Canonical gravity with fermions

@article{Bojowald2008CanonicalGW,
  title={Canonical gravity with fermions},
  author={Martin Bojowald and Rupam Das},
  journal={Physical Review D},
  year={2008},
  volume={78},
  pages={064009}
}
Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are summarized here. This in turn requires adaptations to the known loop quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis. As a result, parity invariance is not manifestly realized in loop quantum gravity. 
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References

SHOWING 1-10 OF 36 REFERENCES
Loop quantum gravity : an outside view
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasize that the off-shell (‘strong’)
Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
The algebraic form of the Hamiltonian or Hamiltonian constraint of various (field) theories simplifies considerably if one uses certain complex-valued phase space variables. We show, for a general
Real and complex connections for canonical gravity
TLDR
It is shown that there is an arbitrary parameter which enters in the definition of the real connection, in the Poisson brackets, and therefore in the scale of the discrete spectra one finds for areas and volumes in the corresponding quantum theory.
Hamiltonian Analysis of General Relativity with the Immirzi Parameter
Starting from a Lagrangian we perform the full constraint analysis of the Hamiltonian for General relativity in the tetrad-connection formulation for an arbitrary value of the Immirzi parameter and
Dirac Fields in Loop Quantum Gravity and Big Bang Nucleosynthesis
Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum
Kinematical Hilbert Spaces for Fermionic and Higgs Quantum Field Theories
We extend the recently developed kinematical framework for diffeomorphism-invariant theories of connections for compact gauge groups to the case of a diffeomorphism-invariant quantum field theory
Quantum spin dynamics (QSD) V: Quantum Gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories
It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague
Spin networks and quantum gravity.
  • Rovelli, Smolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
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 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
...
...