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arXiv · 1307.0465

Representability Conditions by Grassmann Integration

Volker Bach·Hans Konrad Knörr·Edmund Menge
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Abstract

Representability conditions on the one- and two-particle density matrix for fermion systems are formulated by means of Grassmann integrals. A positivity condition for a certain kind of Grassmann integral is established which, in turn, induces the well-known G-, P- and Q-Conditions of quantum chemistry by an appropriate choice of the integrand. Similarly, the T1- and T2-Conditions are derived. Furthermore, quasifree Grassmann states are introduced and it is shown that every so-called generalized one-particle density matrix which is bounded between 0 and 1 corresponds to a unique quasifree Grassmann state.

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Volker Bach, Hans Konrad Knörr, Edmund Menge. 2013-07-01. Representability Conditions by Grassmann Integration. https://doi.org/10.4310/atmp.2015.v19.n6.a1

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