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

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-2 of 2 references

On the Representation of Tr ( e A − λB ) as a Laplace Transform

E. H. Lieb, R. Seiringer
Rev . Math . Phys . • 2000

Monotonic converging variational approximations to the functional integrals in quantum statistical mechan

P. Moussa Bessis, M. Villani
J . Math . Phys . • 1975