We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

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扩大局部对称性：非局部伽利略模型

我们考虑通过在动作中引入无限阶导数算子来扩大在标准局部场论中实现的对称类的可能性，这成为非局部的。特别是，我们关注伽利略位移对称性及其在非局部（无限导数）场论中的推广。首先，我们构建了一个可能是紫外有限的非局部伽利略模型，展示了如何改善环积分的紫外行为。我们还讨论了具有无限多个复共轭极点的传播子的极点结构，但满足树级的幺正性。此外，我们将在线性化重力的背景下引入相同类型的非局部算子。在这种情况下，引力子传播器被证明是无鬼的，并且由点状源产生的时空度量是非奇异的。