On the existence of the real time evolution in Euclidean lattice gauge theories
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.
reflection positive Gibbs state of an Euclidean lattice gauge theory
ground state of the quantum theoretical algebra of local observables
nonexistence of zero eigenvalues of the transfer matrix
scientific article; zbMATH DE number 3929740