2011/10/31 by Michael Wheeler, M. Wheeler, Wheeler, M. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1110.6703
2010 PhD thesis, Department of Mathematics and Statistics, University of Melbourne. 293 pages
arxiv created 2011/10/31 · openalex publication_date 2011/10/31 · arxiv updated 2011/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
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.