Partial and complete observables for canonical general relativity

By B. Dittrich. 2005

317 citations recorded by the source corpus.

In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of this work is that one can compute Dirac observables for general relativity by dealing with just one constraint. For this we have to introduce spatial diffeomorphism invariant Hamiltonian constraints. It will turn out that these can be made to be Abelian. Furthermore the methods outlined here provide a connection between observables in the spacetime picture, i.e. quantities invariant under spacetime diffeomorphisms, and Dirac observables in the canonical picture.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/22c7e13456541aab0a228f0ba8e467f8a2267050

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In Applied Mathematics

In Astronomy and Astrophysics

In Statistical and Nonlinear Physics

Citations in the corpus

Partial and complete observables for Hamiltonian constrained systems (2004, background): “To construct a Dirac observable with respect to all the constraints C H , C D we have to find another spatial diffeomorphism invariant observable g and to compute the complete observable associated to g and to the spatial diffeomorphism invariant clock variables ψd+1(v1 ,...,v d ) with respect to th”
The asymptotic safety scenario in quantum gravity: an introduction (2006, background): “In a conventional field theory S-matrix elements by and large have this property, in canonical general relativity Dirac observables play this role [7, 147, 48].”
From black holes to white holes: a quantum gravitational, symmetric bounce (2017, unknown): “In this context, further developments have been carried out in order to identify classical (partial) Dirac observables [51, 52] and various applications have been studied [53–56].”
Loop Quantum Gravity (2003, background): “These ideas date back to the work of Bergmann and Komar [81–83] in the 1960s and were clarified and developed in the 1990s [84– 87].”
Introduction to Loop Quantum Cosmology (2011, background): “This allows us to define Dirac observables “in evolution”, namely relational observables [101, 102, 169], and in turn, to interpret the physical results.”
The Asymptotic Safety Scenario in Quantum Gravity (2006, background): “In a conventional field theory S-matrix elements by and large have this property, in canonical general relativity Dirac observables play this role [9, 219, 70].”