Free fermions in classical and quantum integrable models

Details Free fermions in classical and quantum integrable models Free fermions in classical and quantum integrable models

2011-10-31

arxiv.org/abs/1110.6703v1

Physics

Mathematical Physics

2010 PhD thesis, Department of Mathematics and Statistics, University of Melbourne. 293 pages

Scientific paper

This thesis studies the role of free fermions in certain classical and quantum integrable models. The classical models studied are the KP and BKP hierarchies of partial differential equations. We review the presence of free fermions in the theory of these hierarchies, a topic which was established in the work of the Kyoto school. The quantum models studied are descendents and relatives of the XYZ model, or its lattice equivalent, the eight-vertex model. We give a number of new results in the context of these models, revealing the presence of fermions in typical quantities such as Bethe eigenvectors, partition functions and scalar products.

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