Geometrical Properties of Cumulant Expansions

K. Kladko; P. Fulde

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arXiv · cond-mat/9709044

Geometrical Properties of Cumulant Expansions

K. Kladko·P. Fulde

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Abstract

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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K. Kladko, P. Fulde. 1997-09-04. Geometrical Properties of Cumulant Expansions. https://arxiv.org/abs/cond-mat/9709044

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