2025/02/27 by Gallone, Matteo, Michelangeli, Alessandro, Noja, Diego
#34L40 #47B25 #47N50 #81Q10 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2502.20318
We characterise the families of self-adjoint Dirac and Schrödinger operators with Aharonov-Bohm magnetic field, and we exploit the non-relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short-scale boundary condition of self-adjointness. This ensures that the scattering length of the Aharonov-Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac-AB operators is mapped, in the non-relativistic limit, into the physically relevant sub-family of s-wave, angular-momentum-commuting, Schrö\-dinger-AB Hamiltonians with relativistic Dirac approximants.