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arXiv · 1704.08206

Renormalization group procedure for potential $-g/r^2$

Sebastian M. Dawid·Rafał Gonsior·Jan Kwapisz·Kamil Serafin·Mariusz Tobolski·Stanisław D. Głazek
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Abstract

Schr\"odinger equation with potential $-g/r^2$ exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at $r=0$. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of $g$.

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Sebastian M. Dawid, Rafał Gonsior, Jan Kwapisz, Kamil Serafin, Mariusz Tobolski, Stanisław D. Głazek. 2017-04-26. Renormalization group procedure for potential $-g/r^2$. https://doi.org/10.1016/j.physletb.2017.12.028

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