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Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering | | M. Gomes
; J. M. C. Malbouisson
; A. J. da Silva
; | | Date: |
28 Dec 1997 | | Journal: | Int.J.Mod.Phys. A13 (1998) 3157-3180 | | Subject: | hep-th | | Abstract: | We study the nonrelativistic limit of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. The renormalization of the relativistic model, in the Coulomb gauge, is discussed. We employ a procedure to calculate scattering amplitudes for low momenta that generates their $|p|/m$ expansion and separates the contributions coming from high and low energy intermediary states. The two body scattering amplitude is calculated up to order $p^2/m^2$. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle scattering amplitude reduces to the Aharonov-Bohm one is a strictly nonrelativistic feature. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering. A nonrelativistic reduction scheme and an effective nonrelativistic Lagrangian to account for the relativistic corrections are proposed. | | Source: | arXiv, hep-th/9801192 | | Services: | Forum | Review | PDF | Favorites | |
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