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Operator techniques in the Hopf algebra for a symmetric group within Racah calculus for Bethe Ansatz eigenfunctions
Author(s) -
Jakubczyk Paweł,
Jakubczyk Dorota,
Lulek Tadeusz
Publication year - 2009
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200881558
Subject(s) - mathematics , hamiltonian (control theory) , linear subspace , eigenfunction , operator (biology) , bethe ansatz , pure mathematics , algebra over a field , mathematical physics , integrable system , quantum mechanics , eigenvalues and eigenvectors , physics , mathematical optimization , biochemistry , chemistry , gene , repressor , transcription factor
We propose some operator techniques, applicable in the procedure of an immediate diagonalization for the Heisenberg chain, such as projection operators for subspaces with definite quasimomentum, total or partial spin, quasimomenta of strings etc. These techniques yield, in particular, matrices of appropriate Clebsch–Gordan coefficients, and reduce significantly the size of an effective Hamiltonian matrix. We apply the basis of wavelets to exploit the translational symmetry, along the Schwinger scheme of unitary geometry, applied to a single N‐dimensional magnon space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)