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Proof of the Cases p≤ 7 of the Lieb-Seiringer Formulation of the Bessis-Moussa-Villani Conjecture

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Abstract

It is shown that the polynomial λ (t)=Tr[(A+ tB)p] has nonnegative coefficients when p≤ 7 and A and B are any two complex positive semidefinite n× n matrices with arbitrary n. This proves 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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References

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  1. Spektroskopie der kondensierten Materie, Ruhr–Universität–Bochum, Universitätsstraß e 150, 44780, Bochum, Germany

    Daniel Hägele

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  1. Daniel Hägele
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Correspondence to Daniel Hägele.

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Hägele, D. Proof of the Cases p≤ 7 of the Lieb-Seiringer Formulation of the Bessis-Moussa-Villani Conjecture. J Stat Phys 127, 1167–1171 (2007). https://doi.org/10.1007/s10955-007-9327-8

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  • DOI: https://doi.org/10.1007/s10955-007-9327-8

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