Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity?

Thébault, Karim P. Y. (31. März 2011): Quantisation, Representation and Reduction; How Should We Interpret the Quantum Hamiltonian Constraints of Canonical Gravity? In: Symmetry, Bd. 3, Nr. 2: S. 134-154

Abstract

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 “quantisation commutes with reduction” 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.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Keywords: problem of time; canonical quantisation; symplectic reduction; Hamiltonian constraints; quantum gravity
• Fakultät: Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) ; Philosophie, Wissenschaftstheorie und Religionswissenschaft > Munich Center for Mathematical Philosophy (MCMP) > Philosophy of Physics
• Themengebiete: 100 Philosophie und Psychologie > 100 Philosophie
• ISSN: 2073-8994
• Bemerkung: This article belongs to the Special Issue "Quantum Symmetry"
• Sprache: Englisch