The Dirac equation on the surface of a tetrahedron is solved for free motion and also in the presence of a magnetic field. The Casimir vacuum energy is calculated in the free case and is shown to be a nonanalytic modular form. The vacuum charge polarization is evaluated in the magnetic case and the 1+1 axial anomaly is briefly considered. Some θ-function identities are incidentally employed.

• Received 21 January 1987

DOI:https://doi.org/10.1103/PhysRevD.36.1095