Schrödinger self-adjoint extension and quantum field theory

We argue that the results obtained using the quantum mechanical method of self-adjoint extension of the Schrödinger Hamiltonian can also be derived using Feynman perturbation theory in the investigation of the corresponding non-relativistic field theories. We show that this is indeed what happens in the study of an anyon system, and, in doing so, we establish a field theoretical description for "colliding anyons", i.e. anyons whose quantum mechanical wave functions satisfy the non-conventional boundary conditions obtained with the method of self-adjoint extension. We also show that analogous results hold for a system of non-abelian Chern-Simons particles.