I would like to know what is the physics definition of the WRT invariant of a 3-manifold $M$. I have the impression this is given by the CS path integral but I cannot find a reference that explicitly states this.
By physics definition I mean exactly that I want to consider some physical quantity. Usually the physical quantities corresponding to invariants of manifolds are partition functions or expectation values of local operators (that is insertion of operators in the path integral).
I am familiar with Witten's late 1980's work but that time the RT part of WRT was not there yet and after it was more mathematical. Therefore any reference would be very welcome.