Renormalization group procedure for potential $-g/r^2$
| Autor: | Dawid, Sebastian M., Gonsior, Rafał, Kwapisz, Jan, Serafin, Kamil, Tobolski, Mariusz, Głazek, Stanisław D. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Physics Letters B 777 (2018) 260 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.physletb.2017.12.028 |
| Popis: | 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 $g$. Comment: 6 pages, 3 figures |
| Databáze: | arXiv |
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