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Today Tuesday 18 September there was an important meeting of the ILQGS
http://relativity.phys.lsu.edu/ilqgs/
The scheduled presentation was by Jonathan Engle at Marseille, talking about the new spinfoam vertices. Several people joined in lively discussion (Abhay at Penn State, Carlo at Marseille, Laurent at Perimeter, Jorge at Louisiana, who was hosting the teleseminar.
Engle's notes PDF
http://relativity.phys.lsu.edu/ilqgs/engle091807.pdf
The better of the two audio options
http://relativity.phys.lsu.edu/ilqgs/engle091807.wav
http://arxiv.org/abs/0709.2433
Toward explaining black hole entropy quantization in loop quantum gravity
Hanno Sahlmann
14 pages, 5 figures
(Submitted on 15 Sep 2007)
"In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking."Alain Connes and Matilde Marcolli NCG lectures on YouTube
http://noncommutativegeometry.blogspot.com/2007/09/you-tube-qft.html
I haven't had time to adequately sample these. They are from two years ago. My guess is that they are going to prove quite useful. Matilde gives the first one, racing thru QFT.http://arxiv.org/abs/0709.2784
Putting a cap on causality violations in CDT
J. Ambjorn, R. Loll, W. Westra, S. Zohren
17 pages, 4 figures
(Submitted on 18 Sep 2007)
"The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum limits have been studied in two, three and four dimensions. Here we investigate a generalization of the two-dimensional CDT model, where the causality constraint is partially lifted by introducing weighted branching points, and demonstrate that the system can be solved analytically in the genus-zero sector."
http://arxiv.org/abs/0709.2905
In Search of Quantum de Sitter Space: Generalizing the Kodama State
Andrew Randono
Ph.D. dissertation, University of Texas at Austin. 150 pages
(Submitted on 18 Sep 2007)
"The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi parameter. The Kodama state takes this parameter to be complex, whereas modern formulations of canonical quantum gravity require that the parameter is real. We generalize the Kodama state to real values of the Immirzi parameter, and find that the generalization opens up a large Hilbert space of states, one of which can be directly interpreted as particular slicing of de Sitter space. We then show that these states resolve, or are expected to resolve many of the problems associated with the original version of the Kodama state. In order to resolve the interpretation of the multitude of states, we develop a new model of covariant classical and quantum gravity where the full Lorentz group is retained as a local symmetry group, and the canonical evolution generated by the constraints has a close relation to a larger group: the de Sitter group. This formalism gives strong evidence that the multitude of generalized Kodama states can be unified into a single quantum state that is quantum de Sitter space."
Thomas Larsson, an occasional poster here at PF Beyond forum, recently put two papers up on arxiv that have been published in past years.
http://arxiv.org/abs/0709.2539
Multi-dimensional Virasoro algebra and quantum gravity
T. A. Larsson
In: Mathematical physics research at the leading edge, ed: Charles V. Benton, pp 91-111, 2004 Nova Science Publishers Inc. ISBN 1-59033-905-3
(Submitted on 17 Sep 2007)
"I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present."
http://arxiv.org/abs/0709.2540
Manifestly covariant canonical quantization of gravity and diffeomorphism anomalies in four dimensions
T. A. Larsson
In: Focus on quantum gravity research, ed: David C. Moore, pp 261-310, 2006 Nova Science Publishers Inc. ISBN 1-59454-660-6
(Submitted on 17 Sep 2007)
"Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field theory, because the relevant cocycles are functionals of the observer's trajectory in spacetime. The multi-dimensional Virasoro algebra acts naturally in the phase space of arbitrary histories, with dynamics playing the role of first-class constraints. General relativity is regularized by expanding all fields in Taylor series around the observer's trajectory, and truncating at some fixed order. This regularized but manifestly general-covariant theory is quantized in the history phase space, and dynamics is imposed afterwards, in analogy with BRST quantization. Infinities arise when the regularization is removed; it is presently unclear how these should be dealt with."
http://relativity.phys.lsu.edu/ilqgs/
The scheduled presentation was by Jonathan Engle at Marseille, talking about the new spinfoam vertices. Several people joined in lively discussion (Abhay at Penn State, Carlo at Marseille, Laurent at Perimeter, Jorge at Louisiana, who was hosting the teleseminar.
Engle's notes PDF
http://relativity.phys.lsu.edu/ilqgs/engle091807.pdf
The better of the two audio options
http://relativity.phys.lsu.edu/ilqgs/engle091807.wav
http://arxiv.org/abs/0709.2433
Toward explaining black hole entropy quantization in loop quantum gravity
Hanno Sahlmann
14 pages, 5 figures
(Submitted on 15 Sep 2007)
"In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this step-like behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step-length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking."Alain Connes and Matilde Marcolli NCG lectures on YouTube
http://noncommutativegeometry.blogspot.com/2007/09/you-tube-qft.html
I haven't had time to adequately sample these. They are from two years ago. My guess is that they are going to prove quite useful. Matilde gives the first one, racing thru QFT.http://arxiv.org/abs/0709.2784
Putting a cap on causality violations in CDT
J. Ambjorn, R. Loll, W. Westra, S. Zohren
17 pages, 4 figures
(Submitted on 18 Sep 2007)
"The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum limits have been studied in two, three and four dimensions. Here we investigate a generalization of the two-dimensional CDT model, where the causality constraint is partially lifted by introducing weighted branching points, and demonstrate that the system can be solved analytically in the genus-zero sector."
http://arxiv.org/abs/0709.2905
In Search of Quantum de Sitter Space: Generalizing the Kodama State
Andrew Randono
Ph.D. dissertation, University of Texas at Austin. 150 pages
(Submitted on 18 Sep 2007)
"The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi parameter. The Kodama state takes this parameter to be complex, whereas modern formulations of canonical quantum gravity require that the parameter is real. We generalize the Kodama state to real values of the Immirzi parameter, and find that the generalization opens up a large Hilbert space of states, one of which can be directly interpreted as particular slicing of de Sitter space. We then show that these states resolve, or are expected to resolve many of the problems associated with the original version of the Kodama state. In order to resolve the interpretation of the multitude of states, we develop a new model of covariant classical and quantum gravity where the full Lorentz group is retained as a local symmetry group, and the canonical evolution generated by the constraints has a close relation to a larger group: the de Sitter group. This formalism gives strong evidence that the multitude of generalized Kodama states can be unified into a single quantum state that is quantum de Sitter space."
Thomas Larsson, an occasional poster here at PF Beyond forum, recently put two papers up on arxiv that have been published in past years.
http://arxiv.org/abs/0709.2539
Multi-dimensional Virasoro algebra and quantum gravity
T. A. Larsson
In: Mathematical physics research at the leading edge, ed: Charles V. Benton, pp 91-111, 2004 Nova Science Publishers Inc. ISBN 1-59033-905-3
(Submitted on 17 Sep 2007)
"I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present."
http://arxiv.org/abs/0709.2540
Manifestly covariant canonical quantization of gravity and diffeomorphism anomalies in four dimensions
T. A. Larsson
In: Focus on quantum gravity research, ed: David C. Moore, pp 261-310, 2006 Nova Science Publishers Inc. ISBN 1-59454-660-6
(Submitted on 17 Sep 2007)
"Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field theory, because the relevant cocycles are functionals of the observer's trajectory in spacetime. The multi-dimensional Virasoro algebra acts naturally in the phase space of arbitrary histories, with dynamics playing the role of first-class constraints. General relativity is regularized by expanding all fields in Taylor series around the observer's trajectory, and truncating at some fixed order. This regularized but manifestly general-covariant theory is quantized in the history phase space, and dynamics is imposed afterwards, in analogy with BRST quantization. Infinities arise when the regularization is removed; it is presently unclear how these should be dealt with."
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