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Invariant subspaces of clustering operators

Research paper by V. A. Malyshev, R. A. Minlos

Indexed on: 01 Sep '79Published on: 01 Sep '79Published in: Journal of Statistical Physics



Abstract

A class of clustering operators is defined which is a generalization of a transfer matrix of a Gibbs lattice field with an exponential decay of correlations. It is proved that for small values ofβ the clustering operator has invariant subspaces which are similar tok-particle subspaces of the Fock space. The restriction of the clustering operator onto these subspaces resembles the operator exp(-Hk, whereHk is thek- particle Schrödinger Hamiltonian in nonrelativistic quantum mechanics. The spectrum of eachHk,k⩾1, is contained in the interval (C1βk,C2βk). These intervals do not intersect with each other.