相关论文: Picture changing operators in supergeometry and su…
We give a survey on projective ring lines and some of their substructures which in turn are more general than a projective line over a ring.
Induced supersymmetry representations on composite operators are studied. In superspace the ensuing transformation rules (trivially) lead to an effective superfield. On the other hand, an induced representation must exist for non-linear…
We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In…
In this short printed version of my talk I consider the generalized action for super-p-branes proposed previously in collaboration with D. Sorokin and Dmitrij V. Volkov. I describe briefly, the derivation doubly supersymmetric geometric…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
A superparticle action which is globally supersymmetric in the target space is proposed. The supersymmetry is the supersymmetric extension of the rotation group O(3).
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…
Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $ \delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot…
N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…
Complex geometry and supergeometry are closely entertwined in superstring perturbation theory, since perturbative superstring amplitudes are formulated in terms of supergeometry, and yet should reduce to integrals of holomorphic forms on…
In this talk, based on work done in collaboration with G. Landi and R.J Szabo, I will review how string theory can be considered as a noncommutative geometry based on an algebra of vertex operators. The spectral triple of strings is…
Inferring 3D structure of a generic object from a 2D image is a long-standing objective of computer vision. Conventional approaches either learn completely from CAD-generated synthetic data, which have difficulty in inference from real…
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
Unsupervised image-to-image translation consists of learning a pair of mappings between two domains without known pairwise correspondences between points. The current convention is to approach this task with cycle-consistent GANs: using a…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…
Supersymmetric quantum mechanics has many applications, and typically uses a raising and lowering operator formalism. For one dimensional problems, we show how such raising and lowering operators may be generalized to include an arbitrary…
We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.