Loop quantum gravity without the Hamiltonian constraint

@article{Bodendorfer2013LoopQG,
  title={Loop quantum gravity without the Hamiltonian constraint},
  author={Norbert Bodendorfer and Alexander Stottmeister and Andreas Thurn},
  journal={Classical and Quantum Gravity},
  year={2013},
  volume={30},
  pages={082001}
}
We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantized on a partially reduced phase space, meaning reduced only with respect to the Hamiltonian constraint and a proper gauge fixing. More precisely, we introduce, in close analogy to shape dynamics, the generator of a local conformal transformation acting on both, the… 
Anisotropic loop quantum cosmology with self-dual variables
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
Loop quantum cosmology with complex Ashtekar variables
We construct and study loop quantum cosmology (LQC) when the Barbero–Immirzi parameter takes the complex value . We refer to this new approach to quantum cosmology as complex LQC. This formulation is
Loop quantum cosmology with self-dual variables
Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the reality
Scalar Material Reference Systems and Loop Quantum Gravity
In the past, the possibility to employ (scalar) material reference systems in order to describe classical and quantum gravity directly in terms of gauge invariant (Dirac) observables has been
Shape Dynamical Loop Gravity from a Conformal Immirzi Parameter
The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum
New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom
In this paper, we generalise the treatment of isolated horizons in loop quantum gravity, resulting in a Chern-Simons theory on the boundary in the four-dimensional case, to non-distorted isolated
The algebra of observables in Gaußian normal spacetime coordinates
A bstractWe discuss the canonical structure of a spacetime version of the radial gauge, i.e. Gaußian normal spacetime coordinates. While it was found for the spatial version of the radial gauge that
On a partially reduced phase space quantization of general relativity conformally coupled to a scalar field
The purpose of this paper is twofold. On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on ‘loop quantum gravity without the
A note on conformally compactified connection dynamics tailored for anti-de Sitter space
A framework conceptually based on the conformal techniques employed to study the structure of the gravitational field at infinity is set up in the context of loop quantum gravity to describe
...
...

References

SHOWING 1-10 OF 50 REFERENCES
Towards conformal loop quantum gravity
A discussion is given of recent developments in canonical gravity that assimilates the conformal analysis of gravitational degrees of freedom. The work is motivated by the problem of time in quantum
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:
Einstein gravity as a 3D conformally invariant theory
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms
New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
We rederive the results of our companion paper, for matching space–time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
The standard geometrodynamics is transformed into a theory of conformal geometrodynamics by extending the Arnowitt-Deser-Misner (ADM) phase space for canonical general relativity to that consisting
Are the spectra of geometrical operators in Loop Quantum Gravity really discrete
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the
Isolated horizons: The Classical phase space
A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are “isolated” near future time-like infinity or for a finite time interval. The underlying
Topological black holes dressed with a conformally coupled scalar field and electric charge
Electrically charged solutions for gravity with a conformally coupled scalar field are found in four dimensions in the presence of a cosmological constant. If a quartic self-interaction term for the
Quantum geometry of isolated horizons and black hole entropy
Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting
...
...