Single-Particle Density of States for the Aharonov-Bohm Potential and Instability of Matter with Anomalous Magnetic Moment in 2+1 Dimensions

Details Single-Particle Density of States for the Aharonov-Bohm Potential and Instability of Matter with Anomalous Magnetic Moment in 2+1 Dimensions Single-Particle Density of States for the Aharonov-Bohm Potential and Instability of Matter with Anomalous Magnetic Moment in 2+1 Dimensions

1994-04-18

arxiv.org/abs/hep-th/9404104v2

Physics

High Energy Physics

High Energy Physics - Theory

(sign change in Eq.'s (30-31), 2 references added) 11pp. plain latex, IPNO/TH 94-20

Scientific paper

In the nonrelativistic case we find that whenever the relation $mc^2/e^2 2$ (note that $g_m=2.00232$ for the electron), then the matter is unstable against formation of the flux $\al$. The result persists down to $g_m=2$ provided the Aharonov-Bohm potential is supplemented with a short range attractive potential. We also show that whenever a bound state is present in the spectrum it is always accompanied by a resonance with the energy proportional to the absolute value of the binding energy. is considered. For the Klein-Gordon equation with the Pauli coupling which exists in (2+1) dimensions without any reference to a spin the matter is again unstable for $g_m>2$. The results are obtained by calculating the change of the density of states induced by the Aharonov-Bohm potential. The Krein-Friedel formula for this long-ranged potential is shown to be valid when supplemented with zeta function regularization. PACS : 03.65.Bz, 03-70.+k, 03-80.+r, 05.30.Fk

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