Singular perturbations of positivity preserving semigroups via path space techniques

Associated with each standard positivity preserving semigroup is a generalized path space. The Feynman-Kac-Nelson formula on path space combined with hypercontractivity of the semigroup allows the control of highly singular perturbations. Applications are given to the Schrodinger equation and quantum field models, including a generalized space cutoff P(φ)2 interaction, P(φ(0))2, and a finite volume (ψ2φ)2 interaction.

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