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Spectral regularization and a QED running coupling without a Landau pole
- Source :
- Nuclear Physics B, Vol 969, Iss, Pp 115467-(2021), Nuclear Physics
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- Divergent integrals in quantum field theory (QFT) can be given well defined existence as Lorentz covariant complex measures, which may be analyzed by means of a spectral calculus. The case of the photon self energy is considered and the spectral vacuum polarization function is shown to have very close agreement with the vacuum polarization function obtained using dimensional regularization / renormalization in the timelike domain. Using the spectral vacuum polarization function a potential function defined in the timelike domain is derived. The Uehling potential function, from which the Uehling contribution to the Lamb shift may be computed, is derived from an analytic continuation into the spacelike domain of this potential function. The spectral running coupling for QED is computed from this analytically continued potential function. The integral defining the spectral running coupling constant is shown to converge for all non-zero energies while that for the running coupling constant computed using dimensional regularization / renormalization is shown to diverge for all non-zero energies. It is seen that the spectral running coupling does not have a Landau pole and agrees both qualitatively and quantitatively with the results of scattering experiments at all energies.
- Subjects :
- Coupling constant
Physics
Nuclear and High Energy Physics
010308 nuclear & particles physics
Analytic continuation
QC770-798
01 natural sciences
Lamb shift
Renormalization
Dimensional regularization
Nuclear and particle physics. Atomic energy. Radioactivity
Regularization (physics)
Quantum electrodynamics
0103 physical sciences
Landau pole
Vacuum polarization
010306 general physics
Subjects
Details
- ISSN :
- 05503213
- Volume :
- 969
- Database :
- OpenAIRE
- Journal :
- Nuclear Physics B
- Accession number :
- edsair.doi.dedup.....f3d5528b70f0ea82f6261f4dd63e7f9e