格超对称与Hopf代数的链接方法
Lattice supersymmetry with Hopf algebra for the link approach
摘要：
本文提出了一种基于格变形超代数的格超对称性的形式，这种超代数最初是在链接方法中引入的。我们提出超代数实际上可以被识别为一个Hopf代数，证明所有的Hopf代数公理和公理都满足显式公式。特别是，“变形”莱布尼茨规则中提出的原始链接的方法，现在建立在Hopf代数的余积结构。作为Hopf代数的表示，该方案中的场服从一种轻度变形统计，并将其解释为一种辫状结构.然后，我们可以构造（至少是微扰地构造）相应的格点场论，它具有形变统计的霍普夫代数对称性，作为奥克尔提出的辫状量子场论的一个例子。
英文摘要：
A formalism of lattice supersymmetry based on a lattice-deformed superalgebra which was originally introduced in the link approach formulation is presented. We propose that the superalgebra can in fact be identified as a Hopf algebra, showing all the Hopf algebra axioms and consistencies are satisfied with explicit formulae. In particular, the "deformed" Leibniz rules proposed in the original link approach are now built in the coproduct structure of the Hopf algebra. Fields in this scheme, as representations of the Hopf algebra, are found to obey a kind of mildly deformed statistics, which is interpreted as a braiding strucutre. We can then construct, at least perturbatively, the corresponding lattice field theory, which has the Hopf algebraic symmetry with the deformed statistics, as an example of braided quantumm field theory formulated by Oeckl.
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