2000/12/06 by A. A. Ovchinnikov, A. A. OVCHINNIKOV
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Eigenvalues and eigenvectors #Matrix (chemical analysis) #Monodromy #Monodromy matrix #Operator (biology) #Operator product expansion #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum many-body systems #Scalar (mathematics) #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1142/s0217751x01003743
published as Int.Journ.Mod.Phys.A, 16 (2001) 2175-2193. · LaTex, 20 pages
arxiv created 2000/12/06 · openalex publication_date 2001/05/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present in a simple terms the theory of the factorizing operator introduced recently by Maillet and Sanches de Santos for the spin-1/2 chains. We obtain the explicit expressions for the matrix elements of the factorizing operator in terms of the elements of the monodromy matrix. We use this results to derive the expression for the general scalar product for the quantum spin chain. We comment on the previous determination of the scalar product of Bethe eigenstate with an arbitrary dual state. We also establish the direct correspondence between the calculations of scalar products in the F-basis and the usual basis.