2009/09/30 by Sergej Moroz, Richard Schmidt · 2 citations
Physics and Astronomy · #Beta function (physics) #Conformal map #Fixed point #Flow (mathematics) #Functional renormalization group #High-Energy Particle Collisions Research #Infrared fixed point #Pulsars and Gravitational Waves Research #Quadratic equation #Renormalization #Renormalization group #Statistical Mechanics and Entropy #cond-mat.other #hep-th #nucl-th
paper · pdf · doi:10.1016/j.aop.2009.10.002
published as Annals Phys.325:491-513,2010 · 33 pages, 11 figures; v2: compact form of the analytic solution found, references added; v3: published version
openalex publication_date 2009/10/13 · arxiv created 2010/01/14 · arxiv updated 2010/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The old problem of a singular, inverse square potential in nonrelativistic quantum mechanics is treated employing a field-theoretic, functional renormalization method. An emergent contact coupling flows to a fixed point or develops a limit cycle depending on the discriminant of its quadratic beta function. We analyze the fixed points in both conformal and non-conformal phases and perform a natural extension of the renormalization group analysis to complex values of the contact coupling. Physical interpretation and motivation for this extension is the presence of an inelastic scattering channel in two-body collisions. We present a geometric description of the complex generalization by considering renormalization group flows on the Riemann sphere. Finally, using bosonization, we find an analytical solution of the extended renormalization group flow equations, constituting the main result of our work.