Ashtekar Constraint Surface as Projection of Hilbert-Palatini One
General Relativity and Quantum Cosmology
2009-10-28 v1
Abstract
The Hilbert-Palatini (HP) Lagrangian of general relativity being written in terms of selfdual and antiselfdual variables contains Ashtekar Lagrangian (which governs the dynamics of the selfdual sector of the theory on condition that the dynamics of antiselfdual sector is not fixed). We show that nonequivalence of the Ashtekar and HP quantum theories is due to the specific form (of the "loose relation" type) of constraints which relate self- and antiselfdual variables so that the procedure of (canonical) quantisation of such the theory is noncommutative with the procedure of excluding antiselfdual variables.
Keywords
Cite
@article{arxiv.gr-qc/9604053,
title = {Ashtekar Constraint Surface as Projection of Hilbert-Palatini One},
author = {V. M. Khatsymovsky},
journal= {arXiv preprint arXiv:gr-qc/9604053},
year = {2009}
}
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9 pages of LaTeX file