On the relation between operator constraint, master constraint, reduced phase space and path integral quantization
Abstract
Path integral formulations for gauge theories must start from the canonical formulation in order to obtain the correct measure. A possible avenue to derive it is to start from the reduced phase space formulation. In this paper we review this rather involved procedure in full generality. Moreover, we demonstrate that the reduced phase space path integral formulation formally agrees with the Dirac's operator constraint quantization and, more specifically, with the master constraint quantization for firstclass constraints. For firstclass constraints with nontrivial structure functions the equivalence can only be established by passing to Abelian(ized) constraints which is always possible locally in phase space. Generically, the correct configuration space path integral measure deviates from the exponential of the Lagrangian action. The corrections are especially severe if the theory suffers from secondclass secondary constraints. In a companion paper we compute these corrections for the Holst and Plebanski formulations of GR on which current spin foam models are based.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2010
 DOI:
 10.1088/02649381/27/22/225019
 arXiv:
 arXiv:0911.3428
 Bibcode:
 2010CQGra..27v5019H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 43 pages