A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

Homology and abelian lattice gauge theories

A simple Abelian model with both Higgs and gauge field degrees of freedom is investigated on a simplicial lattice of arbitrary dimension. We use group character expansion for both fields to get a diagrammatic expansion of the partition function. The diagrams consist of gauge group representation valued 1- and 2-chains. The diagrams are proved to satisfy the constraint that the boundary of the 2-chain representing the gauge field is equal to the 1-chain representing the Higgs field. Otherwise they identically vanish. Simple consequences of this are current conservation and the vanishing of non-null-homologous Wilson loops. Finally we use this picture for giving a lowest order estimate for the critical length of a string. This is the length at which the flux-tube string connecting two opposite charges is likely to break into two pieces due to pair creation.     

Gauge supersymmetric Ising model on a cubic lattice near the critical point in the free field representation

The nature of the set of free fields that represent the system at the critical point has been revealed by studying the correlation functions of the degrees of freedom of the gauge supersymmetric Ising model on the cubic lattice. The same set of free fields represents the continuous supersymmetric Abelian gauge theory. Thus, the name of the lattice system is appropriate. Comparison with the two-dimensional Ising model is given.     

Fields with vanishing colour-currents

We consider spinor, scalar and vector fields with colour degrees of freedom and find the classical solutions when the constraint of vanishing colour currents is imposed. We find that there are no non-trivialc-number solutions for spinor fields transforming as a triplet under SU(3), although solutions exist for scalar and vector fields. We also show that the colour current of spinor fields coupled to an instanton is zero.     

Hamiltonian systems on fibered manifolds

We offer a new geometric theory of Hamiltonian systems with an infinite number of degrees of freedom in which the Hamiltonian operators are nonlinear differential operators on fields. The Poisson bracket is carried into the vertical bracket by the mapping between functionals and Hamitonian operators which is established by a Hamiltonian structure.     

Dual Meissner effect and magnetic displacement currents

The dual Meissner effect is observed without monopoles in quenched SU(2) QCD with Landau gauge fixing. Magnetic displacement currents that are time-dependent Abelian magnetic fields act as solenoidal currents squeezing Abelian electric fields. Monopoles are not always necessary for the dual Meissner effect. A mean-field calculation suggests that the dual Meissner effect through the mass generation of the Abelian electric field is related to a gluon condensate A(a)(mu)A(a)(mu) not equal 0 of mass dimension 2.     

Probability measures on distribution spaces and quantum field theoretical models

It is well known that there is a close connection between (Abelian) fields and probability measures on distribution space, or more generally, on infinite-dimensional vector spaces, and their associated random processes. We establish general criteria for mutual singularity of such measures and apply them to quantum fields. In particular, it is shown that a kind of generalized clustering implies singularity. Then a condition for singularity is given in terms of a natural metric introduced previously. It is used to show that the translate of a measure by a linear functional which is not continuous for this metric is singular to the untranslated measure. The results are applied to processes with independent values at each point, corresponding to the ultra-local model. It is shown that each such measuris singular to any of its translates although its finite-dimensional projections may be equivalent to Lebesgue measure.     

Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates

We propose that the dissipative dynamics of topological defects in a spiral state is responsible for the transport properties in the spin-glass phase of cuprates. Using the collective-coordinate method, we show that topological defects are coupled to a bath of magnetic excitations. By integrating out the bath degrees of freedom, we find that the dynamical properties of the topological defects are dissipative. The calculated damping matrix is related to the in-plane resistivity, which exhibits an anisotropy and linear temperature dependence in agreement with experimental data.     

Abelian and non-Abelian anomalies in monopole-fermion interactions

Taking an example of the standard SU(5) theory, the monopole-fermion system is reduced to an effective 2-dimensional model. This is a generalized Schwinger model containing four Abelian gauge fields interacting with N generations of massless fermions through vector and axialvector couplings. We quantize such a system exactly in the canonical operator formalism. Then, analyzing the cluster property of operators carrying various chiral charges, the roles of the Abelian and non-Abelian anomalies are studied in monopole-induced baryon decay. We demonstrate that the Abelian anomaly and the charge-mixing boundary condition are the driving forces for monopole-induced baryon decay, though the conservation law suggests the importance of the non-Abelian anomaly.     

高阶微商规范不变系统的整体对称性和量子守恒律

分别从Faddeev–Popov(FP)和Faddeev–Senjanovic(FS)路径积分量子化方法对高阶微商规范不变系统导致的位形空间和相空间生成泛函出发,导出规范系统在量子水平下的守恒律,用于高阶Maxwell非AbelChern–Simons(CS)理论.得到了高阶Maxwell非AbelCS理论与标量场耦合系统的量子BRS守恒荷和量子守恒角动量,无论从位形空间或相空间的生成泛函出发,其结果是相同的.并对CS理论中的分数自旋性质给予了讨论.     

On the theory of recursion operator

The general structure and properties of recursion operators for Hamiltonian systems with a finite number and with a continuum of degrees of freedom are considered. Weak and strong recursion operators are introduced. The conditions which determine weak and strong recursion operators are found.In the theory of nonlinear waves a method for the calculation of the recursion operator, which is based on the use of expansion into a power series over the fields and the momentum representation, is proposed. Within the framework of this method a recursion operator is easily calculated via the Hamiltonian of a given equation. It is shown that only the one-dimensional nonlinear evolution equations can posses a regular recursion operator. In particular, the Kadomtsev-Petviashvili equation has no regular recursion operator.     

The Relation Between Gauge and Non-Gauge Abelian Models

This work studies the relationship between gauge-invariant and non gauge-invariant Abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the chiral Schwinger models may both be viewed as gauge-fixed versions of genuinely gauge-invariant models. This leads to the proposal that any consistent Abelian vector model with no gauge symmetry can be understood as a gauge theory that had its gauge fixed, which establishes an equivalence between gauge-invariant and non gauge-invariant models. Finally, we show that a gauge-invariant version of the chiral Schwinger model, after integrating out the fermionic degrees of freedom, can be identified with the two-dimensional Stueckelberg model without the gauge-fixing term.     

Charge screening in a two potential theory of electromagnetism

By surrounding an Abelian Dyon with an axion-like domain wall we calculate the screening effects generated by the domain wall on the dyon degrees of freedom.     

Magnetic field induced ordering in quasi-one-dimensional quantum magnets

Three-dimensional magnetic ordering transitions are studied theoretically in strongly anisotropic quantum magnets. An external magnetic field can drive quasi-one-dimensional subsystems with a spin gap into a gapless regime, thus inducing long-range three-dimensional magnetic ordering due to weak residual magnetic coupling between the subsystems. Compounds with higher spin degrees of freedom, such as N-leg spin-1/2 ladders, are shown to have cascades of ordering transitions. At high magnetic fields, zero-point fluctuations within the quasi-1D subsystems are suppressed, causing quantum corrections to the ordering temperature to be reduced. Received 24 March 2000     

Fields over unsharp coordinates

It has been shown that space-time coordinates can exhibit only very few types of short-distance structures, if described by linear operators: they can be continuous, discrete, or "unsharp" in one of two ways. In the literature, various quantum gravity models of space-time at short distances point towards one of these two types of unsharpness. Here, we investigate the properties of fields over such unsharp coordinates. We find that these fields are continuous--but possess only a finite density of degrees of freedom, similar to fields on lattices. As a special case we recover the Shannon sampling theorem of information theory.     

Edge states for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of Abelian and non-Abelian background magnetic fields. Carrying out an analysis similar to what was done for Abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess–Zumino–Witten (WZW) theory generalized to higher dimensions.