Extended Supersymmetry in One-dimensional Models

基于超场方法，包括谐波超空间方法，我们将在经典和量子水平上，为单粒子和多粒子情况构建新的超对称力学模型。对于它们的超场构造，我们将利用各种类型的N=2，N=4和N=8超多重态，包括半动态自旋多重态，非线性多重态和镜像多重态。我们计划对其中的一些模型进行建模并研究它们的量子谱，具体来说，我们将考虑以下主要任务：-建立由两个或多个不同的多重态组成的变形N=8超对称力学模型，并探究随之而来的目标空间几何。考察这些模型是否存在超共形对称和SU（4）超群的隐世界线实现|2）、- 构造和量子化具有U（n）规范对称性的大质量超场矩阵模型;-构造和研究新的相互作用的动力学和半动力学非线性N=4超多重态;-利用超场规范化方法和半动力学多重态，构造三角和椭圆Calogero模型的N=4超扩展，以及它们由扰动型势引起的变形。推广到N=8，d=1超对称的情况。研究将在参与该项目的俄罗斯和德国科学家之间的密切合作下进行。

Based upon superfield methods, including harmonic superspace ones, we will construct new models of supersymmetric mechanics, at the classical and the quantum level, for both one-particle and many-particle cases. For their superfield construction, we will exploit various types of N=2, N=4 and N=8 supermultiplets, including semi-dynamical spinning multiplets, nonlinear multiplets, and mirror multiplets. We plan to quantize some of the constructed models and study their quantum spectra.In particular, we will consider the following main tasks: - Setting up models of deformed N=8 supersymmetric mechanics composed out of two or more different multiplets, with inquiring the ensuing target-space geometry. Inspecting these models on the presence of superconformal symmetries and hidden worldline realizations of the supergroup SU(4|2);- Constructing and quantizing massive superfield matrix models with U(n) gauge symmetry;- Constructing and studying new interacting dynamical and semi-dynamical nonlinear N=4 supermultiplets;- Constructing N=4 superextensions of trigonometric and elliptic Calogero models, as well as their deformations by oscillator-type potentials, with making use of the superfield gauging approach and semi-dynamical multiplets. Generalizations to the case of N=8, d=1 supersymmetry.The studies will be carried out in close cooperation between Russian and German scientists involved in the project.