Functional measure in Kaluza-Klein theories

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Abstract
The principal features of classical Kaluza-Klein theories for scalar, vector, and gravitational fields are reviewed and summarized. It is then argued that existing forms of the Kaluza-Klein Ansatz are potentially inconsistent on the quantum level due to functional-measure discrepancies. The canonical functional measures for integer-spin fields, derived elsewhere, are used to demonstrate the partial quantum consistency of toroidally compactified Kaluza-Klein theories of scalar, vector, and gravitational fields in an arbitrary number of dimensions. It is shown that the use of any of the other popular functional measures found in the literature would lead to the inconsistency of Kaluza-Klein compactifications. It is argued that the quantum consistency of field theories based on the canonical functional measure is an automatic consequence of the transformation properties of that measure under field redefinitions, with the full quantum consistency of all Kaluza-Klein theories following as a special case of this general rule. Finally it is suggested that nontrivial measure factors may act to stabilize the Kaluza-Klein Casimir effect.