Canonical analysis ofn-dimensional Palatini action without second-class constraints
| Autor: | Ricardo Escobedo, Mariano Celada, Merced Montesinos, Jorge Romero |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
High Energy Physics - Theory
Physics 010308 nuclear & particles physics General relativity FOS: Physical sciences Equations of motion Canonical transformation General Relativity and Quantum Cosmology (gr-qc) Mathematical Physics (math-ph) 01 natural sciences General Relativity and Quantum Cosmology Action (physics) High Energy Physics - Theory (hep-th) 0103 physical sciences ADM formalism Covariant transformation Connection (algebraic framework) 010306 general physics Mathematical Physics Gauge fixing Mathematical physics |
| Zdroj: | Physical Review D. 101 |
| ISSN: | 2470-0029 2470-0010 |
| DOI: | 10.1103/physrevd.101.024042 |
| Popis: | We carry out the canonical analysis of the $n$-dimensional Palatini action with or without a cosmological constant $(n\geq3)$ introducing neither second-class constraints nor resorting to any gauge fixing. This is accomplished by providing an expression for the spatial components of the connection that allows us to isolate the nondynamical variables present among them, which can later be eliminated from the action by using their own equation of motion. As a result, we obtain the description of the phase space of general relativity in terms of manifestly $SO(n-1,1)$ [or $SO(n)$] covariant variables subject to first-class constraints only, with no second-class constraints arising during the process. Afterwards, we perform, at the covariant level, a canonical transformation to a set of variables in terms of which the above constraints take a simpler form. Finally, we impose the time gauge and make contact with the $SO(n-1)$ ADM formalism. Paper's title was changed, expanded analysis, notation was changed a bit, added reference, corrected typos |
| Databáze: | OpenAIRE |
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