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The resolvent of the Nelson Hamiltonian improves positivity

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arxiv 2010.03235 v2 pith:4XKBKPBV submitted 2020-10-07 math.FA math-phmath.MP

Jonas Lampart (CNRS , LICB) This is my paper · ORCID
classification math.FAmath-phmath.MP
keywords hamiltonianimprovesmomentumnelsonpositivityrenormalisedresolventargument
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We prove that the resolvent of the renormalised Nelson Hamiltonian at fixed total momentum P improves positivity in the (momentum) Fock-representation, for every P. Our argument is based on an explcit representation of the renormalised operator and its domain using interior boundary conditions.

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  1. On the Ergodicity of Renormalized Translation-Invariant Nelson-Type Semigroups

    math-ph 2024-12 conditional novelty 7.0 of 10

    For negative coupling, the renormalized non-relativistic and semi-relativistic Nelson semigroups are positivity improving with respect to the Fröhlich cone at every total momentum, proven via Feynman-Kac functional in...

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