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

M. H. Al-Hashimi, A. M. Shalaby, U.-J. Wiese
2014 Physical Review D  
We consider the Schrödinger equation for a relativistic point particle in an external 1-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 pseudo-differential operator H = √(p^2 + m^2). Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation
more » ... it possesses an infra-red conformal fixed point. Thus it can be used to illustrate non-trivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.
doi:10.1103/physrevd.89.125023 fatcat:xyk6glnkx5dkro3yyaegzw6wvi