Ntina Savvidou 2004 Class. Quantum Grav. 21 615 doi:10.1088/0264-9381/21/2/020
Ntina Savvidou
Show affiliationsThe problem of time in canonical quantum gravity is related to the fact that the canonical description is based on the prior choice of a spacelike foliation, hence making a reference to a spacetime metric. However, the metric is expected to be a dynamical, fluctuating quantity in quantum gravity. We show how this problem can be solved in the histories formulation of general relativity. We implement the 3 + 1 decomposition using metric-dependent foliations which remain spacelike with respect to all possible Lorentzian metrics. This allows us to find an explicit relation of covariant and canonical quantities which preserves the spacetime character of the canonical description. In this new construction, we also have the coexistence of the spacetime diffeomorphisms group, Diff(M), and the Dirac algebra of constraints.
04.60.Gw Covariant and sum-over-histories quantization
02.40.-k Geometry, differential geometry, and topology
04.20.Fy Canonical formalism, Lagrangians, and variational principles
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
70H45 Constrained dynamics, Dirac's theory of constraints (See also 70F20, 70F25, 70Gxx)
Issue 2 (21 January 2004)
Received 1 June 2003
Published 10 December 2003
Ntina Savvidou 2004 Class. Quantum Grav. 21 615
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