✍ Scribed by D.K. Park; Sahng-Kyoon Yoo
No coin nor oath required. For personal study only.
The propagator of the spinless Aharonov Bohm Coulomb system is derived by following the Duru Kleinert method. We use this propagator to explore the spin-1Â2 Aharonov Bohm Coulomb system which contains a point interaction as a Zeeman term. Incorporation of the self-adjoint extension method into the Green's function formalism properly allows us to derive the finite propagator of the spin-1Â2 Aharonov Bohm Coulomb system. As a by-product, the relation between the self-adjoint extension parameter and the bare coupling constant is obtained. Bound-state energy spectra of both spinless and spin-1Â2 Aharonov Bohm Coulomb systems are examined.
1998 Academic Press
A great deal of attention has been paid to the Aharonov Bohm(AB) effect [1], which sheds light on the non-trivial physical significance of the scalar and vector potentials at the quantum level, in recent years in the context of anyonic [2], cosmic string [3], and (2+1) D gravity theories [4]. Since anyon, two-dimensional object, carries magnetic flux [5], the dominant interaction between anyons is AB type. Arovas et al. have pointed out in their seminal paper [6] by calculating the second virial coefficient that the statistics of anyon system interpolates between bosons and fermions, which is the most important property of anyon system for the attacking of the high-T c phenomena in superconductivity.
Many authors have investigated whether or not this property is maintained when the spin degree of freedom is included. One remarkable difference of the spin-1Â2 AB problem from the spinless case is a point interaction potential term which occurs as a mathematical description of the Zeeman interaction of spin with a magnetic flux tube. Gerbert dealt with this problem [7] by applying the self-adjoint extension method [8] to the partial wave. He claimed that when |m+:| <1, where Article No. PH975757 295 0003-4916Â98 25.00
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