Anomalyfree formulation of nonperturbative, fourdimensional Lorentzian quantum gravity
Abstract
A WheelerDeWitt quantum constraint operator for fourdimensional, nonperturbative Lorentzian vacuum quantum gravity is defined in the continuum. The regulated WheelerDeWitt constraint operator is finite, does not require any renormalization and the final operator is anomalyfree and at least symmetric. The technique introduced here can also be used to produce a couple of completely welldefined regulated operators including but not exhausting (i) the Euclidean WheelerDeWitt operator, (ii) the generator of the Wick rotation transform that maps solutions to the Euclidean Hamiltonian constraint to solutions to the Lorentzian Hamiltonian constraint, (iii) length operators, (iv) Hamiltonian operators of the matter sector and (v) the generators of the asymptotic Poincaré group including the quantum ADM energy.
 Publication:

Physics Letters B
 Pub Date:
 February 1996
 DOI:
 10.1016/03702693(96)005321
 arXiv:
 arXiv:grqc/9606088
 Bibcode:
 1996PhLB..380..257T
 Keywords:

 PACS;
 04.60;
 LORENTZIAN;
 FOURDIMENSIONAL QUANTUM GRAVITY;
 WHEELERDEWITT CONSTRAINT;
 GENERATOR OF THE WICK ROTATION;
 EUCLIDEAN HAMILTONIAN;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 10 pages, Latex, to appear in Physics Letters B (in press)