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Journal Article

Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators

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

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Hellmann,  Frank
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1209.4539
(Preprint), 546KB

CQG_30_8_085005.pdf
(Any fulltext), 2MB

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Citation

Dittrich, B., Hellmann, F., & Kaminski, W. (2013). Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators. Classical and quantum gravity, 30(8): 085005. doi:10.1088/0264-9381/30/8/085005.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-9607-9
Abstract
In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space. These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.