In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with.
First of all, the S-matrix is a scattering matrix which comes from scattering processes.
In the context of quantum mechanics and quantum field theory, we often compute the S-matrix, and we use well-known formulas, i.e, the LSZ reduction formula
My questions are, then:
Can you give me a clear definition and a governing equation for a R-matrix?
How are S-matrix and R-matrix related to each other?
Why is the R-matrix important in integrability (Yang-Baxter equation)?