SU(2)规范场的恰当形式(欧空间)

应用数学机械化方法研究欧氏空间中SU(2)规范场的正规化问题.首先对Yang-Mills方程的表述进行了讨论,给出了一种具有物理和几何意义的YM-方程,称其为恰当的(exact)YM-方程.对于这种恰当的YM-方程,构造了一类线性微分变换,称之为SU(2)规范场的示性变换.经由示性变换,将非线性的恰当的YM-方程变为一组Laplace方程,实现了SU(2)规范场方程的线性化,即场方程的正规化.从而证明了SU(2)规范场存在3个独立的Yang-Mills规范场.     

Social Motives and Expectations in One-Shot Asymmetric Prisoner's Dilemmas

We propose a formal-behavioral framework with 3 components: nonselfish motives, expectations about others' nonselfish motives, and a game-theoretic component. For nonselfish motives, 3 nonstandard utility models representing altruism, inequality aversion, and norms are considered. Expectations are modeled as certain versus uncertain expectations. The game-theoretic component predicts behavior of actors and actors' expectations about behaviors of others. This framework is applied to asymmetric one-shot prisoner's dilemmas; predictions are tested experimentally. Formal analyses show that asymmetry provides new predictions through which nonstandard utility-expectation models can be distinguished. Empirical tests show that the inequality aversion model does considerably worse than altruistic and normative variants. Statistical tests for own motives, expected motives, and the association between the two are provided, while accounting for decision noise.     

Vierdimensionale ℂ*·SU2ℂ-Ebenen

Examples of 4-dimensional topological affine planes with a 5-dimensional group of automorphisms containing C*·SU₂C are given. They are of Lenz-Barlotti class I.2.     

Non-discrete hybrids in SU(2, 1)

We show that a natural hybridation construction of lattices in SU(n, 1) to produce (non-arithmetic) lattices in SU(n + 1, 1) fails when n = 1 for most triangle groups in SU(1, 1).     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

Pseudodifferential Operators on SU(2)

We construct an algebra of left-invariant pseudodifferential operators on SU(2). We require only that the symbols be homogeneous and C ² . For Fourier-bandlimited symbols, we derive the expected formulae for composition and commutators and construct an orthonormal basis of common approximate eigenvectors that could be used to study spectral theory. Some remarks on applications to matrices of operators are made.     

Form-factors in the SU(2)-invariant Thirring model

In this paper we find explicit formulas for the matrix coefficient of the energy-momentum tensor and current operators in the SU(2)-invariant Thirring model. We show that the operators defined by these matrix coefficients commute on a space-like interval. For current operators we calculate the singularities of commutators at the origin.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 80–120, 1987     

Preconditioning of One-Shot Pseudo-Timestepping Methods for Shape Optimization

One-shot pseudo-timestepping [1, 2] has proven to be a powerful approach for the solution of optimal design problems in engineering applications. It blends well in within pre-existing pseudo-timestepping simulation solvers. The goal of this approach is to transform the equations for the necessary optimality conditions of the optimal design problem into an ordinary differential equation (ODE) and then solve the pseudo-time embedded state, co-state and design equations all at once. Similar approaches have been considered in [4, 5]. An application of this method to a real-world example within the MEGADESIGN-Project has been presented in [3]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Faddeev-Popov Determinant for the SU(2) Yang-Mills Field in Partially Dual Variables

In the present paper, the Faddeev-Popov determinant arising in the partially-dual decomposition of the SU(2) Yang-Mills field is studied. Bibliography: 4 titles.     

HORMANDER MULTIPLIER THEOREM ON SU(2)

ＨＲＡＮＤＥＲＭＵＬＴＩＰＬＩＥＲＴＨＥＯＲＥＭＯＮＳＵ（２）￥ＦＡＮＤＡＳＨＡＮ；ＸＵＺＥＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｕｈｕｉＵｎｉｖｅｒｓｉｔｙｔＨｅｆｅｉ２３００３９，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ａｂｏｕｎｄ...     

On Cocycles with Values in the Group SU(2)

 In this paper we introduce the notion of degree for C ¹-cocycles over irrational rotations on the circle with values in the group SU(2). It is shown that if a C ¹-cocycle over an irrational rotation by α has nonzero degree, then the skew product

The $${\textit{SU}}(2)$$-character variety of the closed surface of genus 2

We study the symplectic geometry of the \({\text {SU}}(2)\)-representation variety of the compact oriented surface of genus 2. We use the Goldman flows to identify subsets of the moduli space with corresponding subsets of \({\mathbb {P}}^3(\mathbb {C})\). We also define and study two antisymplectic involutions on the moduli space and their fixed point sets.     

Spectra of elements in the group ring of SU(2)

We present a new method for establishing the “gap” property for finitely generated subgroups of SU(2), providing an elementary solution of Ruziewicz problem on S² as well as giving many new examples of finitely generated subgroups of SU(2) with an explicit gap. The distribution of the eigenvalues of the elements of the group ring R[SU(2)] in the N-th irreducible representation of SU(2) is also studied. Numerical experiments indicate that for a generic (in measure) element of R[SU(2)], the “unfolded” consecutive spacings distribution approaches the GOE spacing law of random matrix theory (for N even) and the GSE spacing law (for N odd) as N→∞; we establish several results in this direction. For certain special “arithmetic” (or Ramanujan) elements of R[SU(2)] the experiments indicate that the unfolded consecutive spacing distribution follows Poisson statistics; we provide a sharp estimate in that direction. Received June 1, 1998 / final version received September 8, 1998     

R-Matrices for SU(2)-Invariant Two-Leg Spin Ladders

A list of R-matrices for the set of eight integrable spin ladders is presented. Four of these matrices are new. Bibliography: 13 titles.