本文提出对Власов-Poisson方程进行微扰处理的一种重整化方案。利用图形展开方法证明了该理论到任意阶微扰的可重整化性质。给出了重整化传播量的一般形式。分析了相干项和绝对非相干项的物理意义。给出了重整化介电函数的正确表示,并对它的意义做了讨论。通过和以往重整化理论的比较,指出这种重整化方案是一种真正的完全重整化。 关键词：     

Modified action glueballs

The mass of the 0⁺ glueball in 4-dimensional lattice gauge theory with a mixed SU(2)-SO(3) action is obtained via Monte Carlo. We work in a region far from the critical end point in the phase diagram, with an action partly motivated by renormalization group flows in the Migdal-Kadanoff approximation. A large-N resummation of perturbation theory is used to show that the mass gap scales as predicted by the perturbative renormalization group. Independent of this, our results show that the ratio of the glueball mass to the square root of the string tension, obtained from a previous Monte Carlo, is a renormalization group invariant.     

Time transformation for random walks in the quenched trap model

We investigate subdiffusion in the quenched trap model by mapping the problem onto a new stochastic process: Brownian motion stopped at the operational time S(α) = ∑(x=-∞)(∞) (n(x))(α) where n(x) is the visitation number at site x and α is a measure of the disorder. In the limit of zero temperature we recover the renormalization group solution found by Monthus. Our approach is an alternative to the renormalization group and is capable of dealing with any disorder strength.     

Momentum space renormalization for the sine-Gordon model

A momentum space renormalization is presented for the sine-Gordon model with an arbitrary cut-off function. In contrast to previous work the present method reproduces the slope of the critical line as found from the Kosterlitz renormalization of the equivalent Coulomb gas and is also applicable to the case of a sharp cut-off function.     

Nonlinear dynamics of smectics-C

An effective action which makes it possible to take into account dynamic fluctuation effects in smectics-C is constructed. The effects associated with displacements of smectic layers are the most important. The influence of these fluctuations on the dynamics of the director is studied. The corresponding terms in the effective action are constructed and their renormalization is found. The renormalization spectrum of the director mode is obtained.     

Dilatation invariance and spontaneous symmetry breakdown in dimensional renormalization

This paper completes a systematic study of the renormalization of scale invariant models with spontaneous symmetry breakdown discussing an effective scheme for the construction of Feynman amplitudes. From a general point of view the original scale invariance of the models is accounted for by constraining the dilation anomalies with a minimality criterion analyzed in a previous paper. This criterion is basd on a local Ward identity where the anomalies appear oupled to a spurion field. Here the general framework is adapted to a dimensional renormalization scheme and it is shown to be equivalent to a scale invariant choice of all counterterms and as it happens in minimal schemes, to the mass independence of the renormalization constants, thereby allowing a derivation of a renormalization group equation with standard (mass independent) coefficients. The whole analysis refers as an example to the simplest bosonic model containing all the features common to scale invariant theories with spontaneous symmetry breakdown.     

QCD One-Loop Effective Coupling Constant and Quark Mass Given in a Mass-Dependent Renormalization

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.