Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-09-18
Annals Phys.325:491-513,2010
Physics
High Energy Physics
High Energy Physics - Theory
33 pages, 11 figures; v2: compact form of the analytic solution found, references added; v3: published version
Scientific paper
10.1016/j.aop.2009.10.002
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.
Moroz Sergej
Schmidt Richard
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