Inequivalent Quantization in the Field of a Ferromagnetic Wire

2007/08/31 by Pulak Ranjan Giri
Materials Science · Mathematics · Physics and Astronomy · #Bound state #Canonical quantization #Coupling constant #Creation and annihilation operators #Geometry #Hamiltonian (control theory) #Magnetism in coordination complexes #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantization (signal processing) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum gravity #Quantum mechanics #Scaling #Second quantization #Upper and lower bounds #cond-mat.mtrl-sci #hep-th

paper · pdf · doi:10.1007/s10773-008-9692-3

published as Int.J.Theor.Phys.47:2583-2590,2008 · 5 pages, 6 figures, revtex4

arxiv created 2007/11/07 · openalex publication_date 2008/03/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η²∈[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 η²< 0, which supports bound state making the problem re-normalizable.

Citations

• Novel quantum states of the rational Calogero models without the confining interaction
• Quantum Inverse Square Interaction
• Inequivalent quantizations of the N=3 Calogero model with scale and mirror-S3 symmetry
• Origin of the anomalies: The modified Heisenberg equation
• Quantization and conformal properties of a generalized Calogero model
• Mechanical similarity as a generalization of scale symmetry
• On scale invariance and anomalies in quantum mechanics
• Bound states in one-dimensional quantum N-body systems with inverse square interaction
• Singular inverse square potential, limit cycles, and self-adjoint extensions
• Dipole binding in a cosmic string background due to quantum anomalies