Adjointness Relations as a Criterion for Choosing an Inner Product

TL;DR

This paper discusses Ashtekar's criterion for selecting an inner product in quantizing constrained systems, correcting previous errors and providing cautionary insights relevant to canonical gravity.

Contribution

It clarifies and corrects Ashtekar's criterion for inner product selection in quantum constrained systems, with implications for canonical gravity quantization.

Findings

Correction of a previous erroneous claim

Presentation of a cautionary example

Clarification of Ashtekar's criterion

Abstract

This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.