Point-splitting analysis of commutator anomalies in non-abelian chiral gauge theories

A gauge covariant point-splitting regularisation is employed to calculate different anomalous commutators in four dimensional chiral gauge theories. For an external gauge field the fixed time anomalous commutator of the gauge group generators is seen to violate the Jacobi identity. The cohomological prediction can be confirmed provided the electric fields do not commute. Other commutators like the current-current and current-electric field are consistent with the Bjorken-Johnson-Low (BJL) derivation.     

Commutator of gauge generators in non-abelian chiral theory

Commutators among non-abelian fermion currents are calculated using the BJL limit. The relation between the covariant seagull and the gauge dependence of the fermion current is derived for a canonical non-abelian theory using the path integral formulation. We observe that in a non-abelian theory with coupling to chiral fermions this relation is violated and this produces a non-trivial commutator of gauge group generators.     

Non-cocyclic anomaly in the Gauss law commutator

The commutator of the Gauss law operator in chiral gauge theories with background gauge fields is calculated algebraically: the anomalous piece is not a cocycle.     

Berry's phase in chiral gauge theories

Berry's phase in chiral gauge theories is computed. The result implies that the anomalous commutator of gauge transformations is the one previously obtained by Faddeev.     

Lie differentiation of Cartan spinors in an affine-connected space—Time having well-type nonmetricity

It is shown that Lie differentiation that preserves the rank of a spinor and coincides with the commutator for a vector field exists only along the generators of the conformal-motion group in affine-connected space—time having nonmetricity of Weil type.Yakut State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 102–106, November, 1994.     

Commutator anomalies and the Fock bundle

We show that the anomalous finite gauge transformations can be realized as linear operators acting on sections of the bundle of fermionic Fock spaces parametrized by vector potentials, and more generally, by splittings of the fermionic one-particle space into a pair of complementary subspaces. On the Lie algebra level we show that the construction leads to the standard formula for the relevant commutator anomalies.     

Standard complex for quantum Lie algebras

For a quantum Lie algebra Γ, let Γ^ be its exterior extension (the algebra Γ^ is canonically defined). We introduce a differential on the exterior extension algebra Γ^ which provides the structure of a complex on Γ^. In the situation when Γ is a usual Lie algebra, this complex coincides with the “standard complex.” The differential is realized as a commutator with a (BRST) operator Q in a larger algebra Γ^[Ω], with extra generators canonically conjugated to the exterior generators of Γ^. A recurrent relation which uniquely defines the operator Q is given.     

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.     

Review of high energy heavy ion reactions in emulsion

Two dimensional anomalous non-Abelian gauge theories are studied following the recently-proposed scheme of quantization. The Gauss law operator (GLO) is modified by adding the Wess-Zumino action in the new scheme. By means of an explicit canonical operator construction, we confirm that this modified GLO is time independent and has no commutator anomalies in the two dimensionalSU (2) model. Argument for the general validity of this analysis is also presented.     

Lie Algebras and Superalgebras Defined by a Finite Number of Relations: Computer Analysis

Abstract

The presentation of Lie (super)algebras by a finite set of generators and defining relations is one of the most general mathematical and algorithmic schemes of their analysis. It is very important, for instance, for investigation of the particular Lie (super)algebras arising in different (super)symmetric physical models. Generally, one can put the following question: what is the most general Lie algebra or superalgebra satisfying to the given set of Lie polynomial equations? To solve this problem, one has to perform a large volume of algebraic transformations which sharply increases with growth of the number of generators and relations. By this reason, in practice, one needs to use a computer algebra tool. We describe here an algorithm and its implementation in C for constructing the bases of finitely presented Lie (super)algebras and their commutator tables.     

Anomalous commutators in two-dimensional chiral gauge theories

It is shown that in two-dimensional models of chiral fermions coupled with background gauge fields, anomalous commutators of currents as well as of generators of time-independent gauge transformations are completely determined by the anomaly if the gauge group is semisimple. The four-dimensional case is commented on.     

A causal approximation scheme for the commutator of the axial vector-currents

An approximation scheme which fulfils the causality condition is used to compute the matrix elements of the commutator of two axial-vector currents between one proton state. The commutator sum rule is supposed to be saturated by taking into account the nucleon, theN ^*(3/2, 3/2) resonance, and the partially disconnected pion-proton intermediate states. For the axial current form factors pion pole formulas are assumed. It is shown that only the subtraction constants are relevant for the equal time limit of the commutator and so the equivalence with similar earlier methods is proven.     

时间间断式通讯转接器的研制

时间间断式通讯转接器是为在强电磁干扰区进行正常通讯而设计,该通讯转接器的研制,使速调管走廊强电磁干扰区的通讯稳定可靠,从而消除由于外界干扰而造成的通讯错误.     

On the SU(3) Mass Formulae

It is found that in the SU(3) broken quark model the SU(3) generators and their time derivatives belong to the SU(3) × SU(3) algebra. Using this algebra and the infinite momentum method the SU(3) mass sum rules are obtained. The possibility is discussed that normal spin-parity nonets and anomalous ones differ in the structure of the mass spectrum.     

Gauge invariant formulation of non-Abelian chiral gauge theories in two dimensions

We study the gauge invariant version of a chiral non-Abelian gauge theory. A local bosonic effective action is obtained and the covariant conservation of the gauge current is verified. A Hamiltonian analysis of the model and of its constraints is performed. We show that the constraints are first class and that no anomalous term appears in the commutators of the gauge group generators. The current algebra of the model is obtained and the gauge fixing is analyzed.     

Deformations of the Classical W-Algebras Associated to Dn,E6, G2

We give explicit formulas for the generators of q-deformed W-algebras associated to Lie algebras D_n, E₆ and G₂, and compute the Poisson brackets between the generators.     

基于机器视觉的电机换向器质量在线检测系统开发

电机换向器质量检测是换向器生产线中的一个重要工序,但其仍采用人工方式,存在检测效率低、漏检率高等问题。针对此问题,本文运用图像处理和机器视觉技术,开发换向器质量在线视觉检测系统。该系统针对生产过程工艺多变,造成形状检测标准不一致问题,提出自适应学习模板方法;在轴孔孔径检测,提出基于Freeman链码改进的孔径快速检测算法;在端面缺陷中,提出基于改进视觉注意力模型的端面缺陷检测方法。实验结果表明,系统检测精度达到99.80%,漏检率为0%,F-measure值为99.89%。该系统能够快速有效检测换向器存在的外观质量问题,可满足换向器在线质量检测需求。     

Current algebra and Wess-Zumino model in two dimensions

We investigate quantum field theory in two dimensions invariant with respect to conformal (Virasoro) and non-abelian current (Kac-Moody) algebras. The Wess-Zumino model is related to the special case of the representations of these algebras, the conformal generators being quadratically expressed in terms of currents. The anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations. In particular, Witten's non-abelean bosonisation rules are proven.     

Geometry,commutation relations and the quantum fictitious force

We express the commutation relation between the operators of the momentum and the radial unit vectors in D dimensions in differential and integral form. We connect this commutator with the quantum fictitious potential emerging in the radial Schr?dinger equation of an s-wave. Received: 6 August 2002 / Revised version: 30 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-731/502-3086, E-mail: markus.cirone@physik.uni-ulm.de