Reduced Hamiltonians for gravity

DOI10.1088/0264-9381/11/9/009zbMATH Open0855.70013arXivgr-qc/9312020OpenAlexW2060644810WikidataQ60154358 ScholiaQ60154358MaRDI QIDQ4315145

Josep Antoni Rubio, R. P. Woodard

Publication date: 7 December 1994

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Abstract: We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not degenerate, to a system of canonical variables and a non-zero Hamiltonian that generates their evolution. We advocate using this method to infer a canonical formalism, as a prelude to quantization, for systems in which the naive Hamiltonian is constrained to vanish. The construction agrees with the usual results for gauge theories and can be applied as well to gravity, {it even when the spatial manifold is closed.} As an example, we construct such a reduced Hamiltonian in perturbation theory around a flat background on the manifold $T^{3}imesR$. The resulting Hamiltonian is positive semidefinite and agrees with the A.D.M. energy in the limit that deviations from flat space remain localized as the toroidal radii become infinite.

Full work available at URL: https://arxiv.org/abs/gr-qc/9312020

zbMATH Keywords

Lagrangian formalismconstraintscanonical variablesdynamical variablesminisuperspaceHilbert Lagrangiannondegenerate bracketperturbation of flat space

Mathematics Subject Classification ID

Quantization of the gravitational field (83C45) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (1)

Hamiltonian reduction of spin-2 theory and solvable cosmologies

This page was built for publication: Reduced Hamiltonians for gravity