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AuthorAl-Hashimi, M.H.
AuthorShalaby, A.M.
AuthorWiese, U.-J.
Available date2016-02-28T12:50:47Z
Publication Date2014-06
Publication NamePhysical Review D - Particles, Fields, Gravitation and Cosmology
CitationAl-Hashimi, M.H., Shalaby, A.M., Wiese, U.-J., "Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the ? -function potential in one-dimensional relativistic quantum mechanics", (2014) Physical Review D - Particles, Fields, Gravitation and Cosmology, 89 (12), art. no. 125023
ISSN1550-7998
URIhttp://dx.doi.org/10.1103/PhysRevD.89.125023
URIhttp://hdl.handle.net/10576/4192
AbstractWe consider the Schr?dinger equation for a relativistic point particle in an external one-dimensional ?-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.
SponsorNPRP grant #NPRP 5 - 261-1-054 from the Qatar National Research Fund (a member of the Qatar Foundation).
Languageen
PublisherAmerican Physical Society
TitleAsymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the ? -function potential in one-dimensional relativistic quantum mechanics
TypeArticle
Issue Number12
Volume Number89


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