Summary
Reduction to physical degrees of freedom before quantization leads to predictions for one-loop amplitudes in quantum cosmology in the presence of boundaries which disagree with the results obtained from Faddeev-Popov theory and boundary-counterterms technique. However, the mode-by-mode analysis of eigenvalue equations for gauge modes and ghost fields remains a very difficult problem. Hence, the equivalence or inequivalence of various quantization and regularization techniques cannot be easily proved.
References
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Esposito, G. Quantization and regularization in perturbative quantum cosmology. Nuov Cim B 109, 203–205 (1994). https://doi.org/10.1007/BF02727430
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DOI: https://doi.org/10.1007/BF02727430