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arXiv · 1604.05051

Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime

Fabiano M. Andrade·Cleverson Filgueiras·Edilberto O. Silva
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Abstract

In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $μ$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous studies where the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: $\boldsymbol{\nabla} \cdot \mathbf{E}= (2λ/α)δ(r)/r$. Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self--adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, S-matrix and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the S-matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.

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Fabiano M. Andrade, Cleverson Filgueiras, Edilberto O. Silva. 2017-01-31. Scattering and bound states of a spin--1/2 neutral particle in the cosmic string spacetime. https://doi.org/10.1155/2017%2F8934691

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