Abstract
Several aspects of self-consistent dimensional reduction in Kaluza–Klein theory are addressed. First, the validity of the one-loop approximation in quantum gravity with a cosmological constant is discussed. Second, a distinction is made between mathematical self-consistency and physical self-consistency. Finally, the possible gauge dependence of the physical predictions for the radius and gauge coupling constant is analyzed within the context of recent theorems concerning the gauge invariance of the one-loop gravitational effective action.
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