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

@article{Bodendorfer2013NewVF, title={New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis}, author={Norbert Bodendorfer and Thomas Thiemann and A. Thurn}, journal={Classical and Quantum Gravity}, year={2013}, volume={30} }

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. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to…

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## References

SHOWING 1-10 OF 73 REFERENCES

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…

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…

New variables for classical and quantum (super)-gravity in all dimensions

- Physics
- 2013

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…

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…

SU(2) loop quantum gravity seen from covariant theory

- Physics
- 2003

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).…

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…

Modern Canonical Quantum General Relativity

- Physics
- 2008

The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly…

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

- Physics
- 2011

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…

Actions for gravity, with generalizations: A Review

- Physics
- 1993

The search for a theory of quantum gravity has for a long time been almost fruitless. A few years ago, however, Ashtekar found a reformulation of Hamiltonian gravity, which thereafter has given rise…

BF Description of Higher-Dimensional Gravity Theories

- Physics
- 1999

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…