Estimates on Functional Integrals of Non-Relativistic Quantum Field Theory, with Applications to the Nelson and Polaron Models

A tool to provide lower bounds for the ground state energy of quantum mechanical Hamiltonians is developed and applied to two canonical models in non-relativistic quantum field theory: the Nelson and polaron models. The main idea is the application of the Clark-Ocone formula to the action appearing in the Feynman-Kac expression defining the ground state energy of the corresponding Hamiltonian.