We show that quantum electrodynamics (QED) becomes convergent when the
conventional energy and mass operators in Minkowski space are modifie
d by the introduction of a fundamental length R. The limiting case R -
-> infinity of the modified theory coincides formally with standard re
lativistic QED. Electrons are represented by the Dirac equation and ph
otons by the Maxwell equations relative to a corresponding curved metr
ic, which is conformally equivalent to the Minkowskian metric and coin
cident with it within terms of order R-2. The interaction takes the us
ual trilinear form corresponding to the Maxwell-Dirac equations. The i
nteraction and total hamiltonians then become well-defined self-adjoin
t operators on the tensor product of the electron and photon quantized
field Hilbert spaces. Equivalently, adaptation of QED to the Einstein
Universe R1 x S3 is an entirely convergent theory and has conventiona
l relativistic QED as its limiting form as R --> infinity, where R is
the radius of the space S3. The observable implications of the modifie
d theory appear formally indistinguishable from those of conventional
theory, apart from ambiguities resulting from the divergences of the l
atter, assuming that R is at least of the order of the cosmic distance
scale as estimated from redshift observations. The theory has apparen
t potential for explicit computation and adaptation to other relativis
tic interactions. (C) 1994 Academic Press, Inc.