We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the $2+1$ Levin–Wen model to obtain $1+1$ anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems.

我们在上一篇论文中介绍了反射正性（RP）的图形方法的透明代数形式。我们将此量化应用于$2+\mathrm{1个}$ Levin–Wen模型获得 $\mathrm{1个}+\mathrm{1个}$边界上可能存在纠缠的非调子/量子自旋链理论。反射正性在数学和物理学中都发挥了核心作用，并且在这两个主题之间提供了至关重要的联系。在先前的论文中，我们提供了一种新的几何方法来理解图片的反射正性。在这里，我们给出了图形方法的透明代数形式。我们利用从这种翻译中获得的见解，建立了时尚的Levin-Wen模型在真空和体激发方面的反射正性。我们认为这些方法对于理解各种其他问题将是有用的。