Reality conditions and Ashtekar variables: A different perspective

@article{Barbero1995RealityCA,
  title={Reality conditions and Ashtekar variables: A different perspective},
  author={J. Fernando G. Barbero},
  journal={Physical Review D},
  year={1995},
  volume={51},
  pages={5498-5506}
}
  • J. F. Barbero
  • Published 11 October 1994
  • Mathematics
  • Physical Review D
We give in this paper a modified self-dual action that leads to the $SO(3)$-ADM formalism without having to face the difficult second class constraints present in other approaches (for example if one starts from the Hilbert-Palatini action). We use the new action principle to gain some new insights into the problem of the reality conditions that must be imposed in order to get real formulations from complex general relativity. We derive also a real formulation for Lorentzian general relativity… 
Reality conditions for Ashtekar variables as Dirac constraints
We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second-class constraints following Dirac. Thus, counting gravitational degrees of
Quantizing Regge calculus
TLDR
It is shown that, even leaving aside the difficult question of imposing the first class constraints on the states, it is impossible to quantize the model directly, using complex variables and leaving the second class constraints to fix the metric of the quantum Hilbert, because one cannot find a metric which makes the area variables hermitean.
SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter
An so(4,C)-covariant Hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so-called Immirzi parameter) is developed. It encompasses the
Noncommutative gravity with self-dual variables
We build a noncommutative extension of Palatini-Holst theory on a twist-deformed spacetime, generalizing a model that has been previously proposed by Aschieri and Castellani. The twist deformation
Loop Quantum Gravity: An Inside View
This is a (relatively) non -- technical summary of the status of the quantum dynamics in Loop Quantum Gravity (LQG). We explain in detail the historical evolution of the subject and why the results
Beautiful Gauge Field Equations in Clifforms
By combining the tetrads of unholonomic frames of spacetime with the Dirac matrices to a one-form γ, we can reformulate not only the Dirac equation, but also the Einstein equations and supergravity
Fermions in the Ashtekar-Barbero connection formalism for arbitrary values of the Immirzi parameter
The Ashtekar-Barbero-Immirzi formulation of general relativity is extended to include spinor matter fields. Our formulation applies to generic values of the Immirzi parameter and reduces to the
Real sector of the nonminimally coupled scalar field to self-dual gravity
A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real
A new form of Einstein’s equations
We derive the field equations of general relativity from a complex Lagrangian of particular simplicity. In this way we exhibit that Einstein’s vacuum equations are equivalent to the existence of
Role of space-time foam in breaking supersymmetry via the Barbero-Immirzi parameter
We discuss how: (i) a dilaton/axion superfield can play the role of a Barbero-Immirzi field in four-dimensional conformal quantum supergravity theories, (ii) a fermionic component of such a
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
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
Bibliography of Publications related to Classical and Quantum Gravity in terms of the Ashtekar Variables
This bibliography attempts to give a comprehensive overview of all the literature related to the Ashtekar variables. The original version was compiled by Peter H\"ubner in 1989, and it has been
"J."
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)
Rev
  • D42, 4070
  • 1990
Int. J. Mod. Phys A4
  • Int. J. Mod. Phys A4
  • 1989
Jacobson and L. Smolin Class. Quantum Grav
  • Jacobson and L. Smolin Class. Quantum Grav
  • 1987
Int. J. Mod. Phys. D3 J. F. Barbero G. Phys. Rev. D49
  • Int. J. Mod. Phys. D3 J. F. Barbero G. Phys. Rev. D49
  • 1994
Phys. REv. Lett
  • Phys. REv. Lett
  • 1992
REv
  • Lett. 69, 237
  • 1992
Rev
  • D46, 4263
  • 1992
...
1
2
3
...