Inequivalent quantization in the field of a ferromagnetic wire

Details Inequivalent quantization in the field of a ferromagnetic wire Inequivalent quantization in the field of a ferromagnetic wire

2007-08-22

arxiv.org/abs/0708.2969v2

Int.J.Theor.Phys.47:2583-2590,2008

Physics

Condensed Matter

Materials Science

5 pages, 6 figures, revtex4

Scientific paper

10.1007/s10773-008-9692-3

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.

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