Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-01-28
Int.J.Mod.Phys. A13 (1998) 3157-3180
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, 8 figures, revtex, to be published in Int. J. Mod. Phys. A
Scientific paper
10.1142/S0217751X98001566
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.
da Silva Adilson Jose
Gomes Marcelo
Malbouisson J. M. C.
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