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

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

2007-02-08

arxiv.org/abs/math/0702217v2

J. Stat. Phys. 127, 1167 (2007)

Mathematics

Functional Analysis

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

Scientific paper

10.1007/s10955-007-9327-8

It is shown that the polynomial $\lambda(t) = {\rm Tr}[(A + tB)^p]$ 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.

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