On Kinks and Bound States in the Gross-Neveu Model

Abstract

We investigate static space dependent $\sigx=\lag\barψψ\rag$ saddle point configurations in the two dimensional Gross-Neveu model in the large N limit. We solve the saddle point condition for $\sigx$ explicitly by employing supersymmetric quantum mechanics and using simple properties of the diagonal resolvent of one dimensional Schrödinger operators rather than inverse scattering techniques. The resulting solutions in the sector of unbroken supersymmetry are the Callan-Coleman-Gross-Zee kink configurations. We thus provide a direct and clean construction of these kinks. In the sector of broken supersymmetry we derive the DHN saddle point configurations. Our method of finding such non-trivial static configurations may be applied also in other two dimensional field theories.

Revised version. A new section added with derivation of the DHN static configurations in the sector of broken supersymmetry. Some references added as well. 25 pp, latex, e-mail [email protected]

References in corpus (1)

• Non Trivial Saddle Points and Band Structure of Bound States of the Two Dimensional O(N) Vector Model

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