Schroedinger Self-adjoint Extension and Quantum Field Theory

TL;DR

This paper demonstrates that self-adjoint extension methods in quantum mechanics can be translated into Feynman perturbation theory within quantum field theory, providing new insights into anyon systems and non-abelian Chern-Simons particles.

Contribution

It establishes a field theoretical framework for self-adjoint extension results, connecting quantum mechanical boundary conditions with quantum field theory descriptions.

Findings

Field theoretical description of colliding anyons

Extension of results to non-abelian Chern-Simons particles

Equivalence of self-adjoint extension and perturbation theory methods

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.