zbMATH — the first resource for mathematics

Dirac-Weyl operators with a winding gauge potential. (English) Zbl 1069.81028
Miyao extends his previous work [Hokkaido Math. J. 34, 159–184 (2005; Zbl 1068.81039), see the review above], now considering \(N\) charged spin-1/2 particles moving in a plane assuming that each particle feels a magnetic field concentrated at the positions of all the other particles and perpendicular to the plane. Like in his previous work, there are \(N\) different magnetic fields but no common field unless \(N=1\), and so the physical significance of the mathematical setup again remains obscure. The corresponding (singular) vector potentials are called winding gauge potentials by Miyao. They enter the momentum operators and thus the Dirac-Weyl operators acting on spinors. The main aim of the paper is to show the existence and investigate the behavior of zero-energy states, thereby extending the work of A. Arai [J. Math. Phys. 34, 915–935 (1993; Zbl 0809.47057)].
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
47B25 Linear symmetric and selfadjoint operators (unbounded)
47N50 Applications of operator theory in the physical sciences
Full Text: DOI Euclid