Singularities of Bethe Ansatz via Robinson Numbers

• Authors: A. Koper , P. Krasoń , J. Milewski
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

75.10.Jm; 02.40.Xx; 02.10.De; 85.75.Ff

Discipline

• 02.40.Xx: Singularity theory(see also 05.45.-a Nonlinear dynamics and chaos)
• 85.75.Ff: Reprogrammable magnetic logic
• 02.10.De: Algebraic structures and number theory
• 75.10.Jm: Quantized spin models, including quantum spin frustration

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2018
• Volume: 133
• Issue: 3
• Pages: 438-440

Dates

published

2018-03

Contributors

author

A. Koper

• Department of Physics, Adam Mickiewicz University, Poznań 61-614, Poland

author

P. Krasoń

• Department of Mathematics and Physics, Szczecin University, Wielkopolska 15, 70-415 Szczecin, Poland

author

J. Milewski

• Institute of Mathematics Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland

References

• [1] A. Robinson, Non-standard Analysis (revised ed.), Princeton University Press, 1996
• [2] S. Albeverio at al., Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, 1986
• [3] F. Diener, M. Diener, Nonstandard Analysis in Practice, Springer, 1995
• [4] F. Herzberg, Stochastic Calculus with Infinitesimals, Springer, 2013
• [5] J. Milewski, Rep. on Math. Physics 70, 345 (2012), doi: 10.1016/S0034-4877(12)60050-0
• [6] R.I. Nepomechie, Ch. Wang, J. Phys. A: Math. Theor. 46, 325002 (2013), doi: 10.188/1751-8113/46/32/325002
• [7] R. Goldblatt, Lectures on the Hyperreals, An Introduction to Nonstandard Analysis, GTM 188, Springer, 1998
• [8] H. Bethe, Z. Physik 71, 205 (1931), doi: 10.1007/BF01341708
• [9] J. Milewski, G. Banaszak, T. Lulek, M. Łabuz, Physica B 406 520 (2011), doi: 10.1016/j.physb2010.11.027
• [10] G. Banaszak, B. Lulek, T. Lulek, J. Milewski, B. Szydło, Rep. Math. Phys. 71, 205 (2013), doi: 10.1016/S0034-4877(13)60030-0

Identifiers

DOI

10.12693/APhysPolA.133.438