Singular perturbations of positivity preserving semigroups via path space techniques

@inproceedings{Klein1975SingularPO,
  title={Singular perturbations of positivity preserving semigroups via path space techniques},
  author={Abel Klein and Lawrence J. Landau},
  year={1975}
}
Abstract 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 ( ψ 2 φ ) 2 interaction.