CONVERGENCE OF QUANTUM ELECTRODYNAMICS IN A CURVED DEFORMATION OF MINKOWSKI SPACE

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.