Gribov ambiguity in gauge theories

Gribov ambiguity in gauge field theories is discussed and it is shown that such an ambiguity exists even for Abelian theories in covariant gauge at finite temperature. Both geometric and algebraic proofs are presented. In view of the importance of non-perturbative methods, some special gauges are given in which such ambiguities do not exist or are not relevant. The significance of these in the study of confinement in QCD is pointed out.     

On the Consistency of Constraints in Matter Field Theories

We consider how the principles of causality and equivalence restrict the background in which matter field theories are defined; those constraints develop in restrictions for these matter field theories: the simplest matter field theory aside, all other less simple matter field theories are too complex therefore resulting to be inconsistent in general instances.     

Homotopy algebra morphism and geometry of classical string field theories

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background, there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are A_∞-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in A_∞-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structures are governed by L_∞-algebras.     

Braiding matrices,modular transformations and topological field theories in 2+1 dimensions

Relations between 3D topological field theories and rational conformal field theories are discussed. In the former framework, we can define the generalized Verlinde operators. Using these operators, we find modular transformations for conformal blocks of one point functions and two point functions on the torus. The result is generalized to higher genus. The correctness of our formulae is illustrated by some examples. We also emphasize the importance of the fusion algebra.Addresses after October 1, 1989: Institute of Theoretical Physics, Academia Sinica, Beijing, P. R. China     

含有高次微商的量子理论

这篇短文比较了两种含有高次微商的量子理论。一个是在某些情形下可用的,它将变数q表为许多适合二阶方程的Q的线性组合,而在量子化时,各个Q分别地被量子化。另一个是先将q的运动方程正则化,再引入量子条件。我们证明了两个理论,无论就各种量的对易关系而言,或就总哈密顿而言,是等效的。     

Asymptotic freedom: An approach to strong interactions

The discovery of asymptotic freedom has opened up the possibility of extracting new sorts of detailed, dynamical consequences from a strongly interacting quantum field theory. The necessary tools - perturbation theory, the renormalization group, gauge theories, and the operator product expansion - are not new. To anyone familiar with these field theoretic approaches to strong interactions, the novel feature is a simple fact: there is a unique class of theories in which “the origin is an ultraviolet fixed point”. But the consequences are so exciting that it seemed appropriate to review these ideas as they reflect on each other. Many important applications of the renormalization group and the operator product expansion to hadronic physics are omitted; the emphasis here is on recent work based on asymptotically free field theories. No doubt, there are some developments so recent that they are not treated in this article.The discussion of the basic results concerning short distance behavior is informal, but, hopefully, accurate and complete. The specific applications are treated in varying detail.     

Ultralocal spinor field models

Ultralocal spinor (fermion) field theories are distinguished by the independent temporal development of the field at each spacial point. For a wide class of models explicit operator constructions are given, in a positive definite Hilbert space, for the interacting field, the Hamiltonian, and several other operators. Not only do the fermion field operators fail to fulfill canonical anticommutation relations but associated ultralocal boson fields are required for their realization giving rise to both fermion and boson type excitations. Construction of the Hamiltonian from the field, as well as the transition from the interacting to the noninteracting theories entails various infinite renormalizations that are made explicit. The formulation and solution of these models is based solely on symmetry arguments and general principles, and makes no use whatsoever of cutoffs or perturbation theory.     

On modular invariant partition functions for tensor products of conformal field theories

We give two results concerning the construction of modular invariant partition functions for conformal field theories constructed by tensoring together other conformal field theories. First we show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individual conformal field theory factors have been classified. We illustrate the use of these constraints for theories of the type SU(2)_KASU(2)_KB, finding all consistent theories for K_A, K_B odd. Second we show how known diagonal modular invariants can be used to construct some inherently asymmetric ones where the holomorphic and antiholomorphic theories do not share the same chiral algebra. Some explicit examples are given.     

c-Theorem for disordered systems

We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.     

Finite Euler hierarchies and integrable universal equations

Recent work on Euler hierarchies of field theory Lagrangians iteratively constructed from their successive equations of motion is briefly reviewed. On the one hand, a certain triality structure is described, relating arbitrary field theories,classical topological field theories — whose classical solutions span topological classes of manifolds — and reparametrisation invariant theories — generalising ordinary string and membrane theories. On the other hand,finite Euler hierarchies are constructed for all three classes of theories. These hierarchies terminate withuniversal equations of motion, probably defining new integrable systems as they admit an infinity of Lagrangians. Speculations as to the possible relevance of these theories to quantum gravity are also suggested.Presented at the Colloquium on the Quantum Groups, Prague, 18–20 June 1992.The author would like to thank A. Morozov and especially D. B. Fairlie for a very enjoyable and stimulating collaboration, and the organisers of the Colloquium for their efficient organisation of a most pleasant and informative meeting. This work is supported through a Senior Research Assitant position funded by the S.E.R.C.     

Balanced Topological Field Theories

We describe a class of topological field theories called “balanced topological field theories”. These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces. We show that these theories are closely related to the geometry and equivariant cohomology of “iterated superspaces” that carry two differentials. We find the most general action for these theories, which turns out to define Morse theory on field space. We illustrate the constructions with numerous examples. Finally, we relate these theories to topological sigma-models twisted using an isometry of the target space. Received: 2 September 1996 / Accepted: 3 October 1996     

Heavy-particle-induced effective lagrangian in spontaneously broken theories (II). The abelian Higgs-Kibble model

In the context of the abelian Higgs-Kibble model with a charged fermion, we study in detail low-energy effective field theories of light particles when the heavy mass scales in the theory are generated by the Higgs-Kibble mechanism. Our analysis is based on the systematic use of factorization methods, and is valid to all orders in renormalized perturbation theory. Emphasis is given to finding the vestiges of the original (spontaneously broken) local gauge symmetry left in low-energy effective field theories, and general techniques are developed for that purpose. When only Fermi fields or / and physical Higgs fields correspond to light particles, low-energy effective field theories do not exhibit such signs. On the other hand, when physical gauge fields (together with other unphysical fields) correspond to light particles, the original local gauge symmetry restricts the resulting low-energy effective local action to a non-trivial form.     

Symmetries and couplings in heterotic superconformal field theories

We discuss the symmetries of the superpotential in comfactified heterotic superstring theories formed from the product of minimal N = 2 superconformal field theories. It is shown how these symmetries can ensure flatness of the potential involving the moduli, and we derive new results (going beyond those obtained by superconformal techniques alone) for the flatness of the potential involving other massless fields.     

Finite BRST transformation and constrained systems

We establish the connection between the generating functional for the first class theories and the generating functional for the second class theories using the finite field dependent BRST (FFBRST) transformation. We show this connection with the help of explicit calculations in two different models. The generating functional of the Proca model is obtained from the generating functional of the Stueckelberg theory for massive spin 1 vector field using FFBRST transformation. In the other example we relate the generating functionals for gauge invariant and gauge variant theories for a self-dual chiral boson.     

Comprehensive solution to the cosmological constant,zero-point energy,and quantum gravity problems

We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. In our approach quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization.     

场电子发射研究现状及理论概述

由于场发射研究日趋重要，文章就场发射理论的起源，研究现状进行了总结，介绍了电子在几种不同类型材料的场发射理论模型，并对理论本身存在的问题进行了述评，着重指出其理论缺陷的实质及完善的可能性。     

Holomorphic Chern-Simons-Witten theory: From 2D to 4D conformal field theories

It is well known that rational 2D conformal field theories are connected with Chern-Simons theories defined on 3D real manifolds. We consider holomorphic analogues of Chern-Simons theories defined on 3D complex manifolds (six real dimensions) and describe 4D conformal field theories connected with them. All these models are integrable. We describe analogues of the Virasoro and affine Lie algebras, the local action of which on fields of holomorphic analogues of Chern-Simons theories becomes non-local after pushing down to the action on fields of integrable 4D conformal field theories. Quantization of integrable 4D conformal field theories and relations to string theories are briefly discussed.     

赝火花放电产生的异常加速高能粒子

 在赝火花放电过程中观察到异常加速的高能粒子，利用分析磁铁证实了这一物理现象。对照超快激光打靶产生的数百MeV量级的脉冲离子束，以及类星体涡旋结构产生超高能准直宇宙射线等现象，作者提出用涡旋动力学产生的挠场轴向加速来解释这些发生在不同物质运动层次的异常加速现象。阐述了集体场或尾场加速理论在解释这种理论时的不足之处。