Feynman integral treatment of the Bargmann potential

Pavel Exner

Sergio A Albeverio, Sonia Mazzucchi

Sergio A Albeverio, Raphael J. Høegh-Krohn

Mehdi Hage-Hassan

The Feynman propagator of charged harmonic oscillator in a constant magnetic field is found for the first time by a direct calculation using Fock Bargmann space and a new generating function of two dimensional harmonic oscillators. The calculations involve well-known integrals which an undergraduate should understand.

Alexander Dynin

We consider functional Schrödinger equations associated with a wide class of Hamiltonians in all Fock representations of the bosonic canonical commutation relations, in particular the Cook-Fock, Friedrichs-Fock, and Bargmann-Fock models. An infinite-dimensional symbolic calculus allows us to prove the convergence of the corresponding Hamiltonian Feynman integrals for propagators of coherent states.