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Mathematical Physics

Title: Second quantized quantum field theory based on invariance properties of locally conformally flat space-times

Authors: John Mashford
Abstract: Well defined quantum field theory (QFT) for the electroweak force including quantum electrodynamics (QED) and the weak force is obtained by considering a natural unitary representation of a group $K\subset SU(2,2)$, where $K\cong SL(2,{\bf C})\times U(1)$, on a state space of Schwartz spinors, a Fock space ${\mathcal F}$ of multiparticle states and a space ${\mathcal H}$ of fermionic multiparticle states which forms a Grassman algebra. These algebras are defined constructively and emerge from the requirement of covariance associated with the geometry of space-time. (Here $K$ is the structure group of a certain principal bundle associated with a given M\"{o}bius structure modeling space-time.) Scattering processes are associated with intertwining operators between various algebras, which are encoded in an associated bundle of kernel algebras. Supersymmetry emerges naturally from the algebraic structure of the theory. Kernels can be generated using $K$ invariant matrix valued measures given a suitable definition of invariance. It is shown how Feynman propagators, fermion loops and the electron self energy can be given well defined interpretations as measures invariant in this sense. An example of the methods described in the paper is given in which the first order Feynman amplitude of electron-electron scattering ($ee\rightarrow ee$) is derived from a simple order (2,2) kernel. A second example is given explaining electron-neutrino scattering ($ee_{\nu}\rightarrow ee_{\nu}$), which is a manifestation of the weak force.
Comments: 50 pages, version for submission to journal. Minor modifications including adding a reference
Subjects: Mathematical Physics (math-ph)
Cite as: arXiv:1709.09226 [math-ph]
  (or arXiv:1709.09226v4 [math-ph] for this version)

Submission history

From: John Mashford PhD [view email]
[v1] Mon, 25 Sep 2017 12:03:34 GMT (23kb)
[v2] Mon, 9 Oct 2017 11:15:04 GMT (23kb)
[v3] Tue, 26 Dec 2017 03:07:58 GMT (28kb)
[v4] Mon, 19 Mar 2018 12:08:20 GMT (28kb)