Abstract
The functional-differential equation which governs the conformal transformation of the renormalized effective action for a massless, conformally invariant quantized field is solved exactly. The formula so obtained can be used to obtain the effective action in any background spacetime once there exists a conformally related spacetime in which the effective action is known. A simple example is presented to see how our formula is useful to obtain the renormalized stress tensor in the \ensuremath{\zeta}-functional regularization scheme.
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