A generalized Feynman–Kac formula based on the Wiener measure is presented. Within the setting of a quantum particle in an electromagnetic field it yields the standard Feynman–Kac formula for the corresponding Schrödinger semigroup. In this case rigorous criteria for its validity are compiled. Finally, phase–space path–integral representations for more general quantum Hamiltonians are derived. ...

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's famous formula for the free energy per site in the termodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of K...

We consider the quantum mechanics of a charged particle in presence Dirac’s magnetic monopole. Wave functions are sections complex line bundle and potential is connection on bundle. use continuum eigenfunction expansion to find an invariant domain essential self-adjointness for Hamiltonian. This leads proof Feynman–Kac formula expressing solutions imaginary time Schrödinger equation as stochast...

In this paper we provide a generalization of Feynmac–Kac formula under volatility uncertainty in presence linear term the PDE due to discounting. We state our result different hypothesis with respect derivation given by Hu et al. (2014), where Lipschitz continuity some functionals is assumed which not necessarily satisfied setting. particular, show that G-conditional expectation discounted payo...

In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman–Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.

We establish a Feynman-Kac-type formula to define fractional Schrödinger operators for (fractional) Kato-class potentials as self-adjoint operators. In this functional integral representation symmetric α-stable processes appear instead of Brownian motion. We derive asymptotic decay estimates on the ground state for potentials growing at infinity. We prove intrinsic ultracontractivity of the Fey...