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

We prove existence, finite degeneracy, discreteness and stability of ground states of energy forms satisfying logarithmic Sobolev inequalities with respect to not necessarily tracial states on von Neumann algebras. The results are then applied to discuss existence and properties of ground states of Hamiltonians considered by L. Gross in QFT, describing, on a suitable Clifford algebra, spin 1/2 Dirac particles, subject to interactions with an unbounded external scalar field.