# New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis

@article{Bodendorfer2011NewVF, title={New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis}, author={Norbert Bodendorfer and Thomas Thiemann and A. Thurn}, journal={Classical and Quantum Gravity}, year={2011}, volume={30} }

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 Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our…

## 45 Citations

New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis

- Physics
- 2013

Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact.…

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- 2013

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…

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

- Physics
- 2013

We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of…

Canonical analysis ofn-dimensional Palatini action without second-class constraints

- Computer SciencePhysical Review D
- 2020

The canonical analysis of the Palatini action with or without a cosmological constant is carried out, obtaining the description of the phase space of general relativity in terms of manifestly SO(n-1,1)$ [or $SO(n)$] covariant variables subject to first-class constraints only, with no second- class constraints arising during the process.

Towards loop quantum supergravity (LQSG): II. p-form sector

- Physics
- 2013

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…

Coherent intertwiner solution of simplicity constraint in all dimensional loop quantum gravity

- PhysicsPhysical Review D
- 2019

We propose a new treatment of the quantum simplicity constraints appearing in the general ${SO(D+1)}$ formulation of loop quantum gravity for the ${(1+D)}$-dimensional space-time. Instead of strongly…

New variables for classical and quantum gravity in all dimensions: V. Isolated horizon boundary degrees of freedom

- Physics
- 2013

In this paper, we generalize 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: III. Quantum theory

- Physics
- 2011

We quantize 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…

Towards loop quantum supergravity (LQSG): I. Rarita–Schwinger sector

- Mathematics, Physics
- 2013

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…

Higher dimensional and supersymmetric extensions of loop quantum gravity

- Physics
- 2013

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…

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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…

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

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We quantize 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…

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