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Binding Energy of Scalar Bound State by Topologically Massive Interaction: Fermion and Anti-fermion System with Heavy Mass

Toyoki Matsuyama·Hideko Nagahiro
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Abstract

A bound state problem in a topologically massive quantum electrodynamics is investigated by using a non-perturbative method. We formulate the Bethe- Salpeter equation for scalar bound states composed of massive fermion and anti-fermion pair under the lowest ladder approximation. In a large mass expansion for the (anti-) fermion, we derive the Schr{ö}dinger equation and solve it by a numerical method. The energy eigenvalues of bound states are evaluated for various values of a topological mass and also a fermion mass. Then we find a novel logarithmic scaling behaviour of the binding energy in varying the topological mass, fermion mass and also a quantum number. There exists a critical value of the topological mass, beyond which the bound states disappear. As the topological mass decreases, the energy eigenvalues of the bound states, which are negative, also decrease with a logarithmic dependence on the topological mass. A Chern-Simons term gives the bound system a repulsive effect.

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Toyoki Matsuyama, Hideko Nagahiro. 2002-06-17. Binding Energy of Scalar Bound State by Topologically Massive Interaction: Fermion and Anti-fermion System with Heavy Mass. https://doi.org/10.1016/s0370-2693(02)01810-5

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