Schroedinger Self-adjoint Extension and Quantum Field Theory

Abstract

We argue that the results obtained using the quantum mechanical method of self-adjoint extension of the Schr\"odinger 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", {\it 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.