Quantum Interactions of Topological Solitons from Electrodynamics

Abstract

The Casimir energy for the classically stable configurations of the topological solitons in 2D quantum antiferromagnets is studied by performing the path-integral over quantum fluctuations. The magnon fluctuation around the solitons saturating the Bogomol'nyi inequality may be viewed as a charged scalar field coupled with an effective magnetic field induced by the solitons. The magnon-soliton couping is closely related to the Pauli Hamiltonian, with which the effective action is calculated by adapting the worldline formulation of the derivative expansion for the 2+1d quantum electrodynamics in an external field. The resulting framework is more flexible than the conventional scattering analysis based on the Dashen-Hasslacher-Neveu formula. We obtain a short-range attractive well and a universal long-range $1/r$-type repulsive potential between two solitons.