Zitat:
Zitat von Ich
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Jetzt sind wir aber sicher jenseits der Standardphysik :-)
Ich kann mich erinnern, dass Smolin die Idee hatte, die DSR mit der LQG in Zusammenhang zu bringen. Darüberhinaus gab es Überlegungen zur dynamischen Brechung der Lorentzinvarianz. Dies ist im Kontext LQG aber schon länger vom Tisch:
https://physics.stackexchange.com/qu...rentz-symmetry
The answer is roughly that LQG does not in fact violate Lorentz invariance. The discretisation of area and volume operators does not imply a broken symmetry, any more than discretisation of angular momentum states imply breaking of rotational symmetry --- symmetries in quantum theories are equations of the operator algebra, not of the states!
und
This is the correct answer. LQG is Lorentz invariant. To see details, see the two papers fr.arxiv.org/abs/1012.1739 (recent, shows the Lorentz covanraince of LGG explicitly) and fr.arxiv.org/abs/gr-qc/0205108 (explains in detail why the argument about shrinking of the minimal area is wrong. that is, gives the details behind the point made by gennetg.)
[Carlo Rovelli Jan 28 '11]
https://arxiv.org/abs/1012.1739
Lorentz covariance of loop quantum gravity
Carlo Rovelli, Simone Speziale
(Submitted on 8 Dec 2010 (v1), last revised 18 Apr 2011 (this version, v3))
The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.