Anomalous bootstrap on the halfline
Abstract
We study carefully the problem of the bootstrap on the halfline. We show why one needs the full set of constraints derived from the Stieltjes theorem on the moment problem by reexamining previous results on the hydrogen atom. We also study the hydrogen atom at continuous angular momentum. We show that the constraints on the moment problem alone do not fix the boundary conditions in all cases and at least one of the positive matrices needs to be slightly enlarged to remove unphysical branches. We explain how to solve the more general problem of the bootstrap for Robin boundary conditions. The recursion relations that are usually used receive additional anomalous contributions. These corrections are necessary to compute the moments of the measure. We apply these to the linear potential and we show how the bootstrap matches the analytical results, based on the Airy function, for this example.
 Publication:

Physical Review D
 Pub Date:
 August 2022
 DOI:
 10.1103/PhysRevD.106.045029
 arXiv:
 arXiv:2206.01765
 Bibcode:
 2022PhRvD.106d5029B
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 31 pages, 11 figures. v2: We added an anomaly for n=0 that was omitted accidentally. Fixed a problem of conventions of factors of 2 between the text on the paper and the code we developed for the Airy function. v3: typos fixed