论文标题
量化类别和反问题类别
Category of Quantizations and Inverse Problem
论文作者
论文摘要
我们介绍了一个由所有泊松代数的所有量化组成的类别。按类别，我们可以以统一的方式对待所有泊松代数的各种量化，并开发新的经典限制表达式。该公式提出了一种针对逆问题的新方法，即从量化空间中找到经典限制的问题。量化的等效性是通过使用此类别来定义的，并且研究了两个量化等效的条件。在类别理论的上下文中，将两种类型的经典限制定义为限制，它们是通过给出一系列对象来确定的。使用这些经典限制，我们讨论了从某些非交通性谎言代数确定经典限制的逆问题。从谎言代数中，我们构建了一系列量化空间，从中确定泊松代数。我们还提出了一种通过使用矩阵正则化来从最小作用的原理中获得这种量化序列的方法。除上述所有泊松代数的量化类别外，还介绍了固定单泊松代数的量化类别。在此类别中，定义了另一个经典限制，并自动确定该类别。
We introduce a category composed of all quantizations of all Poisson algebras. By the category, we can treat in a unified way the various quantizations for all Poisson algebras and develop a new classical limit formulation. This formulation proposes a new method for the inverse problem, that is, the problem of finding the classical limit from a quantized space. Equivalence of quantizations is defined by using this category, and the conditions under which the two quantizations are equivalent are investigated. Two types of classical limits are defined as the limits in the context of category theory, and they are determined by giving a sequence of objects. Using these classical limits, we discuss the inverse problem of determining the classical limit from some noncommutative Lie algebra. From a Lie algebra, we construct a sequence of quantized spaces, from which we determine a Poisson algebra. We also present a method to obtain this sequence of quantizations from the principle of least action by using matrix regularization. Apart from the above category of quantizations of all Poisson algebras, a category of quantizations of a fixed single Poisson algebra is also introduced. In this category, the other classical limit is defined, and it is automatically determined for the category.
