New variables for classical and quantum gravity in all dimensions: IV. Matter coupling

@article{Bodendorfer2013NewVF,
  title={New variables for classical and quantum gravity in all dimensions: IV. Matter coupling},
  author={Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal={Classical and Quantum Gravity},
  year={2013},
  volume={30},
  pages={045004}
}
We employ the techniques introduced in the companion papers [1, 2, 3] to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D + 1 ≥ 3 with compact gauge group. The technique that accomplishes that is similar to the one that has been introduced in 3 + 1 dimensions already: First one performs a canonical analysis of Lorentzian General Relativity using the time gauge and then introduces an extension of the phase space analogous to the one… 
New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is
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
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
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
New variables for classical and quantum (super)-gravity in all dimensions
Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached
On the Implementation of the Canonical Quantum Simplicity Constraint
In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and
Higher dimensional and supersymmetric extensions of loop quantum gravity
In this work, we extend loop quantum gravity (LQG) both, to higher dimensions and supersymmetry (i.e. supergravity theories), thus overcoming the current limitation to 3+1 dimensions with standard
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime
1 3 M ar 2 01 2 From Classical To Quantum Gravity : Introduction to Loop Quantum Gravity
We present an introduction to the canonical quantization of gravity performed in loop quantum gravity, based on lectures held at the 3rd quantum geometry and quantum gravity school in Zakopane in
...
...

References

SHOWING 1-10 OF 35 REFERENCES
New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for
Towards Loop Quantum Supergravity (LQSG) I. Rarita-Schwinger Sector
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is
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
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
We rederive the results of our companion paper, for matching spacetime and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the
New variables for classical and quantum (super)-gravity in all dimensions
Supergravity was originally introduced in the hope of finding a theory of gravity without the shortcoming of perturbative non-renormalisability. Although this goal does not seem to have been reached
On the Implementation of the Canonical Quantum Simplicity Constraint
In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and
BF Description of Higher-Dimensional Gravity Theories
It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime
New variables for gravity: Inclusion of matter.
TLDR
The Lagrangian and Hamiltonian formulations of general relativity in terms of soldering forms and self-dual connections are extended to include matter sources and the cosmological constant and have several potential applications especially to the nonperturbative canonical quantization program.
New variables for classical and quantum gravity.
  • Ashtekar
  • Physics
    Physical review letters
  • 1986
TLDR
A Hamiltonian formulation of general relativity based on certain spinorial variables is introduced that enables one to imbed the constraint surface in the phase space of Einstein's theory into that of Yang-Mills theory.
...
...