The Construction of Spin Foam Vertex Amplitudes

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2013
• Main Authors: Bianchi, E., Hellmann, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2013
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149216
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ.

Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine.