Degenerate Plebanski Sector and its Spin Foam Quantization

Sergey Alexandrov (1)

1 L2C - Laboratoire Charles Coulomb

We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact provides its spin foam quantization and allows to test various approaches of imposing the simplicity constraints. Our analysis suggests a unique method of imposing the constraints which leads to a consistent and well defined spin foam model.

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

Sergey Alexandrov. Degenerate Plebanski Sector and its Spin Foam Quantization. Classical and Quantum Gravity, 2012, 29 (14), pp.145018. ⟨10.1088/0264-9381/29/14/145018⟩. ⟨hal-00673769⟩