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http://arxiv.org/abs/1007.3368
The Definition of Mach's Principle
Julian Barbour
30 pages. To be published in Foundations of Physics as invited contribution to Peter Mittelstaedt's 80th Birthday Festschrift.
(Submitted on 20 Jul 2010)
"Two definitions of Mach's principle are proposed. Both are related to gauge theory, are universal in scope and amount to formulations of causality that take into account the relational nature of position, time, and size. One of them leads directly to general relativity and may have relevance to the problem of creating a quantum theory of gravity."
http://arxiv.org/abs/1007.3723
Vertex Expansion for the Bianchi I model
Miguel Campiglia, Adam Henderson, William Nelson
15 pages, 2 figures
(Submitted on 21 Jul 2010)
"A perturbative expansion of Loop Quantum Cosmological transitions amplitudes of Bianchi I models is performed. Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion. This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of 'colouring' of the spin foams. Furthermore, the isotropic expansion is recovered by integrating out the anisotropies."
http://arxiv.org/pdf/1007.3732v1
Chiral Effects in Quantum Gravity as Consequence of Instantonic Transitions
Simone Mercuri
8 pages
(Submitted on 21 Jul 2010)
"Instantonic solutions of the Holst modified action for General Relativity indicate that gravity becomes chiral through quantum effects. The resulting violation of parity reflects in a different Newton's constant for right and left modes: a measurement of the TB correlation on CMB can reveal the existence of such an effect."
==sample excerpt from Mercuri's paper==
" In this paper, by using a WKB approximation, we demonstrate that in fact the Holst action can produce a parity violation in the quantum regime. This provides a clear theoretical support to the assumption made in [1] that left and right gravitons are characterized by a different gravitational constant.
Furthermore, this fact is particularly interesting in consideration of the fact that the Holst action is the Lagrangian counterpart of the Ashtekar–Barbero reformulation of canonical General Relativity [5, 6], which is the basis of the non-perturbative quantization of GR, i.e. Loop Quantum Gravity [7–10].
Therefore a result indicating that in fact a parity violation can be generated by the quantization of the Holst action, even in the WKB approximation, would suggest that the same effect could characterize the full LQG theory.
==endquote==
Simone Mercuri is one of Ashtekar's group at Penn State IGC.
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