Galileons的UV性质：谱密度
UV properties of Galileons: Spectral Densities
摘要：
我们提出了一个图片的紫外性质的伽利略场论。我们猜想，伽利略，所有的理论纳入Vainshtein机制，属于贾菲的类“非定域”场论的特点是指数增长的卡伦-莱曼谱密度。类似的性质也出现在小弦论和M理论中。对于这样的理论，微观因果关系的概念和用于定义的S-矩阵和关联函数的时间顺序必须修改，我们给出了如何实现这一点的洛伦兹不变处方。与广义相对论（GR）一样，伽利略子的散射振幅不再满足远离前向散射或固定物理动量传递极限的多项式有界性。这反映了这样一个事实，即这些理论基本上是引力理论，而不是局部场论。我们把这归因于存在的一个局部约束Galileons，类似于Giddings-Lippert局部约束GR。我们利用最近开发的Galileon对偶定义一个UV有限，洛伦兹不变，量子化的一个特定的Galileon理论的能量的所有状态是正定的。我们执行一个明确的计算的Wightman函数为这个理论，并证明了指数增长与局部约束。与GR类似，该界与伽利略对偶（即同构）不变局部观测量的缺乏相关。我们认为，这些理论可以量子化的方式，保持洛伦兹不变性和宏观因果关系，后者确保在低能量有效理论中发现的superluminalities是不存在的完整的理论。
英文摘要：
We propose a picture for the UV properties of Galileon field theories. We conjecture that Galileons, and all theories incorporating the Vainshtein mechanism, fall into Jaffe's class of `non-localizable' field theories characterized by an exponential growth in their Kallen-Lehmann spectral densities. Similar properties have been argued to arise for Little String Theories and M-theory. For such theories, the notion of micro-causality and the time ordering used to define the S-matrix and correlation functions must be modified, and we give a Lorentz invariant prescription for how this can be achieved. In common with General Relativity (GR), the scattering amplitudes for Galileons are no longer expected to satisfy polynomial boundedness away from the forward scattering or fixed physical momentum transfer limits. This is a reflection of the fact that these theories are fundamentally gravitational and not local field theories. We attribute this to the existence of a locality bound for Galileons, analogous to the Giddings-Lippert locality bound for GR. We utilize the recently developed Galileon duality to define a UV finite, Lorentz invariant, quantization of a specific Galileon theory for which the energy of all states are positive definite. We perform an explicit computation of the Wightman functions for this theory, and demonstrate the exponential growth associated with the locality bound. In analogy with GR, the bound is correlated with the absence of Galileon Duality (i.e. Diffeomorphism) invariant local observables. We argue that these theories can be quantized in a manner which preserves Lorentz invariance and macro-causality and that the latter ensures that the superluminalities found in the low energy effective theory are absent in the full theory.
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