Real Formulations of Complex Gravity and a Complex Formulation of Real Gravity

Details Real Formulations of Complex Gravity and a Complex Formulation of Real Gravity Real Formulations of Complex Gravity and a Complex Formulation of Real Gravity

1994-05-02

arxiv.org/abs/gr-qc/9405002v1

Nucl.Phys. B430 (1994) 460-484

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages, CGPG-94/4-6

Scientific paper

10.1016/0550-3213(94)00379-3

Two gauge and diffeomorphism invariant theories on the Yang-Mills phase space are studied. They are based on the Lie-algebras $so(1,3)$ and $\widetilde{so(3)}$ -- the loop-algebra of $so(3)$. Although the theories are manifestly real, they can both be reformulated to show that they describe complex gravity and an infinite number of copies of complex gravity, respectively. The connection to real gravity is given. For these theories, the reality conditions in the conventional Ashtekar formulation are represented by normal constraint-like terms.

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