Proof of the cases $p \leq 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

Daniel Haegele

doi:10.1007/s10955-007-9327-8

paper

Proof of the cases $p \leq 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture

arXiv:math/0702217 · doi:10.1007/s10955-007-9327-8

Abstract

It is shown that the polynomial $λ (t) = Tr [(A + tB)^{p}]$ has nonnegative coefficients when $p \leq 7$ and A and B are any two complex positive semidefinite $n \times n$ 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.

5 pages; typos corrected; accepted for publication in Journal of Statistical Physics

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

Abstract

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Proof of the cases $p \leq 7$ of the Lieb-Seiringer formulation of the Bessis-Moussa-Villani conjecture