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Translation invariant models in QFT without ultraviolet cutoffs

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arxiv 1506.07514 v1 pith:A6FVVUW7 submitted 2015-06-24 math-ph math.MP

Fumio Hiroshima This is my paper · ORCID
classification math-phmath.MP
keywords invariantmodeltranslationultravioletfunctionalintegrationsmomentumnelson
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The translation invariant model in quantum field theory is considered by functional integrations. Ultraviolet renormalization of the translation invariant Nelson model with a fixed total momentum is proven by functional integrations. As a corollary it can be shown that the Nelson Hamiltonian with zero total momentum has a ground state for arbitrary values of coupling constants in two dimension. Furthermore the ultraviolet renormalization of the polaron model is also studied.

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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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