Existence, degeneracy and stability of ground states by logarithmic Sobolev inequalities on Clifford algebras

We prove existence and finite degeneracy of ground states of energy forms satisfying logarithmic Sobolev inequalities with respect to non vacuum states of Clifford algebras. We then derive the stability of the ground state with respect to certain unbounded perturbations of the energy form. Finally, we show how this provides an infinitesimal approach to existence and uniqueness of the ground state of Hamiltonians considered by L. Gross in QFT, describing spin $1\mathrm{/}2$ Dirac particles subject to interactions with an external scalar field.