超空间上高阶Teodorescu算子

本文首先由超空间上Cauchy-Pompeiu公式定义了超空间上高阶Teodorescu算子,研究了此类算子的一些基本性质.其次,利用此类算子,我们得到了$k$-超正则函数的Almansi型展开. 最后运用这个展开,我们证明了$k$-超正则函数的Morera型定理、开拓定理和唯一性定理.     

Chern-simons theory in the SO(5)/U(2) harmonic superspace

We consider the superspace of D=3, N=5 supersymmetry using SO(5)/U(2) harmonic coordinates. Three analytic N=5 gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates. Decomposing these superfields in Grassmann and harmonic coordinates yields infinite-dimensional supermultiplets including a three-dimensional gauge Chern-Simons field and auxiliary bosonic and fermionic fields carrying SO(5) vector indices. The superfield action of this theory is invariant with respect to the D=3, N=6 conformal supersymmetry realized on N=5 superfields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 2, pp. 217–234, November, 2008.     

Four‐Dimensional Space Groups for Pedestrians: Composite Structures

Higher‐dimensional crystals have been studied for the last thirty years. However, most practicing chemists, materials scientists, and crystallographers continue to eschew the use of higher‐dimensional crystallography in their work. Yet it has become increasingly clear in recent years that the number of higher‐dimensional systems continues to grow from hundreds to as many as a thousand different compounds. Part of the problem has to do with the somewhat opaque language that has developed over the past decades to describe higher‐dimensional systems. This language, while well‐suited to the specialist, is too sophisticated for the neophyte wishing to enter the field, and as such can be an impediment. This Focus Review hopes to address this issue. The goal of this article is to show the regular chemist or materials scientist that knowledge of regular 3D crystallography is all that is really necessary to understand 4D crystal systems. To this end, we have couched higher‐dimensional composite structures in the language of ordinary 3D crystals. In particular, we developed the principle of complementarity, which allows one to identify correctly 4D space groups solely from examination of the two 3D components that make up a typical 4D composite structure.     

A superspace path integral proof of the Gauss-Bonnet-Chern theorem

A rigorous theory of integration in the space of paths in super space is developed, by extending Berezin's method of integration to spaces of anticommuting variables with an uncountably high dimension. A Feynmam-Kac-Ito formula for the heat kernel of a wide class of superspace differential operators is established. This formula is then used to make rigorous the supersummetric proofs of the Gauss-Bonnet-Chern theorem [1, 2].     

Deformations of Euclidean supersymmetries

We consider quantum supergroups that arise in nonanticommutative deformations of the N=(1/2, 1/2) and N=(1, 1) four-dimensional Euclidean supersymmetric theories. Twist operators in the corresponding superspaces and deformed superfield algebras contain left spinor generators. We show that nonanticommutative *-products of superfields transform covariantly under the deformed supersymmetries. This covariance guarantees the invariance of the deformed superfield actions of models involving *-products of superfields. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 270–289, May, 2006.     

Trefoil Symmetry IV: Basic Enhanced Superspace for the Minimal Vector Clover Extension

We construct a differential representation and covariant derivatives of the minimal vector clover extension of the Poincaré algebra. In analogous way as in the supersymmetric case, there arises an enhanced superspace which allows to define superfields. The action of group transformations on such superfields determines a representation out of which the covariant derivatives are obtained.     

M-Theory in the Gaugeon Formalism

In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory in N = 1 superspace formalism.We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism.We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the S-matrix.     

Singlet Deformation of <Emphasis Type="Italic">N</Emphasis> = (1,1) Superspace

We discuss the SO(4) × SU(2) invariant deformation of the Euclidean N = (1,1) supersymmetric theories in the framework of the harmonic superspace.     

A Geometrical Interpretation of Grassmannian Coordinates

A geometrical interpretation of Grassmannian anticommuting coordinates is given. They are taken to represent an indefiniteness inherent in every spacetime point on the level of the spacetime foam. This indeterminacy is connected with the fact that in quantum gravity in some approximation we do not know the following information: are two points connected by a quantum wormhole or not? It is shown that: (a) such indefiniteness can be represented by Grassmannian numbers, (b) a displacement of the wormhole mouth is connected with a change of the Grassmannian numbers (coordinates). In such an interpretation of supersymmetry the corresponding supersymmetrical fields must be described in an invariant manner on the background of the spacetimefoam.