{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:43Z","timestamp":1760243803370,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,3,31]],"date-time":"2011-03-31T00:00:00Z","timestamp":1301529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Hamiltonian constraints feature in the canonical formulation of general relativity. Unlike typical constraints they cannot be associated with a reduction procedure leading to a non-trivial reduced phase space and this means the physical interpretation of their quantum analogues is ambiguous. In particular, can we assume that \u201cquantisation commutes with reduction\u201d and treat the promotion of these constraints to operators annihilating the wave function, according to a Dirac type procedure, as leading to a Hilbert space equivalent to that reached by quantisation of the problematic reduced space? If not, how should we interpret Hamiltonian constraints quantum mechanically? And on what basis do we assert that quantisation and reduction commute anyway? These questions will be refined and explored in the context of modern approaches to the quantisation of canonical general relativity.<\/jats:p>","DOI":"10.3390\/sym3020134","type":"journal-article","created":{"date-parts":[[2011,4,4]],"date-time":"2011-04-04T10:07:21Z","timestamp":1301911641000},"page":"134-154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?"],"prefix":"10.3390","volume":"3","author":[{"given":"Karim P. Y.","family":"Th\u00e9bault","sequence":"first","affiliation":[{"name":"Centre for Time, School of Philosophical and Historical Enquiry, University of Sydney, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,3,31]]},"reference":[{"unstructured":"Dirac, P.A.M. (1964). 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