Singularities of Bethe Ansatz via Robinson Numbers

A. Kopera, P. Krasońb and J. Milewskic aDepartment of Physics, Adam Mickiewicz University, Poznań 61-614, Poland bDepartment of Mathematics and Physics, Szczecin University, Wielkopolska 15, 70-415 Szczecin, Poland cInstitute of Mathematics Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

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In this work we suggest a rigorous mathematical approach for explanation of singular solutions of Bethe Ansatz by means of Robinson complex hypernumbers. There are several approaches towards these singular solutions eg. formal infinitesimals or germs of meromorphic functions. Our aim is to make them precise using non-standard analysis and show that they are essentially equivalent.

DOI: 10.12693/APhysPolA.133.438 PACS numbers: 75.10.Jm, 02.40.Xx, 02.10.De, 85.75.Ff