Self-dual variables, positive semi-definite action, and discrete transformations in four-dimensional quantum gravity

Details Self-dual variables, positive semi-definite action, and discrete transformations in four-dimensional quantum gravity Self-dual variables, positive semi-definite action, and discrete transformations in four-dimensional quantum gravity

1995-04-25

arxiv.org/abs/gr-qc/9504042v2

Phys.Rev.D52:3484-3493,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, LaTeX. Minor corrections. (To appear in Phys. Rev. D.)

Scientific paper

10.1103/PhysRevD.52.3484

A positive semi-definite Euclidean action for arbitrary four-topologies can be constructed by adding appropriate Yang-Mills and topological terms to the Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables. Moreover, on-shell, the (anti)self-dual sector of the new theory corresponds precisely to all Einstein manifolds in four dimensions. The Lorentzian signature action, and its analytic continuations are also considered. A self-contained discussion is given on the effects of discrete transformations C, P and T on the Samuel-Jacobson-Smolin action, and other proposed actions which utilize self- or anti-self-dual variables as fundamental variables in the description of four-dimensional gravity.

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