Convergence of Quantum Electrodynamics in a Curved Deformation of Minkowski Space

Details Convergence of Quantum Electrodynamics in a Curved Deformation of Minkowski Space Convergence of Quantum Electrodynamics in a Curved Deformation of Minkowski Space

May 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994anphy.232...61s&link_type=abstract

Annals of Physics, Volume 232, Issue 1, p. 61-87.

Physics

4

Scientific paper

We show that quantum electrodynamics (QED) becomes convergent when the conventional energy and mass operators in Minkowski space are modified by the introduction of a fundamental length R. The limiting case R --> ∞ of the modified theory coincides formally with standard relativistic QED. Electrons are represented by the Dirac equation and photons by the Maxwell equations relative to a corresponding curved metric, which is conformally equivalent to the Minkowskian metric and coincident with it within terms of order R-2. The interaction takes the usual trilinear form corresponding to the Maxwell-Dirac equations. The interaction and total hamiltonians then become well-defined self-adjoint operators on the tensor product of the electron and photon quantized field Hilbert spaces. Equivalently, adaptation of QED to the Einstein Universe R1 × S3 is an entirely convergent theory and has conventional relativistic QED as its limiting form as R --> ∞, where R is the radius of the space S3. The observable implications of the modified theory appear formally indistinguishable from those of conventional theory, apart from ambiguities resulting from the divergences of the latter, assuming that R is at least of the order of the cosmic distance scale as estimated from redshift observations. The theory has apparent potential for explicit computation and adaptation to other relativistic interactions.

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