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A Strict Positivstellensatz for the Weyl Algebra

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arxiv math/0403076 v2 pith:I2DVNOR2 submitted 2004-03-03 math.AG math.FA

Konrad Schmuedgen This is my paper · ORCID
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keywords algebraweylconditionselementelementsexistfinitegiven
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abstract

Let $c$ be an element of the Weyl algebra $W(d)$ which is given by a strictly positive operator in the Schr"odinger representation. It is shown that, under some conditions, there exist elements $b_1,...,b_d$ in $W(d)$ such that $b_1 c b_1^* + ... + b_d c b_d^*$ is a finite sum of squares.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stationarity is not enough: tightness of the quantum mechanical bootstrap and the copositive cone

    cs.SC 2026-08 accept novelty 8.0 of 10

    The stationary quantum bootstrap is provably not tight in two dimensions, while the eigenstate bootstrap appears to remain tight in the tested settings.

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