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首页> 外文期刊>Infinite dimensional analysis, quantum probability, and related topics >Family of measures on a space of curves that are quasi-invariant with respect to some action of diffeomorphisms group
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Family of measures on a space of curves that are quasi-invariant with respect to some action of diffeomorphisms group

机译：关于拟同态群作用的准不变曲线空间上的度量族

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摘要

A family of quasi-invariant measures on the special functional space of curves in a finite-dimensional Euclidean space with respect to the action of diffeomorphisms is constructed. The main result is an explicit expression for the Radon-Nikodym derivative of the transformed measure relative to the original one. The stochastic Ito integral allows to express the result in an invariant form for a wider class of diffeomorphisms. These measures can be used to obtain irreducible unitary representations of the diffeomorphisms group which will be studied in future research. A geometric interpretation of the action considered together with a generalization to the multidimensional case makes such representations applicable to problems of quantum mechanics.
机译：构造了关于微分同构作用的有限维欧几里得空间中曲线的特殊函数空间的准不变度量族。主要结果是相对于原始量度的变换量度的Radon-Nikodym导数的显式表达。随机的Ito积分允许以不变的形式表示结果，以用于更广泛的一类亚纯性。这些措施可用于获得亚纯态群的不可约表示，这将在以后的研究中进行研究。对动作的几何解释以及对多维情况的概括，使得这种表示可应用于量子力学问题。

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