Real Ashtekar variables for Lorentzian signature space-times.

  title={Real Ashtekar variables for Lorentzian signature space-times.},
  author={J. Fernando G. Barbero},
  journal={Physical Review D},
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 Ashtekar formalism related to the geometrical nature of the new variables are retained; in particular… 
Note on the phase space of asymptotically flat gravity in Ashtekar–Barbero variables
We describe the canonical phase space of asymptotically flat gravity in Ashtekar–Barbero (AB) variables. We show that the Gauss constraint multiplier must fall off slower than previously considered
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The Hamiltonian constraint is the key element of the canonical formulation of LQG coding its dynamics. In Ashtekar-Barbero variables it naturally splits into the so called Euclidean and Lorentzian
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In Loop Quantum Gravity, tremendous progress has been made using the Ashtekar-Barbero variables. These variables, defined in a gauge-fixing of the theory, correspond to a parametrization of the
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A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory
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The Hartle-Hawking state is a proposal for a preferred initial state for quantum gravity, based on a path integral over all compact Euclidean four-geometries which have a given threegeometry as a
Loop quantum cosmology with complex Ashtekar variables
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Spontaneous Breaking of Lorentz Symmetry for Canonical Gravity
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however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
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