Real Ashtekar variables for Lorentzian signature spacetimes
Abstract
I suggest in this paper a new strategy to attack the problem of the reality conditions in the Ashtekar approach to classical and quantum general relativity. By writing a modified Hamiltonian constraint in the usual SO(3) YangMills phase space I show that it is possible to describe spacetimes with a Lorentzian signature without the introduction of complex variables. All the features of the Ashtekar formalism related to the geometrical nature of the new variables are retained; in particular, it is still possible, in principle, to use the loop variables approach in the passage to the quantum theory. The key issue in the new formulation is how to deal with the more complicated Hamiltonian constraint that must be used in order to avoid the introduction of complex fields.
 Publication:

Physical Review D
 Pub Date:
 May 1995
 DOI:
 10.1103/PhysRevD.51.5507
 arXiv:
 arXiv:grqc/9410014
 Bibcode:
 1995PhRvD..51.5507B
 Keywords:

 04.20.Cv;
 04.20.Fy;
 Fundamental problems and general formalism;
 Canonical formalism Lagrangians and variational principles;
 General Relativity and Quantum Cosmology
 EPrint:
 10 pages, LATEX, Preprint CGPG94/103