Proof of the cases p ≤ 7 of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

@inproceedings{Hgele2008ProofOT,
title={Proof of the cases p ≤ 7 of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture},
author={Daniel H{\"a}gele},
year={2008}
}

It is shown that the polynomial λ(t) = Tr[(A + tB) p ] has non-negative coefficients when p ≤ 7 and A and B are any two complex positive semidefinite n × n matrices with arbitrary n. This proofs a general nontrivial case of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture which is a long standing problem in theoretical physics. In 1975 Bessis, Moussa, and Villani (BMV) stated the following, now widely known, conjecture. For arbitrary hermitian matrices G and H the function… CONTINUE READING