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Ultraviolet Renormalization of the Nelson Hamiltonian through Functional Integration

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arxiv 1304.6662 v2 pith:HYC6RIHZ submitted 2013-04-24 math-ph math.FAmath.MPmath.PR

classification math-phmath.FAmath.MPmath.PR
keywords hamiltonianultravioletcutoffinteractionlimitnelsonrenormalizationterm
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Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the zero cutoff limit a self-adjoint operator exists after a logarithmically divergent term is subtracted from the original Hamiltonian. We obtain this term as the diagonal part of a pair interaction appearing in the density of a Gibbs measure derived from the Feynman-Kac representation of the Hamiltonian. Also, we show existence of a weak coupling limit of the renormalized Hamiltonian and derive an effective Yukawa interaction potential between the particles.

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Cited by 3 Pith papers

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

  1. Ultraviolet Renormalization of Spin Boson Models I. Normal and 2-Nilpotent Interactions

    math-ph 2025-02 conditional novelty 7.0 of 10

    The paper proves that generalized spin-boson models with normal or 2-nilpotent interactions can be ultraviolet renormalized, with norm resolvent convergence of the regularized Hamiltonians to an explicitly constructed...

  2. 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...

  3. Feynman-Kac formula for fiber Hamiltonians in the relativistic Nelson model in two spatial dimensions

    math-ph 2023-09 unverdicted novelty 4.0 of 10

    Derives new Feynman-Kac formulas for fiber Hamiltonians of the 2D relativistic Nelson model by applying estimates from the authors' recent preprint.

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