We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension. These theories are either ghost free or power-counting renormalizable but they cannot be both at the same time. However, some of them are one-loop unitary and finite, and possibly unitary and finite at all orders.

中文翻译：

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带有分数算子的量子标量场理论

我们研究了一类微扰标量量子场论，其中动力学以分数阶的洛伦兹不变或洛伦兹破非局部算子为特征，并且基础时空具有不同的光谱维度。这些理论要么是无鬼的，要么是可重整化幂计数的，但它们不能同时存在。然而，它们中的一些是单环幺正和有限的，并且可能在所有阶次上都是单环和有限的。