共查询到20条相似文献,搜索用时 15 毫秒
1.
《Nuclear Physics B》1999,537(1-3):397-442
Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum Chromodynamics. We calculate these anomalies in the leading order of perturbation theory in the minimal subtraction scheme. From the conformal consistency relation we derive then the off-diagonal part of the anomalous dimension matrix of the conformally covariant operators in the two-loop approximation of the coupling constant in terms of these quantities. We deduce corresponding off-diagonal parts of the Efremov-Radyushkin-Brodsky-Lepage kernels responsible for the evolution of the exclusive distribution amplitudes and non-forward parton distributions in the next-to-leading order in the flavour singlet channel for the chiral-even parity-odd and -even sectors as well as for the chiral-odd one. We also give the analytical solution of the corresponding evolution equations exploiting the conformal partial wave expansion. 相似文献
2.
Hiroyuki Kawamura 《Zeitschrift fur Physik C Particles and Fields》1997,75(1):27-33
We analyze the twist-4 contributions to Bjorken and Ellis-Jaffe sum rules for spin-dependent structure function g 1(x, Q 2). We investigate the anomalous dimensions of the twist-4 operators which determine the logarithmic correction to the 1/Q 2 behavior of the twist-4 contribution by evaluating off-shell Green’s functions in both flavor non-singlet and singlet case. It is shown that the operators which are proportional to the equation of motion play an important role to extract the anomalous dimensions of physical operators. The calculations to solve the operator mixing of higher-twist operators are given in detail 相似文献
3.
A systematic treatment of multipole selection rules of non-rigid molecules is presented, based on the isomorphism of the isometric group to the symmetry group of the rotation-internal motion hamiltonian. A classification of isometric groups and relations among the representations of the isometric group on various substrates are discussed. A set of general transformation formulae for irreducible tensor operators of semi-rigid molecular models is derived. These formulae are used for the derivation of dipole and quadrupole selection rules of a considerable number of semi-rigid models. The relations among the representations of the isometric group give rise to some theorems which allow a compact presentation of selection rules of non-rigid molecules. 相似文献
4.
5.
S.É. Derkachov J.A. Gracey A.N. Manashov 《The European Physical Journal C - Particles and Fields》1998,2(3):569-579
We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in in theory as a function of the operator moment . These operators are similar to the twist-2 operators which arise in QCD in the operator product expansion in deep inelastic
scattering. By regarding their inverse Mellin transform as being equivalent to the DGLAP splitting functions we explore to
what extent taking a restricted set of operator moments can give a good approximation to the exact four loop result.
Received: 12 May 1997 / Published online: 20 February 1998 相似文献
6.
A. V. Kotikov 《Physics of Atomic Nuclei》2011,74(6):936-943
We present results for the universal anomalous dimension γ
uni(j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory in the first four orders of perturbation theory. These expressions are obtained by extracting
the most complicated contributions from the corresponding anomalous dimensions in QCD. 相似文献
7.
A. V. Kotikov 《Physics of Particles and Nuclei》2010,41(6):951-953
We show results for the universal anomalous dimension γuni(j) of Wilson twist-2 operators in the $
\mathcal{N}
$
\mathcal{N}
= 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by
extracting the most complicated contributions from the corresponding anomalous dimensions in QCD. 相似文献
8.
Jan M. Pawlowski 《Annals of Physics》2007,322(12):2831-2915
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation. 相似文献
9.
Th. Braunschweig J. Hořcjší D. Robaschik 《Zeitschrift fur Physik C Particles and Fields》1984,23(1):19-29
Light-cone dominated scattering processes are studied within the framework of the nonlocal operator product expansion. An integral representation for the Fourier transform of matrix elements of the renormalized product of two currents in the Bjorken region of the momentum space is derived and shown to be convergent everywhere. Renormalization group equations (RGE) for the coefficient functions pertinent to the forward scattering are discussed. It is demonstrated how the evolution equation for the forward amplitude and/or its absorptive part immediately follow (in theleading order) from such RGE. Anomalous dimensions of all relevant nonlocal operators in QCD are calculated in the one-loop approximation and shown to be simply related to the Altarelli-Parisi probability functions. 相似文献
10.
G. Parisi 《Nuclear Physics B》1973,58(2):641-646
We show that the anomalous dimension of the fundamental field is connected to the anomalous dimensions of the high spin bilinear operators. The dimensions of these operators can be determined by examining the violations of the Bjorken scaling law in deep-inelastic electron-proton scattering. The structure function at field ω near to one has a power dependence of q2, the exponent being the anomalous dimension of the “parton” field. 相似文献
11.
This paper presents the second part of our study devoted to the construction of Baxter operators for the homogeneous closed XXX spin chain with the quantum space carrying infinite or finite-dimensional s?2 representations. We consider the Baxter operators used in Bazhanov et al. (1996, 1997, 1999, 2010) [1] and [2], formulate their construction uniformly with the construction of our previous paper. The building blocks of all global chain operators are derived from the general Yang-Baxter operators and all operator relations are derived from general Yang-Baxter relations. This leads naturally to the comparison of both constructions and allows to connect closely the treatment of the cases of infinite-dimensional representation of generic spin and finite-dimensional representations of integer or half-integer spin. We prove not only the relations between the operators but present also their explicit forms and expressions for their action on polynomials representing the quantum states. 相似文献
12.
When rearrangement reactions are too strong to be treated by a one-step DWBA, they must be described by coupled reaction channel (CRC) equations or by a multistep DWBA derived from them. The derivation of these equations requires the use of projection operators on subspaces which are in general not orthogonal and which may be linearly dependent. We consider the case of many coupled two-cluster channels, and show how solving the non-orthogonality kernel to give an orthogonalized CRC formally simplifies the structure of the equation and clarifies the relations between different methods, including connected kernel approaches. We use the requirement that the distorted Faddeev (N = 3) or LBRS equations (general N) be satisfied in the two-cluster model space. We demonstrate that this determines the distortion potentials and that the resulting pole approximation yields the orthogonalized CRC equations. A modified one- and two-step DWBA is written in which non-orthogonality corrections are summed to all orders in each step. Methods of generating the non-orthogonality correction operator are discussed. 相似文献
13.
L. Mankiewicz G. Piller T. Weigl 《The European Physical Journal C - Particles and Fields》1998,5(1):119-128
We present an analysis of twist-2, leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of
double/nonforward parton distribution functions. After reviewing some general features of nonforward nucleon matrix elements
of twist-2 QCD string operators, we propose a phenomenological model for quark and gluon nonforward distribution functions.
The corresponding QCD evolution equations are solved in the leading logarithmic approximation for flavor nonsinglet distributions.
We derive explicit expressions for hard exclusive , , and neutral vector meson production amplitudes and discuss general features of the corresponding cross sections.
Received: 12 November 1997 / Published online: 26 February 1998 相似文献
14.
Symplectic and optical joint probability representations of quantum mechanics are considered, in which the functions describing the states are the probability distributions with all random arguments (except the argument of time). The general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations is given. Taking the Gaussian functions as the distributions of the tomographic parameters the correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators in the form of singular and regular generalized functions are derived. Evolution equations and stationary states equations for symplectic and optical joint probability distributions are obtained. 相似文献
15.
《中国科学:物理学 力学 天文学(英文版)》2020,(7)
Form factors are quantities that involve both asymptotic on-shell states and gauge invariant operators. They provide a natural bridge between on-shell amplitudes and off-shell correlation functions of operators, thus allowing us to use modern on-shell amplitude techniques to probe into the off-shell side of quantum field theory. In particular, form factors have been successfully used in computing the cusp(soft) anomalous dimensions and anomalous dimensions of general local operators. This review is intended to provide a pedagogical introduction to some of these developments. We will first review some amplitudes background using four-point amplitudes as main examples. Then we generalize these techniques to form factors, including(1) tree-level form factors,(2) Sudakov form factor and infrared singularities, and(3) form factors of general operators and their anomalous dimensions. Although most examples we consider are inN= 4 super-Yang-Mill theory, the on-shell methods are universal and are expected to be applicable to general gauge theories. 相似文献
16.
Hong-Yi FAN 《理论物理通讯》1992,17(3):355-360
Two types of canonical transformations in two-mode classical phase space are mapped into the quantum mechanical Hilbert space to produce some new normally ordered unitary operators. These operators are evaluated in the coordinate (momentum) representations using the "integration within ordered product technique, and the mapping is maniferrtly apparent in the derivation. New generalixed coherent states are constructed in terms of these operators, and the uncertainty relations for these states are analysed. 相似文献
17.
18.
V. N. Velizhanin 《JETP Letters》2009,89(12):593-596
The result of the direct component calculation of the nonplanar contribution to the four-loop anomalous dimension of the Konishi operator in the \(\mathcal{N}\) = 4 supersymmetric Yang-Mills theory is reported. The result contains only the ζ(5) term proportional to the ζ(5) contribution in the planar case, which comes only from wrapping corrections. The previous calculations of the leading transcendent contribution to the anomalous dimension of the twist-2 operators for first three even moments are also expanded to the nonplanar case and the same results as in the planar case are obtained up to a general factor. These two results imply that the nonplanar contribution of the four-loop universal anomalous dimension of the twist-2 Wilson operators with an arbitrary Lorentz spin j is proportional to S 1 2 (j)ζ(5). This result provides a nonstandard square logarithmic asymptotic behavior ln2 j for large Lorentz spins j of the operators. 相似文献
19.
20.
S. Sarkar 《Nuclear Physics B》1974,82(3):447-460
The tree-loop theorem of 't Hooft and Veltman is used in Fermi type gauges to show that gauge invariant operators in Wilson expansions mix in general with non-gauge invariant operators. Background field gauges are proposed in which this does not occur. Calculations of anomalous dimensions in these gauges are discussed. 相似文献