Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-05-24
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, to appear in IJTP. Title, abstract and introduction slightly modified
Scientific paper
The structure of the interaction Hamiltonian in the first order $S-$matrix element of a Dirac particle in an Aharonov-Bohm (AB) field is analyzed and shown to have interesting algebraic properties. It is demonstrated that as a consequence of these properties, this interaction Hamiltonian splits both the incident and outgoing waves in the the first order $S-$matrix into their $\frac{\Sigma_3}{2}-$components (eigenstates of the third component of the spin). The matrix element can then be viewed as the sum of two transitions taking place in these two channels of the spin. At the level of partial waves, each partial wave of the conserved total angular momentum is split into two partial waves of the orbital angular momentum in a manner consistent with the conservation of the total angular momentum quantum number.
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