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Classification of gauge orbit types for SU(n) gauge theories (in preparation
"... A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SUn in spacetime dimension d ≤ 4 is presented. The method is based on the 1:1correspondence between orbit types and holonomyinduced Howe subb ..."
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A method for determining the orbit types of the action of the group of gauge transformations on the space of connections for gauge theories with gauge group SUn in spacetime dimension d ≤ 4 is presented. The method is based on the 1:1correspondence between orbit types and holonomyinduced Howe subbundles of the underlying principal SUnbundle. It is shown that the orbit types are labelled by certain cohomology elements of spacetime satisfying two relations. Thus, for every principal SUnbundle the corresponding stratification of the gauge orbit space can be determined explicitly. As an application, a criterion characterizing kinematical nodes for physical states in 2 + 1dimensional ChernSimons theory proposed by
Deceased
, 2007
"... Abstract. We give explicit formulas for conformally invariant operators with leading term an mth power of Laplacian on the product of spheres with the natural pseudoRiemannian product metric for all m. Key words: conformally invariant operators; pseudoRiemannian product of shperes; Fefferman–Grah ..."
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Abstract. We give explicit formulas for conformally invariant operators with leading term an mth power of Laplacian on the product of spheres with the natural pseudoRiemannian product metric for all m. Key words: conformally invariant operators; pseudoRiemannian product of shperes; Fefferman–Graham ambient space; intertwining operator of the conformal group O(p + 1, q + 1) 2000 Mathematics Subject Classification: 53A30; 53C50 1
Translation to Bundle Operators
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2007
"... We give explicit formulas for conformally invariant operators with leading term an mth power of Laplacian on the product of spheres with the natural pseudoRiemannian product metric for all m. ..."
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We give explicit formulas for conformally invariant operators with leading term an mth power of Laplacian on the product of spheres with the natural pseudoRiemannian product metric for all m.
THE INITIAL VALUE PROBLEM FOR WEAKLY NONLINEAR PDE
"... Abstract. We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem. Our generalization of their algorithm can be used to solve initial value problems for a wide class of evolution equatio ..."
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Abstract. We will discuss an extension of the pseudospectral method developed by Wineberg, McGrath, Gabl, and Scott for the numerical integration of the KdV initial value problem. Our generalization of their algorithm can be used to solve initial value problems for a wide class of evolution equations that are "weakly nonlinear" in a sense that we will make precise. This class includes in particular the other classical soliton equations (SGE and NLS). As well as being very simple to implement, this method exhibits remarkable speed and stability, making it ideal for use with visualization tools where it makes it possible to experiment in realtime with soliton interactions and to see how a general solution decomposes into solitons. We will analyze the structure of the algorithm, discuss some of the reasons behind its robust numerical behavior, and finally describe a fixed point theorem we have found that proves that the pseudospectral stepping algorithm converges.