We give the conformal transformation law for the effective action for conformally invariant field theories on general curved space-times. It is shown that this law can be used to obtain almost all known renormalized stress tensors for such theories. It can also be used to obtain approximate renormalized stress tensors; for example, we derive as a special case Page's approximation for static Einstein space-times.
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Brown et al. (1985) studied this question.
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