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1997•Civil War Book ReviewOpen access

On the consistency of the constraint algebra in spin network quantum gravity

Rodolfo Gambini, Jerzy Lewandowski, Donald Marolf, Jorge Pullin

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Abstract

We point out several features of the quantum Hamiltonian constraints recently introduced by Thiemann for Euclidean gravity. In particular we discuss the issue of the constraint algebra and of the quantum realization of the object $q^{ab}V_b$, which is classically the Poisson Bracket of two Hamiltonians.

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What this paper is about

We point out several features of the quantum Hamiltonian constraints recently introduced by Thiemann for Euclidean gravity. In particular we discuss the issue of the constraint algebra and of the quantum realization of the object $q^{ab}V_b$, which is classically the Poisson Bracket of two Hamiltonians.

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OpenAlex reports 67 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We point out several features of the quantum Hamiltonian constraints recently introduced by Thiemann for Euclidean gravity. In particular we discuss the issue of the constraint algebra and of the quantum realization of the object $q^{ab}V_b$, which is classically the Poisson Bracket of two Hamiltonians.

Key concepts: Hamiltonian constraint, Physics, Spin network, Loop quantum gravity, First class constraint, Spin foam, Wheeler–DeWitt equation, Hamiltonian (control theory)

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