弯曲时空中框架变换下的 Ward 恒等式
Ward identities under the frame transformations in curved spacetime
AI总结：
本文研究标量–张量引力理论中 Jordan 与 Einstein 框架的量子等价性，证明 Ward 恒等式无法由框架变换联系，并以有效作用量验证两框架下量子场论不等价。
摘要：
标量–张量引力理论被认为是 Einstein 广义相对论在描述经典引力方面的竞争理论，因为它们被用于构建可行的宇宙暴胀模型。这些理论既可以在 Jordan 框架中表述，也可以在 Einstein 框架中表述；两种框架通过 Weyl 变换及一个场变换相联系，二者合称为框架变换。从经典理论的观点来看，以上述两种框架表述的这些理论通常被认为是等价的。然而，从量子场论的角度看，情况不再如此。在本文中，我们证明，在上述两种框架中导出的 Ward 恒等式并不能通过框架变换相互联系。这表明，在这两种框架中表述的量子场论彼此并不等价。此外，通过比较在这两种框架中导出的有效作用量，也证明了这种不等价性。
英文摘要：
Scalar-tensor theories of gravity are considered to be competitors to Einstein's theory of general relativity for the description of classical gravity, as they are used to build feasible models for cosmic inflation. These theories can be formulated both in the Jordan and Einstein frame, which are related by a Weyl transformation with a field transformation, known together as a frame transformation. These theories formulated in the above two frames are often considered to be equivalent from the point of view of classical theory. However, this is no longer true from the quantum field theoretical perspective. In the present article, we show that the Ward identities derived in the above two frames are not connected through the frame transformation. This shows that the quantum field theories formulated in these two frames are not equivalent to each other. Moreover, this inequivalence is also shown by comparing the effective actions derived in these two frames.
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