Axisymmetric gravity in real Ashtekar variables: the quantum theory

Ashtekar Approach to Quantum Gravity

Some of the recent developments in the Ashtekar program of quantization of gravity are discussed in this talk.

Loop Quantum Gravity in Ashtekar and Lagrange–Finsler Variables and Fedosov Quantization of General Relativity

We propose an unified approach to loop quantum gravity and Fedosov quantization of gravity following the geometry of double spacetime fibrations and their quantum deformations. There are considered pseudo–Riemannian manifolds enabled with 1) a nonholonomic 2+2 distribution defining a nonlinear connection (N–connection) structure and 2) an Arnowitt–Deser–Misner 3+1 decomposition. The Ashtekar– B...

Horava-Lifshitz theory as a fermionic aether in Ashtekar gravity

Real Ashtekar variables for Lorentzian signature space-times.

I suggest in this letter 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) Yang-Mills phase space I show that it is possible to describe space-times with Lorentzian signature without the introduction of complex variables. All the features of the Asht...

BRST cohomology of Yang-Mills gauge fields in the presence of gravity in Ashtekar variables

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity described by Ashtekar variables are obtained by using the so-called Maurer-Cartan horizontality conditions. The BRST cohomology group expressed by the Wess-Zumino consistency condition is solved with the help of an operator δ introduced by S.P. Sorella which in our case has a very simple form and generates, toge...