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Journal of Mathematical Physics

Some aspects of the N-representability problem in finite dimensions. I. Operator endomorphisms which induce necessary conditions

H. Kummer, Ilyas Absar, A. J. Coleman

Published Feb 1, 1977ā€¢ 21 citations
Publisher

Abstract

The connection between operator endomorphisms and conditions for N-representability is established. The sets š’©N and š’®N are defined as the sets of operator endomorphisms which induce necessary conditions and sufficient conditions respectively. A detailed characterization of š’©N is presented.
DOI
10.1063/1.523269

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Given the set š’®N of all operator endomorphisms T with the property that whenever D is any 2-density operator, then T (D) is N-representable is considered. We specify a pair {Q2,PN} of extreme points of š’®N which are related to each other via the particle-hole duality (Theorem 1.2). The rest of the paper is devoted to a complete characterization of the set ŜN of all operator endomorphisms T with the property that whenever D is any 2-density operator then T (D) is quasi-N-representable, i.e., satisfies the necessary conditions Id, QN, BN, and CN.
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