Nonrelativistic inverse square potential, scale anomaly, and complex extension

• Verfasst von: Moroz, Sergej [VerfasserIn]
• Verfasst von: Schmidt, Richard [VerfasserIn]
• Titel: Nonrelativistic inverse square potential, scale anomaly, and complex extension
• Verf.angabe: Sergej Moroz, Richard Schmidt
• Jahr: 2010
• Umfang: 23 S.
• Fussnoten: Erstmals am 12. Oktober 2009 online veröffentlicht ; Gesehen am 04.05.2023
• Titel Quelle: Enthalten in: Annals of physics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1957
• Jahr Quelle: 2010
• Band/Heft Quelle: 325(2010), 2, Seite 491-513
• DOI: doi:10.1016/j.aop.2009.10.002
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Conformal quantum mechanics
• Sach-SW: Functional renormalization group
• Sach-SW: Limit cycles
• Sach-SW: Nonrelativistic conformal anomaly
• K10plus-PPN: 1844627039

Abstract

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 nonconformal 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.