Ashtekar Constraint Surface as Projection of Hilbert-Palatini One

Details Ashtekar Constraint Surface as Projection of Hilbert-Palatini One Ashtekar Constraint Surface as Projection of Hilbert-Palatini One

1996-04-29

arxiv.org/abs/gr-qc/9604053v1

Phys.Lett. B394 (1997) 57-61

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages of LaTeX file

Scientific paper

10.1016/S0370-2693(96)01691-7

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.

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