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On a 1 + 1 - dimensional interacting soliton-fermion system with supersymmetry Keil, Werner H.


A supersymmetric interacting soliton-fermion system in one space and one time dimension is investigated. We construct the soliton sector of the quantum theory using a generalization of the "method of collective coordinates" previously developed for purely bosonic theories. A canonical transformation leads to a set of "collective" field variables with constraints and the transformed theory is quantized in the canonical way using Dirac's method for constrained systems. The Hamiltonian is evaluated in collective coordinates and the equations of motion are solved to first order in a perturbative expansion. We find that the field equations admit zero-energy solutions for both the boson and the fermion field. The presence of the soliton has nontrivial consequences for the supersymmetry of the theory. The supersymmetry algebra has to be modified to include topological charges and as a result supersymmetry is spontaneously broken. It follows that the ground state is doubly degenerate. Finally, the zero-energy solutions are found to be connected with the symmetries of the theory broken by the soliton. The boson zero-mode corresponds to spatial translations, the fermion zero-mode is associated with the supersymmetry

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