Nonrelativistic inverse square potential, scale anomaly, and complex extension

Journal Article · Mon Feb 15 04:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.10.002· OSTI ID:21336101

Moroz, Sergej ^[1]; Schmidt, Richard ^[2]

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1. Institut fuer Theoretische Physik Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
2. Physik Department, Technische Universitaet Muenchen, James-Franck-Strasse, D-85748 Garching (Germany)

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.

• OSTI ID: 21336101
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 325; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BOSON EXPANSION
EQUATIONS
FUNCTIONS
INELASTIC SCATTERING
LIMIT CYCLE
POTENTIALS
QUANTUM MECHANICS
RENORMALIZATION
RIEMANN SPACE
TWO-BODY PROBLEM