ON THE VALIDITY OF THE FEYNMAN-JENSEN INEQUALITY EXPRESSED IN THE HAMILTONIAN-FORMULATION FOR A POLARON IN A MAGNETIC-FIELD

For the Feynman-Jensen inequality in unmodified form to remain valid i f a magnetic field is present, we have shown that additional constrain ts have to be imposed on the variational parameters of the trial syste m. Because of the hermiticity of the Hamiltonian. one intuitively expe cts that an operator formulation of the Feynman-Jensen inequality woul d not require modifications in the presence of a magnetic field. We sh ow that, contrary to this expectation, the Hamiltonian formulation and the path-integral formulation of the Feynman-Jensen inequality have t he same limitations, and that our additional constraints found earlier have to be imposed in both representations.