Ie. Segal et Z. Zhou, CONVERGENCE OF QUANTUM ELECTRODYNAMICS IN A CURVED MODIFICATION OF MINKOWSKI SPACE, Proceedings of the National Academy of Sciences of the United Statesof America, 91(3), 1994, pp. 962-963
The interaction and total hamiltonians for quantum electrodynamics, in
the interaction representation, are entirely regular self-adjoint ope
rators in Hilbert space, in the universal covering manifold M of the c
onformal compactification of Minkowski space M(o). (M is conformally e
quivalent to the Einstein universe E, in which M(o) may be canonically
imbedded.) In a fixed Lorentz frame this may be expressed as converge
nce in a spherical space with suitable periodic boundary conditions in
time. The traditional relativistic theory is the formal limit of the
present variant as the space curvature vanishes.