Inequivalent quantization in the field of a ferromagnetic wire

Abstract

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann's method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter \Sigma\in\mathbb{R}({mod}2\pi). There exists a single bound state for the coupling constant \eta^2\in[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region \eta^2< 0, which supports bound state making the problem re-normalizable.