Geometrical Properties of Cumulant Expansions

Details Geometrical Properties of Cumulant Expansions Geometrical Properties of Cumulant Expansions

1997-09-04

arxiv.org/abs/cond-mat/9709044v1

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY,v.66(#5),377-389 FEB 15,1998

Physics

Condensed Matter

28 pages, Revtex

Scientific paper

Cumulants represent a natural language for expressing macroscopic properties of a solid. We show that cumulants are subject to a nontrivial geometry. This geometry provides an intuitive understanding of a number of cumulant relations which had been obtained so far by using algebraic considerations. We give general expressions for their infinitesimal and finite transformations and represent a cumulant wave operator through an integration over a path in the Hilbert space. Cases are investigated where this integration can be done exactly. An expression of the ground-state wavefunction in terms of the cumulant wave operator is derived. In the second part of the article we derive the cumulant counterpart of Faddeev`s equations and show its connection to the method of increments.

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