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Simplicity in simplicial phase space

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons20705

Dittrich,  Bianca
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Volltexte (frei zugänglich)

1006.4295
(Preprint), 409KB

prd064026.pdf
(beliebiger Volltext), 314KB

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Zitation

Dittrich, B., & Ryan, J. P. (2010). Simplicity in simplicial phase space. Physical Review D., 82: 064026. doi:10.1103/PhysRevD.82.064026.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0012-C11B-1
Zusammenfassung
A key point in the spin foam approach to quantum gravity is the implementation of simplicity constraints in the partition functions of the models. Here, we discuss the imposition of these constraints in a phase space setting corresponding to simplicial geometries. On the one hand, this could serve as a starting point for a derivation of spin foam models by canonical quantisation. On the other, it elucidates the interpretation of the boundary Hilbert space that arises in spin foam models. More precisely, we discuss different versions of the simplicity constraints, namely gauge-variant and gauge-invariant versions. In the gauge-variant version, the primary and secondary simplicity constraints take a similar form to the reality conditions known already in the context of (complex) Ashtekar variables. Subsequently, we describe the effect of these primary and secondary simplicity constraints on gauge-invariant variables. This allows us to illustrate their equivalence to the so-called diagonal, cross and edge simplicity constraints, which are the gauge-invariant versions of the simplicity constraints. In particular, we clarify how the so-called gluing conditions arise from the secondary simplicity constraints. Finally, we discuss the significance of degenerate configurations, and the ramifications of our work in a broader setting.