The Holst Spin Foam Model via Cubulations

Understand

Spin foam models are an attempt for a covariant, or path integral formulation of canonical loop quantum gravity.

• The construction of such models usually rely on the Plebanski formulation of general relativity as a constrained BF theory and is based on the discretization of the action on a simplicial triangulation, which may be viewed as an ultraviolet regulator.
• The triangulation dependence can be removed by means of group field theory techniques, which allows one to sum over all triangulations.
• The main tasks for these models are the correct quantum implementation of the Plebanski constraints, the existence of a semiclassical sector implementing additional "Regge-like" constraints arising from simplicial triangulations, and the definition of the physical inner product of loop quantum gravity via group field theory.