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Renormalization group procedure for potential $-g/r^2$
- Source :
- Physics Letters B 777 (2018) 260
- Publication Year :
- 2017
-
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 $g$.<br />Comment: 6 pages, 3 figures
- Subjects :
- Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Physics Letters B 777 (2018) 260
- Publication Type :
- Report
- Accession number :
- edsarx.1704.08206
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.physletb.2017.12.028