The volume operator in covariant quantum gravity

Understand

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity.

• In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity.
• Here we discuss the volume observable.
• We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area.