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The unitary group formulation of the N ‐ particle problem
Author(s) -
Matsen F. A.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560080841
Subject(s) - unitary state , unitary group , hamiltonian (control theory) , irreducible representation , mathematics , unitary representation , symmetry group , group (periodic table) , infinitesimal , pure mathematics , mathematical physics , quantum mechanics , physics , lie group , mathematical analysis , geometry , mathematical optimization , political science , law
The representation of an N ‐particle Hamiltonian on an N th rank orbital product space is exactly modeled by a second‐degree polynomial in the infinitesimal generators of the unitary group. Symmetry adaptation of the product space with respect to the symmetric group yields Gel'fand states which are bases for the irreducible representations of the unitary group. These exist in closed form, as, in consequence, does the representation of the model Hamiltonian. The exclusion principle is imposed by restricting the irreducible representations of the unitary group. The unitary group formulation is equivalent to standard many‐body theory for the particle‐conserving case.