Quantization and Regularization in Perturbative Quantum Cosmology

TL;DR

This paper investigates different quantization and regularization methods in perturbative quantum cosmology, highlighting discrepancies and the challenges in establishing their equivalence due to complex eigenvalue problems.

Contribution

It critically examines the impact of reduction to physical degrees of freedom on one-loop amplitude predictions and discusses the difficulties in comparing quantization techniques.

Findings

Discrepancies between reduction-based and Faddeev-Popov methods for one-loop amplitudes.

Mode-by-mode analysis of gauge and ghost eigenvalue equations is highly complex.

The equivalence of various quantization and regularization approaches remains unproven.

Abstract

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.