Ashtekar Constraint Surface as Projection of Hilbert-Palatini One

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.

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References in corpus (2)

• Actions for Gravity, with Generalizations: A Review
• Geometrodynamics vs. Connection Dynamics

Cited by in corpus (2)

• Path integral for the Hilbert-Palatini and Ashtekar gravity
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables