Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

Al-Hashimi, Munir; Shalaby, A.M.; Wiese, Uwe-Jens (2014). Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics. Physical review. D - particles, fields, gravitation, and cosmology, D89(12), p. 125023. Melville, N.Y.: American Physical Society 10.1103/PhysRevD.89.125023

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We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-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.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Al-Hashimi, Munir and Wiese, Uwe-Jens

Subjects:

500 Science > 530 Physics

ISSN:

1550-7998

Publisher:

American Physical Society

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

15 Dec 2014 09:54

Last Modified:

05 Feb 2016 12:20

Publisher DOI:

10.1103/PhysRevD.89.125023

BORIS DOI:

10.7892/boris.60812

URI:

https://boris.unibe.ch/id/eprint/60812

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