Simplicity in simplicial phase space
- MPI fuer Gravitationsphysik, Albert Einstein Institute, Am Muehlenberg 1, D-14476 Potsdam (Germany)
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 quantization. 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.
- OSTI ID:
- 21421168
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.064026; (c) 2010 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Simplicial decomposition and dual methods for nonlinear networks
Spin foam models for quantum gravity from lattice path integrals