The quantum theory of free automorphic fields

Heuristic spectral theory is developed for a symmetric operator on the universal covering space of a multiply connected static spacetime and is used to construct the quantum field theory of a multiplet of scalar fields in the customary sum-over-modes fashion. The non-local symmetries necessary to the theory are explicitly contructed, as are the projections on the field operators. The non-existence of a standard charge conjugation for certain types of representation is noted. Gauge transformations are used to give a simple and complete classification of automorphic field theories. The relationship between the unprojected and projected field algebras is clarified, and the implications for Fock space (vacuum degeneracy, etc) are discussed - earlier work being criticised. The analogy to black hole physics is pointed out, and the possible role of the Reeh-Schlieder theorems is speculated upon. (author)