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Physics > General Physics

Title: Divergence free quantum field theory using a spectral calculus of Lorentz invariant measures

Authors: John Mashford
Abstract: This paper presents a spectral calculus for computing the spectrum of a causal Lorentz invariant Borel complex measure on Minkowski space, thereby enabling one to compute the density for such a measure with respect to Lebesque measure. A general spectral theorem establishing the spectral representation of arbitrary Lorentz invariant Borel complex measures is proved. It is proved that the convolution of arbitrary causal Lorentz invariant measures exists and the product of such measures exists in a wide class of cases. Techniques for their computation are presented. Divergent integrals in quantum field theory (QFT) are shown to have a well defined existence as Lorentz invariant complex measures. The case of vacuum polarization is considered and the spectral vacuum polarization function is shown to have very close agreement with the vacuum polarization function obtained using dimensional regularization in the real mass domain. The spectral running coupling constant is shown to converge for all energies while the running coupling constant obtained using dimensional regularization is shown to diverge for all non-zero energies. The Uehling contribution to the Lamb shift for the H atom is computed.
Comments: 75 pages, 3 figures. Minor modifications. (mainly typos) Version2
Subjects: General Physics (physics.gen-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1803.05732 [physics.gen-ph]
  (or arXiv:1803.05732v2 [physics.gen-ph] for this version)

Submission history

From: John Mashford PhD [view email]
[v1] Tue, 13 Mar 2018 14:35:01 GMT (68kb,D)
[v2] Mon, 19 Mar 2018 11:39:40 GMT (68kb,D)