On the existence of the real time evolution in Euclidean lattice gauge theories (Q1067567)

Each reflection positive Gibbs state of an Euclidean lattice gauge theory is shown to induce a (locally normal) ground state of the quantum theoretical algebra of local observables. The transfer matrix implements a densely defined (non *-)automorphism of this algebra. This fact is used to derive the nonexistence of zero eigenvalues of the transfer matrix, thus a densely defined selfadjoint Hamiltonian always exists.