在格上驯服莱布尼茨规则
Taming the Leibniz Rule on the Lattice
摘要：
在格场论的一般框架下，研究了一个乘积规则和一个带有Leibniz规则的差分算子。证明了差分算子可以由乘积规则和一些初始数据通过莱布尼茨规则确定。这个观察导致了一个不可行的定理，即不可能在格上构造任何具有（i）平移不变性，（ii）局部性和（iii）莱布尼茨规则的差分算子和乘积规则。我们提出了一种形式主义来克服这个困难，通过一个无限的味道扩展或矩阵表示的格场论。
英文摘要：
We study a product rule and a difference operator equipped with Leibniz rule in a general framework of lattice field theory. It is shown that the difference operator can be determined by the product rule and some initial data through the Leibniz rule. This observation leads to a no-go theorem that it is impossible to construct any difference operator and product rule on a lattice with the properties of (i) translation invariance, (ii) locality and (iii) Leibniz rule. We present a formalism to overcome the difficulty by an infinite flavor extension or a matrix expression of a lattice field theory.
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