Quantisation, representation and reduction; How should we interpret the quantum Hamiltonian constraints of canonical gravity?

Karim P Y Thébault*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)134-154
Number of pages21
JournalSymmetry
Volume3
Issue number2
DOIs
Publication statusPublished - Jun 2011

Keywords

  • Canonical quantisation
  • Hamiltonian constraints
  • Problem of time
  • Quantum gravity
  • Symplectic reduction

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