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

We present a simple functional integration based proof that the semigroups generated by the ultraviolet-renormalized translation-invariant non- and semi-relativistic Nelson Hamiltonians are positivity improving (and hence ergodic) with respect to the Fröhlich cone for arbitrary values of the total momentum. Our argument simplifies known proofs for ergodicity and the result is new in the semi-relativistic case.