二维球面实现为空间形式中极小曲面的度量特征

利用高阶密切空间及其基本形式的工具给出了二维度量球面等距极小浸入到空间形式中的一个必要条件，从而给出中主要结果的另一个证明。     

Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Precanonical quantization of pure Yang-Mills fields, which is based on the covariant De Donder-Weyl (DW) Hamiltonian formulation, and its connection with the functional Schrödinger representation in the temporal gauge are discussed. The mass gap problem is related to the finite-dimensional spectral problem for a generalized Clifford-valued magnetic Schrödinger operator which represents the DW Hamiltonian operator.     

Differential geometrical structures related to forecasting error variance ratios

Differential geometrical structures (Riemannian metrics, pairs of dual affine connections, divergences and yokes) related to multi-step forecasting error variance ratios are introduced to a manifold of stochastic linear systems. They are generalized to nonstationary cases. The problem of approximating a given time series by a specific model is discussed. As examples, we use the established scheme to discuss the AR (1) approximations and the exponential smoothing of ARMA series for multi-step forecasting purpose. In the process, some interesting results about spectral density functions are derived and applied.     

Effective bandwidths at multi-class queues

Consider a queue which serves traffic from a number of distinct sources and which is required to deliver a performance guarantee, expressed in terms of the mean delay or the probability the delay exceeds a threshold. For various simple models we show that an effective bandwidth can be associated with each source, and that the queue can deliver its performance guarantee by limiting the sources served so that their effective bandwidths sum to less than the capacity of the queue.     

Moduli space of potentials in the Aharonov-Bohm effect

We present a simplified derivation of the fact that the set of gauge equivalence classes or moduli space of flat connections (potentials) in the abelian Aharonov-Bohm effect, is isomorphic to the circle. The length of this circle is the absolute value of the electric charge.     

A singularity removal theorem for Yang-Mills fields in higher dimensions

In four and higher dimensions, we show that any stationary admissible Yang-Mills field can be gauge transformed to a smooth field if the norm of the curvature is sufficiently small. There are three main ingredients. The first is Price's monotonicity formula, which allows us to assert that the curvature is small not only in the norm, but also in the Morrey norm . The second ingredient is a new inductive (averaged radial) gauge construction and truncation argument which allows us to approximate a singular gauge as a weak limit of smooth gauges with curvature small in the Morrey norm. The second ingredient is a variant of Uhlenbeck's lemma, allowing one to place a smooth connection into the Coulomb gauge whenever the Morrey norm of the curvature is small; This variant was also proved independently by Meyer and Rivière. It follows easily from this variant that a -connection can be placed in the Coulomb gauge if it can be approximated by smooth connections whose curvatures have small Morrey norm.

     

Two-Dimensional Helmholtz Spaces

We study two-dimensional manifolds whose infinitesimally small neighborhoods have the structures of Helmholtz planes. We deal with the main objects related to Helmholtz spaces: in particular, we determine the metric function f and introduce the concept of quasimetric connection and geodesic. For some Helmholtz spaces we prove the existence of isothermal coordinates.     

Fluctuations in SU(2) Yang-Mills theory

The nonlinear differential equation resulting from the use of the ’t Hooft-Corrigan-Fairlie-Wilczek ansatz in SU(2) Yang-Mills gauge theory is solved by the bilinear operator method. The solutions which are singular are interpreted as fluctuations involving no flux transport. However, these objects may play a tunnelling role similar to that of merons.     

On YM2 measures and area-preserving diffeomorphisms

For a given gauge group and compact Riemannian two-manifold, it is known that the associated Yang-Mills measure can be defined directly as a finitely additive measure on the space of connections, and this finitely additive measure is invariant with respect to SDiff, the group of all area-preserving diffeomorphisms of the surface. The first question we address is whether this symmetry essentially characterizes the projection of the Yang-Mills measure to the space of gauge equivalence classes. The proper formulation of this question entails the construction of an SDiff-equivariant equivariant completion of the space of continuous connections, such that the projection of the Yang-Mills measure to the space of gauge equivalence classes has a countably additive extension. We also consider the coupling of the Yang-Mills measure to determinants of Dirac operators. The basic problems are to prove that the coupled measure is absolutely continuous with respect to the background Yang-Mills measure, to find a reasonable formula for the Radon-Nikodym derivative, and to analyze the action of SDiff.     

Space of Hermitian Triples and Ashtekar–Isham Quantization

We generalize the Ashtekar–Isham construction for quantizing gauge fields to the case where the configuration variables belong to the space of Hermitian triples, not Hermitian connections.