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marcus

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## Main Question or Discussion Point

Each quarter last year we put down our predictions about which recent papers will have most impact on future QG research: efforts to reach a fundamental empirical understanding of spacetime geometry and matter. For example, here's the forecast poll from third quarter 2006.

https://www.physicsforums.com/showthread.php?t=134513

The idea of this poll is to continue the series.

Here are the four candidate papers:

http://arxiv.org/abs/gr-qc/0702125

Winston Fairbairn, Etera R. Livine

17 pages, 1 figure

"An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models."

PF discussion of the F-L paper:

https://www.physicsforums.com/showthread.php?t=161857

http://arxiv.org/abs/hep-th/0701113

Laurent Freidel, Florian Girelli, Etera R. Livine

14 pages

"We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead to a structure very similar to the non-commutative geometry of Deformed Special Relativity (DSR). In this framework, it appears natural to consider the 4d relativistic particle as a five dimensional massless particle. We study its quantization in terms of wave functions on the 5d light cone. We introduce the corresponding five-dimensional action principle and analyze how it reproduces the physics of the 4d relativistic particle. The formalism is naturally subject to divergences and we show that DSR arises as a natural regularization: the 5d light cone is regularized as the de Sitter space. We interpret the fifth coordinate as the particle's proper time while the fifth moment can be understood as the mass. Finally, we show how to formulate the Feynman propagator and the Feynman amplitudes of quantum field theory in this context in terms of Dirac observables. This provides new insights for the construction of observables and scattering amplitudes in DSR."

PF discussion of the F-G-L paper:

https://www.physicsforums.com/showthread.php?t=151411

http://arxiv.org/abs/gr-qc/0703002

Kirill Krasnov

This continues Krasnov's short introductory paper of November 2006

http://arxiv.org/abs/hep-th/0611182

"We argue that four-dimensional quantum gravity may be essentially renormalizable provided one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the connection as well as the curvature are all independent variables and the usual relations among these quantities are only on-shell...There is a new coupling constant that controls the non-metric character of the theory...non-metricity becomes important in the infra red. The new IR-relevant term in the action is akin to a curvature dependent cosmological 'constant' and may provide a mechanism for naturally small 'dark energy'. "

Link to video of Krasnov explaining the idea at Perimeter Institute:

http://pirsa.org/06110041/

Here is the abstract of the longer paper, first of a series, that appeared this quarter:

"We describe and study a certain class of modified gravity theories. Our starting point is Plebanski formulation of gravity in terms of a triple of 2-forms, a connection A and a 'Lagrange multiplier' field Psi...The equations are of second order in derivatives. An analog of the Bianchi identity is still present in the theory, as well as its contracted version tantamount to energy conservation equation. The arising modifications to the later are possibly of experimental significance."

related PF discussion:

https://www.physicsforums.com/showthread.php?t=158874 (thread started by Jal)

https://www.physicsforums.com/showthread.php?t=162078 (Bengtsson response to Krasnov)

http://arxiv.org/abs/astro-ph/0703566

Joao Magueijo, Parampreet Singh

10 pages

from the abstract:

"Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider loop modifications to the behavior of the inverse scale factor below a critical scale in closed models and assume a purely thermal origin for the fluctuations...

...more fully work out this complex aspect of loop cosmology, since the full picture would not only fix the free parameters of the theory, but also provide a model for a non-inflationary, thermal origin for the structures of the Universe."

from the conclusions section:

...Loop quantum cosmology has the potential to relate observational physics and quantum gravity, allowing concrete calculations to be made in the quantum gravity regime as long as a minisuperspace approximation is assumed to be valid. The approach is known to modify the equation of state of ordinary matter, thereby permitting a solution of the horizon problem without resorting to scalar fields. It is then natural to ask whether in such scenarios thermal fluctuations could be behind the observed structure of the Universe..."

related PF thread:

https://www.physicsforums.com/showthread.php?t=161941

===================

UPDATE: In addition to the forecasts that show up on the poll, we have a "write-in" choice of the recent three-paper series by E.E. Ita. See the next post by ensabah and my post #4.

https://www.physicsforums.com/showthread.php?t=134513

The idea of this poll is to continue the series.

Here are the four candidate papers:

http://arxiv.org/abs/gr-qc/0702125

**3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory**Winston Fairbairn, Etera R. Livine

17 pages, 1 figure

"An effective field theory for matter coupled to three-dimensional quantum gravity was recently derived in the context of spinfoam models in hep-th/0512113. In this paper, we show how this relates to group field theories and generalized matrix models. In the first part, we realize that the effective field theory can be recasted as a matrix model where couplings between matrices of different sizes can occur. In a second part, we provide a family of classical solutions to the three-dimensional group field theory. By studying perturbations around these solutions, we generate the dynamics of the effective field theory. We identify a particular case which leads to the action of hep-th/0512113 for a massive field living in a flat non-commutative space-time. The most general solutions lead to field theories with non-linear redefinitions of the momentum which we propose to interpret as living on curved space-times. We conclude by discussing the possible extension to four-dimensional spinfoam models."

PF discussion of the F-L paper:

https://www.physicsforums.com/showthread.php?t=161857

http://arxiv.org/abs/hep-th/0701113

**The Relativistic Particle: Dirac observables and Feynman propagator**Laurent Freidel, Florian Girelli, Etera R. Livine

14 pages

"We analyze the algebra of Dirac observables of the relativistic particle in four space-time dimensions. We show that the position observables become non-commutative and the commutation relations lead to a structure very similar to the non-commutative geometry of Deformed Special Relativity (DSR). In this framework, it appears natural to consider the 4d relativistic particle as a five dimensional massless particle. We study its quantization in terms of wave functions on the 5d light cone. We introduce the corresponding five-dimensional action principle and analyze how it reproduces the physics of the 4d relativistic particle. The formalism is naturally subject to divergences and we show that DSR arises as a natural regularization: the 5d light cone is regularized as the de Sitter space. We interpret the fifth coordinate as the particle's proper time while the fifth moment can be understood as the mass. Finally, we show how to formulate the Feynman propagator and the Feynman amplitudes of quantum field theory in this context in terms of Dirac observables. This provides new insights for the construction of observables and scattering amplitudes in DSR."

PF discussion of the F-G-L paper:

https://www.physicsforums.com/showthread.php?t=151411

http://arxiv.org/abs/gr-qc/0703002

**Non-Metric Gravity I: Field Equations**Kirill Krasnov

This continues Krasnov's short introductory paper of November 2006

http://arxiv.org/abs/hep-th/0611182

*Renormalizable Non-Metric Quantum Gravity?*"We argue that four-dimensional quantum gravity may be essentially renormalizable provided one relaxes the assumption of metricity of the theory. We work with Plebanski formulation of general relativity in which the metric (tetrad), the connection as well as the curvature are all independent variables and the usual relations among these quantities are only on-shell...There is a new coupling constant that controls the non-metric character of the theory...non-metricity becomes important in the infra red. The new IR-relevant term in the action is akin to a curvature dependent cosmological 'constant' and may provide a mechanism for naturally small 'dark energy'. "

Link to video of Krasnov explaining the idea at Perimeter Institute:

http://pirsa.org/06110041/

Here is the abstract of the longer paper, first of a series, that appeared this quarter:

"We describe and study a certain class of modified gravity theories. Our starting point is Plebanski formulation of gravity in terms of a triple of 2-forms, a connection A and a 'Lagrange multiplier' field Psi...The equations are of second order in derivatives. An analog of the Bianchi identity is still present in the theory, as well as its contracted version tantamount to energy conservation equation. The arising modifications to the later are possibly of experimental significance."

related PF discussion:

https://www.physicsforums.com/showthread.php?t=158874 (thread started by Jal)

https://www.physicsforums.com/showthread.php?t=162078 (Bengtsson response to Krasnov)

http://arxiv.org/abs/astro-ph/0703566

**Thermal fluctuations in loop cosmology**Joao Magueijo, Parampreet Singh

10 pages

from the abstract:

"Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider loop modifications to the behavior of the inverse scale factor below a critical scale in closed models and assume a purely thermal origin for the fluctuations...

...more fully work out this complex aspect of loop cosmology, since the full picture would not only fix the free parameters of the theory, but also provide a model for a non-inflationary, thermal origin for the structures of the Universe."

from the conclusions section:

...Loop quantum cosmology has the potential to relate observational physics and quantum gravity, allowing concrete calculations to be made in the quantum gravity regime as long as a minisuperspace approximation is assumed to be valid. The approach is known to modify the equation of state of ordinary matter, thereby permitting a solution of the horizon problem without resorting to scalar fields. It is then natural to ask whether in such scenarios thermal fluctuations could be behind the observed structure of the Universe..."

related PF thread:

https://www.physicsforums.com/showthread.php?t=161941

===================

UPDATE: In addition to the forecasts that show up on the poll, we have a "write-in" choice of the recent three-paper series by E.E. Ita. See the next post by ensabah and my post #4.

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