Relativistic particle dynamics: Lagrangian proof of the no-interaction theorem

An economical proof is given, in the Lagrangian framework, of the no-interaction theorem of relativistic particle mechanics.. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first-class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs